Analysis/evaluationCurvesAndAnalysis.R

+library(ggplot2) 
+setwd('../Results')
+
+### GRAPH FOR THE ENERGY MODEL USED - using the data from Ahvar et al. Parasilo server
+####Begin
+powerCore =c(98,148,161,176,178,180,184,200,208,212,215,217,218,221,230,237,241)
+
+piecewisePowerAccordingToUse <- function(utilization){
+  j <- floor(utilization * 16) #utilization should be between 0 and 1
+  print(j)
+  index<- j+1 #R indexes vector from 1
+  powerRes <- (powerCore[index+1]-powerCore[index])*16*utilization+((j+1)*powerCore[index]-j*powerCore[index+1])
+}
+
+##Calculate the values for devices 6 and devices 8
+oneCoreUtilizationParasilo= 1/16
+
+utilizationPrevious_d5=0.3592 #Between 0 and 1
+start_d5 = piecewisePowerAccordingToUse(utilizationPrevious_d5)
+end_d5=piecewisePowerAccordingToUse(utilizationPrevious_d5+oneCoreUtilizationParasilo)
+diff_d5=end_d5-start_d5
+
+utilizationPrevious_d7=0.5165 #Between 0 and 1
+start_d7 = piecewisePowerAccordingToUse(utilizationPrevious_d7)
+end_d7=piecewisePowerAccordingToUse(utilizationPrevious_d7+oneCoreUtilizationParasilo)
+diff_d7=end_d7-start_d7
+
+##Highlight these areas on the curve
+highlight <- data.frame(start=c(utilizationPrevious_d5,utilizationPrevious_d7), 
+                        end=c(utilizationPrevious_d5+oneCoreUtilizationParasilo,utilizationPrevious_d7+oneCoreUtilizationParasilo),
+                        group=c("device 5", "device 7"))
+ggplot()+xlim(0,1) + ylim(0,250)+ geom_function(fun=piecewisePowerAccordingToUse)+
+  geom_rect(data=highlight, inherit.aes=FALSE, aes(xmin=start, xmax=end, ymin=min(0),
+                                                   ymax=max(250), group=group), color="transparent", fill=c("#0072B2","#F0E442"), alpha=0.3)+
+  theme_minimal()+
+  ylab("Power (W)")+
+  xlab("Utilization")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 20),
+        axis.text.x = element_text(size = 20),
+        axis.title.y = element_text(size = 20),
+        axis.text.y = element_text(size = 20),
+        legend.text=element_text(size = 20),
+        legend.title=element_text(size = 20))
+####End
+
+
+### INITIAL STUDY
+# Device and links loaded
+
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./InitialStudy/resultsParsed_40rep_DeviceLinkVar_2replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+#Number of different placements - = length of the utilizationDiff variable
+#27.84%
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+
+##Visualizing the difference
+#Calculate the difference - for Overall Energy
+diffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy - loadLevel0_Overall$OverallEnergy
+diffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy - loadLevel1_Overall$OverallEnergy
+diffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy - loadLevel2_Overall$OverallEnergy
+diffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy - loadLevel3_Overall$OverallEnergy
+diffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy - loadLevel4_Overall$OverallEnergy
+diffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy - loadLevel5_Overall$OverallEnergy
+diffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy - loadLevel6_Overall$OverallEnergy
+diffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy - loadLevel7_Overall$OverallEnergy
+diffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy - loadLevel8_Overall$OverallEnergy
+diffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy - loadLevel9_Overall$OverallEnergy
+diffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy - loadLevel10_Overall$OverallEnergy
+diffLoadLevel_Overall = list(diffLoadLevel0_Overall,diffLoadLevel1_Overall,diffLoadLevel2_Overall,
+                             diffLoadLevel3_Overall,diffLoadLevel4_Overall,diffLoadLevel5_Overall,
+                             diffLoadLevel6_Overall,diffLoadLevel7_Overall,diffLoadLevel8_Overall,
+                             diffLoadLevel9_Overall,diffLoadLevel10_Overall)
+#Calculating how many are same, different and infeasible
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+for (levelNb in seq(1,11)){
+  print(levelNb)
+  print(diffLoadLevel_Overall[levelNb])
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    print(diff)
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1}
+  }
+}
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 20),
+        axis.text.x = element_text(size = 20),
+        axis.title.y = element_text(size = 20),
+        axis.text.y = element_text(size = 20),
+        legend.text=element_text(size = 20),
+        legend.title=element_text(size = 20))
+
+###Looking at run 12 for loadlevel 5 for a in-depth analysis
+####End
+
+
+## LOAD HETEROGENEITY STUDIES
+#Only devices loaded
+
+### FIXED LOAD
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./FixedLoad/resultsParsed_40rep_DeviceOnlyVar_2replicas_Uniform_RequestDevice4.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+
+##Working on visualizing the difference
+#Calculate the difference - for Overall Energy
+diffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy - loadLevel0_Overall$OverallEnergy
+diffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy - loadLevel1_Overall$OverallEnergy
+diffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy - loadLevel2_Overall$OverallEnergy
+diffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy - loadLevel3_Overall$OverallEnergy
+diffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy - loadLevel4_Overall$OverallEnergy
+diffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy - loadLevel5_Overall$OverallEnergy
+diffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy - loadLevel6_Overall$OverallEnergy
+diffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy - loadLevel7_Overall$OverallEnergy
+diffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy - loadLevel8_Overall$OverallEnergy
+diffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy - loadLevel9_Overall$OverallEnergy
+diffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy - loadLevel10_Overall$OverallEnergy
+diffLoadLevel_Overall = list(diffLoadLevel0_Overall,diffLoadLevel1_Overall,diffLoadLevel2_Overall,
+                             diffLoadLevel3_Overall,diffLoadLevel4_Overall,diffLoadLevel5_Overall,
+                             diffLoadLevel6_Overall,diffLoadLevel7_Overall,diffLoadLevel8_Overall,
+                             diffLoadLevel9_Overall,diffLoadLevel10_Overall)
+#Calculating how many are same, different and infeasible
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+for (levelNb in seq(1,11)){
+  print(levelNb)
+  print(diffLoadLevel_Overall[levelNb])
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    print(diff)
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1}
+  }
+}
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 24),
+        axis.text.x = element_text(size = 24),
+        axis.title.y = element_text(size = 24),
+        axis.text.y = element_text(size = 24),
+        legend.text=element_text(size = 24),
+        legend.title=element_text(size = 24))
+####End
+
+## NORMALLY DISTRIBUTED LOAD - STD 10 (2 function instances/replicas)
+
+#Graphs for the categorization of placements and the relative difference in overall/marginal energy
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./NormallyDistributedLoad/resultsParsed_40rep_DeviceOnlyVar_2replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+
+##Working on visualizing the difference
+#Calculate the difference - for Overall Energy
+diffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy - loadLevel0_Overall$OverallEnergy
+diffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy - loadLevel1_Overall$OverallEnergy
+diffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy - loadLevel2_Overall$OverallEnergy
+diffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy - loadLevel3_Overall$OverallEnergy
+diffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy - loadLevel4_Overall$OverallEnergy
+diffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy - loadLevel5_Overall$OverallEnergy
+diffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy - loadLevel6_Overall$OverallEnergy
+diffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy - loadLevel7_Overall$OverallEnergy
+diffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy - loadLevel8_Overall$OverallEnergy
+diffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy - loadLevel9_Overall$OverallEnergy
+diffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy - loadLevel10_Overall$OverallEnergy
+diffLoadLevel_Overall = list(diffLoadLevel0_Overall,diffLoadLevel1_Overall,diffLoadLevel2_Overall,
+                             diffLoadLevel3_Overall,diffLoadLevel4_Overall,diffLoadLevel5_Overall,
+                             diffLoadLevel6_Overall,diffLoadLevel7_Overall,diffLoadLevel8_Overall,
+                             diffLoadLevel9_Overall,diffLoadLevel10_Overall)
+#Calculate the relative difference - for Overall Energy
+reldiffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy / loadLevel0_Overall$OverallEnergy
+reldiffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy / loadLevel1_Overall$OverallEnergy
+reldiffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy / loadLevel2_Overall$OverallEnergy
+reldiffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy / loadLevel3_Overall$OverallEnergy
+reldiffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy / loadLevel4_Overall$OverallEnergy
+reldiffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy / loadLevel5_Overall$OverallEnergy
+reldiffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy / loadLevel6_Overall$OverallEnergy
+reldiffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy / loadLevel7_Overall$OverallEnergy
+reldiffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy / loadLevel8_Overall$OverallEnergy
+reldiffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy / loadLevel9_Overall$OverallEnergy
+reldiffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy / loadLevel10_Overall$OverallEnergy
+reldiffLoadLevel_Overall = list(reldiffLoadLevel0_Overall,reldiffLoadLevel1_Overall,reldiffLoadLevel2_Overall,
+                                reldiffLoadLevel3_Overall,reldiffLoadLevel4_Overall,reldiffLoadLevel5_Overall,
+                                reldiffLoadLevel6_Overall,reldiffLoadLevel7_Overall,reldiffLoadLevel8_Overall,
+                                reldiffLoadLevel9_Overall,reldiffLoadLevel10_Overall)
+#Calculate the relative difference - for Marginal Energy
+reldiffLoadLevel0_Marginal <- loadLevel0_Overall$MarginalEnergy / loadLevel0_Marginal$MarginalEnergy
+reldiffLoadLevel1_Marginal <- loadLevel1_Overall$MarginalEnergy / loadLevel1_Marginal$MarginalEnergy
+reldiffLoadLevel2_Marginal <- loadLevel2_Overall$MarginalEnergy / loadLevel2_Marginal$MarginalEnergy
+reldiffLoadLevel3_Marginal <- loadLevel3_Overall$MarginalEnergy / loadLevel3_Marginal$MarginalEnergy
+reldiffLoadLevel4_Marginal <- loadLevel4_Overall$MarginalEnergy / loadLevel4_Marginal$MarginalEnergy
+reldiffLoadLevel5_Marginal <- loadLevel5_Overall$MarginalEnergy / loadLevel5_Marginal$MarginalEnergy
+reldiffLoadLevel6_Marginal <- loadLevel6_Overall$MarginalEnergy / loadLevel6_Marginal$MarginalEnergy
+reldiffLoadLevel7_Marginal <- loadLevel7_Overall$MarginalEnergy / loadLevel7_Marginal$MarginalEnergy
+reldiffLoadLevel8_Marginal <- loadLevel8_Overall$MarginalEnergy / loadLevel8_Marginal$MarginalEnergy
+reldiffLoadLevel9_Marginal <- loadLevel9_Overall$MarginalEnergy / loadLevel9_Marginal$MarginalEnergy
+reldiffLoadLevel10_Marginal <- loadLevel10_Overall$MarginalEnergy / loadLevel10_Marginal$MarginalEnergy
+reldiffLoadLevel_Marginal = list(reldiffLoadLevel0_Marginal,reldiffLoadLevel1_Marginal,reldiffLoadLevel2_Marginal,
+                                 reldiffLoadLevel3_Marginal,reldiffLoadLevel4_Marginal,reldiffLoadLevel5_Marginal,
+                                 reldiffLoadLevel6_Marginal,reldiffLoadLevel7_Marginal,reldiffLoadLevel8_Marginal,
+                                 reldiffLoadLevel9_Marginal,reldiffLoadLevel10_Marginal)
+
+#Calculating how many are same, different and infeasible, also storing the data about the difference
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+datadiff=vector()
+datareldiff=vector()
+datareldiff_m=vector()
+datadiffloc=vector()
+for (levelNb in seq(1,11)){
+  difference=vector()
+  reldifference=vector()
+  reldifference_m=vector()
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1
+    difference=append(difference,diff)}
+  }
+  for(diff in reldiffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference=append(reldifference,diff)}
+  }
+  datadiffloc=append(datadiffloc,rep((levelNb-1)*10,length(difference)))
+  datadiff=append(datadiff,difference)
+  datareldiff=append(datareldiff,reldifference)
+  for(diff in reldiffLoadLevel_Marginal[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference_m=append(reldifference_m,diff)}
+  }
+  datareldiff_m=append(datareldiff_m,reldifference_m)
+}
+
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 24),
+        axis.text.x = element_text(size = 24),
+        axis.title.y = element_text(size = 24),
+        axis.text.y = element_text(size = 24),
+        legend.text=element_text(size = 24),
+        legend.title=element_text(size = 24))
+
+##Create the dataframe for statistics about the difference - OVERALL ENERGY
+statisticsPlacement=data.frame(datadiffloc,datareldiff)
+
+#Get numbers for the text
+quantile(statisticsPlacement$datareldiff,0.10)
+quantile(statisticsPlacement$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot (Overall energy)
+ggplot(data=statisticsPlacement, aes(x=factor(datadiffloc), y=datareldiff)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in overall energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+
+##Create the dataframe for statistics about the difference - MARGINAL ENERGY
+statisticsPlacement_m=data.frame(datadiffloc,datareldiff_m)
+
+#Get numbers for the text
+quantile(statisticsPlacement_m$datareldiff,0.10)
+quantile(statisticsPlacement_m$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement_m, aes(x=factor(datadiffloc), y=datareldiff_m)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in marginal energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Average included device utilization data graph
+####Begin
+### Getting the data - different placements ONLY
+result_data_csv <- read.csv(file="./NormallyDistributedLoad/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_2replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10
+
+#Create a dataframe with only the device utilization information
+utilization=data.frame(result_data_csv$Device0,result_data_csv$Device1,result_data_csv$Device2,result_data_csv$Device3,
+                       result_data_csv$Device4,result_data_csv$Device5,result_data_csv$Device6,result_data_csv$Device7,
+                       result_data_csv$Device8,result_data_csv$Device9,result_data_csv$Device10)
+
+#Calculating the mean utilization for each data line
+meanUt=rowMeans(utilization,na.rm=TRUE)
+
+#Create data frame for plotting
+mean_data_utilization= data.frame(result_data_csv$LoadLevel,result_data_csv$Alternative,meanUt)
+
+###Plot - Statistics about the utilization, violin plot
+ggplot(data=mean_data_utilization, aes(x=factor(result_data_csv$LoadLevel), y=meanUt, fill=result_data_csv$Alternative)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Mean device utilization when placements are different (%)")+
+  xlab("Average load level in %")+
+  labs(fill = "Optimization objective")+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Completion Time graph for different placements 
+####Begin
+## Getting the data - different placements ONLY
+result_data_csv_ut_DifferentOnly <- read.csv(file="./NormallyDistributedLoad/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_2replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+## Getting the data - all placements
+result_data_csv_ev_All <- read.csv(file="./NormallyDistributedLoad/resultsParsed_40rep_DeviceOnlyVar_2replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+result_data_csv_ev_All$LoadLevel <- result_data_csv_ev_All$Scenario*10 
+
+##Adding a column for the combination Repetition_Scenario to be able to filter
+result_data_csv_ut_DifferentOnly$id <- paste(result_data_csv_ut_DifferentOnly$Repetition,result_data_csv_ut_DifferentOnly$Scenario,sep = "_")
+result_data_csv_ev_All$id <- paste(result_data_csv_ev_All$Repetition,result_data_csv_ev_All$Scenario,sep = "_")
+
+##Filter the all data from the combination Repetition/Scenario/Alternative? to get only the info when placements are different
+library(dplyr)
+result_data_csv_ev_DifferentOnly = result_data_csv_ev_All %>% filter(id %in% result_data_csv_ut_DifferentOnly$id)
+
+#Boxplot
+ggplot(data=result_data_csv_ev_DifferentOnly, aes(x=factor(LoadLevel), y=CompletionTime,
+                                                  fill=Alternative)) +
+  geom_boxplot()+
+  theme_minimal()+
+  ylab("Request completion time when placements are different (ms)")+
+  xlab("Average load level in %")+
+  ylim(0,100)+
+  labs(fill = "Optimization objective")+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+## LARGER STANDARD DEVIATION - NORMALLY DISTRIBUTED LOAD - STD 30 (2 function instances/replicas)
+
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./LargerStandardDeviation/resultsParsed_40rep_DeviceOnlyVar_2replicas_Std30_RequestDevice4.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+#Calculating how many are same, different and infeasible, also storing the data about the difference
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+datadiff=vector()
+datareldiff=vector()
+datareldiff_m=vector()
+datadiffloc=vector()
+for (levelNb in seq(1,11)){
+  difference=vector()
+  reldifference=vector()
+  reldifference_m=vector()
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1
+    difference=append(difference,diff)}
+  }
+  for(diff in reldiffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference=append(reldifference,diff)}
+  }
+  datadiffloc=append(datadiffloc,rep((levelNb-1)*10,length(difference)))
+  datadiff=append(datadiff,difference)
+  datareldiff=append(datareldiff,reldifference)
+  for(diff in reldiffLoadLevel_Marginal[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference_m=append(reldifference_m,diff)}
+  }
+  datareldiff_m=append(datareldiff_m,reldifference_m)
+}
+
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 24),
+        axis.text.x = element_text(size = 24),
+        axis.title.y = element_text(size = 24),
+        axis.text.y = element_text(size = 24),
+        legend.text=element_text(size = 24),
+        legend.title=element_text(size = 24))
+####End
+
+## AVAILABILITY OF FUNCTION INSTANCES STUDIES
+
+## NORMALLY DISTRIBUTED LOAD - STD 10 (4 function instances/replicas)
+
+#Graphs for the categorization of placements and the relative difference in overall/marginal energy
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./4FunctionInstances/resultsParsed_40rep_DeviceOnlyVar_4replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+
+##Working on visualizing the difference
+#Calculate the difference - for Overall Energy
+diffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy - loadLevel0_Overall$OverallEnergy
+diffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy - loadLevel1_Overall$OverallEnergy
+diffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy - loadLevel2_Overall$OverallEnergy
+diffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy - loadLevel3_Overall$OverallEnergy
+diffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy - loadLevel4_Overall$OverallEnergy
+diffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy - loadLevel5_Overall$OverallEnergy
+diffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy - loadLevel6_Overall$OverallEnergy
+diffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy - loadLevel7_Overall$OverallEnergy
+diffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy - loadLevel8_Overall$OverallEnergy
+diffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy - loadLevel9_Overall$OverallEnergy
+diffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy - loadLevel10_Overall$OverallEnergy
+diffLoadLevel_Overall = list(diffLoadLevel0_Overall,diffLoadLevel1_Overall,diffLoadLevel2_Overall,
+                             diffLoadLevel3_Overall,diffLoadLevel4_Overall,diffLoadLevel5_Overall,
+                             diffLoadLevel6_Overall,diffLoadLevel7_Overall,diffLoadLevel8_Overall,
+                             diffLoadLevel9_Overall,diffLoadLevel10_Overall)
+#Calculate the relative difference - for Overall Energy
+reldiffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy / loadLevel0_Overall$OverallEnergy
+reldiffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy / loadLevel1_Overall$OverallEnergy
+reldiffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy / loadLevel2_Overall$OverallEnergy
+reldiffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy / loadLevel3_Overall$OverallEnergy
+reldiffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy / loadLevel4_Overall$OverallEnergy
+reldiffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy / loadLevel5_Overall$OverallEnergy
+reldiffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy / loadLevel6_Overall$OverallEnergy
+reldiffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy / loadLevel7_Overall$OverallEnergy
+reldiffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy / loadLevel8_Overall$OverallEnergy
+reldiffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy / loadLevel9_Overall$OverallEnergy
+reldiffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy / loadLevel10_Overall$OverallEnergy
+reldiffLoadLevel_Overall = list(reldiffLoadLevel0_Overall,reldiffLoadLevel1_Overall,reldiffLoadLevel2_Overall,
+                                reldiffLoadLevel3_Overall,reldiffLoadLevel4_Overall,reldiffLoadLevel5_Overall,
+                                reldiffLoadLevel6_Overall,reldiffLoadLevel7_Overall,reldiffLoadLevel8_Overall,
+                                reldiffLoadLevel9_Overall,reldiffLoadLevel10_Overall)
+#Calculate the relative difference - for Marginal Energy
+reldiffLoadLevel0_Marginal <- loadLevel0_Overall$MarginalEnergy / loadLevel0_Marginal$MarginalEnergy
+reldiffLoadLevel1_Marginal <- loadLevel1_Overall$MarginalEnergy / loadLevel1_Marginal$MarginalEnergy
+reldiffLoadLevel2_Marginal <- loadLevel2_Overall$MarginalEnergy / loadLevel2_Marginal$MarginalEnergy
+reldiffLoadLevel3_Marginal <- loadLevel3_Overall$MarginalEnergy / loadLevel3_Marginal$MarginalEnergy
+reldiffLoadLevel4_Marginal <- loadLevel4_Overall$MarginalEnergy / loadLevel4_Marginal$MarginalEnergy
+reldiffLoadLevel5_Marginal <- loadLevel5_Overall$MarginalEnergy / loadLevel5_Marginal$MarginalEnergy
+reldiffLoadLevel6_Marginal <- loadLevel6_Overall$MarginalEnergy / loadLevel6_Marginal$MarginalEnergy
+reldiffLoadLevel7_Marginal <- loadLevel7_Overall$MarginalEnergy / loadLevel7_Marginal$MarginalEnergy
+reldiffLoadLevel8_Marginal <- loadLevel8_Overall$MarginalEnergy / loadLevel8_Marginal$MarginalEnergy
+reldiffLoadLevel9_Marginal <- loadLevel9_Overall$MarginalEnergy / loadLevel9_Marginal$MarginalEnergy
+reldiffLoadLevel10_Marginal <- loadLevel10_Overall$MarginalEnergy / loadLevel10_Marginal$MarginalEnergy
+reldiffLoadLevel_Marginal = list(reldiffLoadLevel0_Marginal,reldiffLoadLevel1_Marginal,reldiffLoadLevel2_Marginal,
+                                 reldiffLoadLevel3_Marginal,reldiffLoadLevel4_Marginal,reldiffLoadLevel5_Marginal,
+                                 reldiffLoadLevel6_Marginal,reldiffLoadLevel7_Marginal,reldiffLoadLevel8_Marginal,
+                                 reldiffLoadLevel9_Marginal,reldiffLoadLevel10_Marginal)
+
+#Calculating how many are same, different and infeasible, also storing the data about the difference
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+datadiff=vector()
+datareldiff=vector()
+datareldiff_m=vector()
+datadiffloc=vector()
+for (levelNb in seq(1,11)){
+  difference=vector()
+  reldifference=vector()
+  reldifference_m=vector()
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1
+    difference=append(difference,diff)}
+  }
+  for(diff in reldiffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference=append(reldifference,diff)}
+  }
+  datadiffloc=append(datadiffloc,rep((levelNb-1)*10,length(difference)))
+  datadiff=append(datadiff,difference)
+  datareldiff=append(datareldiff,reldifference)
+  for(diff in reldiffLoadLevel_Marginal[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference_m=append(reldifference_m,diff)}
+  }
+  datareldiff_m=append(datareldiff_m,reldifference_m)
+}
+
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 24),
+        axis.text.x = element_text(size = 24),
+        axis.title.y = element_text(size = 24),
+        axis.text.y = element_text(size = 24),
+        legend.text=element_text(size = 24),
+        legend.title=element_text(size = 24))
+
+##Create the dataframe for statistics about the difference - OVERALL ENERGY
+statisticsPlacement=data.frame(datadiffloc,datadiff,datareldiff)
+
+#Get numbers for the text
+quantile(statisticsPlacement$datareldiff,0.10)
+quantile(statisticsPlacement$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement, aes(x=factor(datadiffloc), y=datareldiff)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in overall energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+
+##Create the dataframe for statistics about the difference - MARGINAL ENERGY
+statisticsPlacement_m=data.frame(datadiffloc,datareldiff_m)
+
+#Get numbers for the text
+quantile(statisticsPlacement_m$datareldiff,0.10)
+quantile(statisticsPlacement_m$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement_m, aes(x=factor(datadiffloc), y=datareldiff_m)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in marginal energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Average included device utilization data graph
+####Begin
+### Getting the data - different placements ONLY
+result_data_csv <- read.csv(file="./4FunctionInstances/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_4replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10
+
+#Create a dataframe with only the device utilization information
+utilization=data.frame(result_data_csv$Device0,result_data_csv$Device1,result_data_csv$Device2,result_data_csv$Device3,
+                       result_data_csv$Device4,result_data_csv$Device5,result_data_csv$Device6,result_data_csv$Device7,
+                       result_data_csv$Device8,result_data_csv$Device9,result_data_csv$Device10)
+
+#Calculating the mean utilization for each data line
+meanUt=rowMeans(utilization,na.rm=TRUE)
+
+#Create data frame for plotting
+mean_data_utilization= data.frame(result_data_csv$LoadLevel,result_data_csv$Alternative,meanUt)
+
+###Plot - Statistics about the utilization, violin plot
+ggplot(data=mean_data_utilization, aes(x=factor(result_data_csv$LoadLevel), y=meanUt, fill=result_data_csv$Alternative)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Mean device utilization when placements are different (%)")+
+  xlab("Average load level in %")+
+  labs(fill = "Optimization objective")+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Completion Time graph for different placements 
+####Begin
+## Getting the data - different placements ONLY
+result_data_csv_ut_DifferentOnly <- read.csv(file="./4FunctionInstances/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_4replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+## Getting the data - all placements
+result_data_csv_ev_All <- read.csv(file="./4FunctionInstances/resultsParsed_40rep_DeviceOnlyVar_4replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+result_data_csv_ev_All$LoadLevel <- result_data_csv_ev_All$Scenario*10 
+
+##Adding a column for the combination Repetition_Scenario to be able to filter
+result_data_csv_ut_DifferentOnly$id <- paste(result_data_csv_ut_DifferentOnly$Repetition,result_data_csv_ut_DifferentOnly$Scenario,sep = "_")
+result_data_csv_ev_All$id <- paste(result_data_csv_ev_All$Repetition,result_data_csv_ev_All$Scenario,sep = "_")
+
+##Filter the all data from the combination Repetition/Scenario/Alternative? to get only the info when placements are different
+library(dplyr)
+result_data_csv_ev_DifferentOnly = result_data_csv_ev_All %>% filter(id %in% result_data_csv_ut_DifferentOnly$id)
+
+#Boxplot
+ggplot(data=result_data_csv_ev_DifferentOnly, aes(x=factor(LoadLevel), y=CompletionTime,
+                                                  fill=Alternative)) +
+  geom_boxplot()+
+  theme_minimal()+
+  ylab("Request completion time when placements are different (ms)")+
+  xlab("Average load level in %")+
+  ylim(0,100)+
+  labs(fill = "Optimization objective")+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+
+## NORMALLY DISTRIBUTED LOAD - STD 10 (6 function instances/replicas)
+
+#Graphs for the categorization of placements and the relative difference in overall/marginal energy
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./6FunctionInstances/resultsParsed_40rep_DeviceOnlyVar_6replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+
+##Working on visualizing the difference
+#Calculate the difference - for Overall Energy
+diffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy - loadLevel0_Overall$OverallEnergy
+diffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy - loadLevel1_Overall$OverallEnergy
+diffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy - loadLevel2_Overall$OverallEnergy
+diffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy - loadLevel3_Overall$OverallEnergy
+diffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy - loadLevel4_Overall$OverallEnergy
+diffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy - loadLevel5_Overall$OverallEnergy
+diffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy - loadLevel6_Overall$OverallEnergy
+diffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy - loadLevel7_Overall$OverallEnergy
+diffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy - loadLevel8_Overall$OverallEnergy
+diffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy - loadLevel9_Overall$OverallEnergy
+diffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy - loadLevel10_Overall$OverallEnergy
+diffLoadLevel_Overall = list(diffLoadLevel0_Overall,diffLoadLevel1_Overall,diffLoadLevel2_Overall,
+                             diffLoadLevel3_Overall,diffLoadLevel4_Overall,diffLoadLevel5_Overall,
+                             diffLoadLevel6_Overall,diffLoadLevel7_Overall,diffLoadLevel8_Overall,
+                             diffLoadLevel9_Overall,diffLoadLevel10_Overall)
+#Calculate the relative difference - for Overall Energy
+reldiffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy / loadLevel0_Overall$OverallEnergy
+reldiffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy / loadLevel1_Overall$OverallEnergy
+reldiffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy / loadLevel2_Overall$OverallEnergy
+reldiffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy / loadLevel3_Overall$OverallEnergy
+reldiffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy / loadLevel4_Overall$OverallEnergy
+reldiffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy / loadLevel5_Overall$OverallEnergy
+reldiffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy / loadLevel6_Overall$OverallEnergy
+reldiffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy / loadLevel7_Overall$OverallEnergy
+reldiffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy / loadLevel8_Overall$OverallEnergy
+reldiffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy / loadLevel9_Overall$OverallEnergy
+reldiffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy / loadLevel10_Overall$OverallEnergy
+reldiffLoadLevel_Overall = list(reldiffLoadLevel0_Overall,reldiffLoadLevel1_Overall,reldiffLoadLevel2_Overall,
+                                reldiffLoadLevel3_Overall,reldiffLoadLevel4_Overall,reldiffLoadLevel5_Overall,
+                                reldiffLoadLevel6_Overall,reldiffLoadLevel7_Overall,reldiffLoadLevel8_Overall,
+                                reldiffLoadLevel9_Overall,reldiffLoadLevel10_Overall)
+#Calculate the relative difference - for Marginal Energy
+reldiffLoadLevel0_Marginal <- loadLevel0_Overall$MarginalEnergy / loadLevel0_Marginal$MarginalEnergy
+reldiffLoadLevel1_Marginal <- loadLevel1_Overall$MarginalEnergy / loadLevel1_Marginal$MarginalEnergy
+reldiffLoadLevel2_Marginal <- loadLevel2_Overall$MarginalEnergy / loadLevel2_Marginal$MarginalEnergy
+reldiffLoadLevel3_Marginal <- loadLevel3_Overall$MarginalEnergy / loadLevel3_Marginal$MarginalEnergy
+reldiffLoadLevel4_Marginal <- loadLevel4_Overall$MarginalEnergy / loadLevel4_Marginal$MarginalEnergy
+reldiffLoadLevel5_Marginal <- loadLevel5_Overall$MarginalEnergy / loadLevel5_Marginal$MarginalEnergy
+reldiffLoadLevel6_Marginal <- loadLevel6_Overall$MarginalEnergy / loadLevel6_Marginal$MarginalEnergy
+reldiffLoadLevel7_Marginal <- loadLevel7_Overall$MarginalEnergy / loadLevel7_Marginal$MarginalEnergy
+reldiffLoadLevel8_Marginal <- loadLevel8_Overall$MarginalEnergy / loadLevel8_Marginal$MarginalEnergy
+reldiffLoadLevel9_Marginal <- loadLevel9_Overall$MarginalEnergy / loadLevel9_Marginal$MarginalEnergy
+reldiffLoadLevel10_Marginal <- loadLevel10_Overall$MarginalEnergy / loadLevel10_Marginal$MarginalEnergy
+reldiffLoadLevel_Marginal = list(reldiffLoadLevel0_Marginal,reldiffLoadLevel1_Marginal,reldiffLoadLevel2_Marginal,
+                                 reldiffLoadLevel3_Marginal,reldiffLoadLevel4_Marginal,reldiffLoadLevel5_Marginal,
+                                 reldiffLoadLevel6_Marginal,reldiffLoadLevel7_Marginal,reldiffLoadLevel8_Marginal,
+                                 reldiffLoadLevel9_Marginal,reldiffLoadLevel10_Marginal)
+
+#Calculating how many are same, different and infeasible, also storing the data about the difference
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+datadiff=vector()
+datareldiff=vector()
+datareldiff_m=vector()
+datadiffloc=vector()
+for (levelNb in seq(1,11)){
+  difference=vector()
+  reldifference=vector()
+  reldifference_m=vector()
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1
+    difference=append(difference,diff)}
+  }
+  for(diff in reldiffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference=append(reldifference,diff)}
+  }
+  datadiffloc=append(datadiffloc,rep((levelNb-1)*10,length(difference)))
+  datadiff=append(datadiff,difference)
+  datareldiff=append(datareldiff,reldifference)
+  for(diff in reldiffLoadLevel_Marginal[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference_m=append(reldifference_m,diff)}
+  }
+  datareldiff_m=append(datareldiff_m,reldifference_m)
+}
+
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 24),
+        axis.text.x = element_text(size = 24),
+        axis.title.y = element_text(size = 24),
+        axis.text.y = element_text(size = 24),
+        legend.text=element_text(size = 24),
+        legend.title=element_text(size = 24))
+
+##Create the dataframe for statistics about the difference - OVERALL ENERGY
+statisticsPlacement=data.frame(datadiffloc,datadiff,datareldiff)
+
+#Get numbers for the text
+quantile(statisticsPlacement$datareldiff,0.10)
+quantile(statisticsPlacement$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement, aes(x=factor(datadiffloc), y=datareldiff)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in overall energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+
+##Create the dataframe for statistics about the difference - MARGINAL ENERGY
+statisticsPlacement_m=data.frame(datadiffloc,datareldiff_m)
+
+#Get numbers for the text
+quantile(statisticsPlacement_m$datareldiff,0.10)
+quantile(statisticsPlacement_m$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement_m, aes(x=factor(datadiffloc), y=datareldiff_m)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in marginal energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Average included device utilization data graph
+####Begin
+### Getting the data - different placements ONLY
+result_data_csv <- read.csv(file="./6FunctionInstances/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_6replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10
+
+#Create a dataframe with only the device utilization information
+utilization=data.frame(result_data_csv$Device0,result_data_csv$Device1,result_data_csv$Device2,result_data_csv$Device3,
+                       result_data_csv$Device4,result_data_csv$Device5,result_data_csv$Device6,result_data_csv$Device7,
+                       result_data_csv$Device8,result_data_csv$Device9,result_data_csv$Device10)
+
+#Calculating the mean utilization for each data line
+meanUt=rowMeans(utilization,na.rm=TRUE)
+
+#Create data frame for plotting
+mean_data_utilization= data.frame(result_data_csv$LoadLevel,result_data_csv$Alternative,meanUt)
+
+###Plot - Statistics about the utilization, violin plot
+ggplot(data=mean_data_utilization, aes(x=factor(result_data_csv$LoadLevel), y=meanUt, fill=result_data_csv$Alternative)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Mean device utilization when placements are different (%)")+
+  xlab("Average load level in %")+
+  labs(fill = "Optimization objective")+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Completion Time graph for different placements 
+####Begin
+## Getting the data - different placements ONLY
+result_data_csv_ut_DifferentOnly <- read.csv(file="./6FunctionInstances/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_6replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+## Getting the data - all placements
+result_data_csv_ev_All <- read.csv(file="./6FunctionInstances/resultsParsed_40rep_DeviceOnlyVar_6replicas_Std10_RequestDevice4.csv", header=TRUE, sep=",")
+result_data_csv_ev_All$LoadLevel <- result_data_csv_ev_All$Scenario*10 
+
+##Adding a column for the combination Repetition_Scenario to be able to filter
+result_data_csv_ut_DifferentOnly$id <- paste(result_data_csv_ut_DifferentOnly$Repetition,result_data_csv_ut_DifferentOnly$Scenario,sep = "_")
+result_data_csv_ev_All$id <- paste(result_data_csv_ev_All$Repetition,result_data_csv_ev_All$Scenario,sep = "_")
+
+##Filter the all data from the combination Repetition/Scenario/Alternative? to get only the info when placements are different
+library(dplyr)
+result_data_csv_ev_DifferentOnly = result_data_csv_ev_All %>% filter(id %in% result_data_csv_ut_DifferentOnly$id)
+
+#Boxplot
+ggplot(data=result_data_csv_ev_DifferentOnly, aes(x=factor(LoadLevel), y=CompletionTime,
+                                                  fill=Alternative)) +
+  geom_boxplot()+
+  theme_minimal()+
+  ylab("Request completion time when placements are different (ms)")+
+  xlab("Average load level in %")+
+  labs(fill = "Optimization objective")+
+  ylim(0,100)+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+## FULL CO-LOCATION STUDY
+
+## NORMALLY DISTRIBUTED LOAD - STD 10 (6 function instances/replicas)
+
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./FullColocation/resultsParsed_40rep_DeviceOnlyVar_6replicas_Std10_RequestDevice0.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+#Calculating how many are same, different and infeasible, also storing the data about the difference
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+datadiff=vector()
+datareldiff=vector()
+datareldiff_m=vector()
+datadiffloc=vector()
+for (levelNb in seq(1,11)){
+  difference=vector()
+  reldifference=vector()
+  reldifference_m=vector()
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1
+    difference=append(difference,diff)}
+  }
+  for(diff in reldiffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference=append(reldifference,diff)}
+  }
+  datadiffloc=append(datadiffloc,rep((levelNb-1)*10,length(difference)))
+  datadiff=append(datadiff,difference)
+  datareldiff=append(datareldiff,reldifference)
+  for(diff in reldiffLoadLevel_Marginal[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference_m=append(reldifference_m,diff)}
+  }
+  datareldiff_m=append(datareldiff_m,reldifference_m)
+}
+
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 20),
+        axis.text.x = element_text(size = 20),
+        axis.title.y = element_text(size = 20),
+        axis.text.y = element_text(size = 20),
+        legend.text=element_text(size = 20),
+        legend.title=element_text(size = 20))
+####End
+
+## RANDOM BEGINNING DEVICE STUDIES
+
+### FIXED LOAD - RANDOM BEGINNING DEVICE
+
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./RandomBeginningDevice/Fixed/resultsParsed_40rep_DeviceOnlyVar_2replicas_Uniform_RequestDeviceRandom.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+
+##Working on visualizing the difference
+#Calculate the difference - for Overall Energy
+diffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy - loadLevel0_Overall$OverallEnergy
+diffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy - loadLevel1_Overall$OverallEnergy
+diffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy - loadLevel2_Overall$OverallEnergy
+diffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy - loadLevel3_Overall$OverallEnergy
+diffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy - loadLevel4_Overall$OverallEnergy
+diffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy - loadLevel5_Overall$OverallEnergy
+diffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy - loadLevel6_Overall$OverallEnergy
+diffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy - loadLevel7_Overall$OverallEnergy
+diffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy - loadLevel8_Overall$OverallEnergy
+diffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy - loadLevel9_Overall$OverallEnergy
+diffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy - loadLevel10_Overall$OverallEnergy
+diffLoadLevel_Overall = list(diffLoadLevel0_Overall,diffLoadLevel1_Overall,diffLoadLevel2_Overall,
+                             diffLoadLevel3_Overall,diffLoadLevel4_Overall,diffLoadLevel5_Overall,
+                             diffLoadLevel6_Overall,diffLoadLevel7_Overall,diffLoadLevel8_Overall,
+                             diffLoadLevel9_Overall,diffLoadLevel10_Overall)
+#Calculating how many are same, different and infeasible
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+for (levelNb in seq(1,11)){
+  print(levelNb)
+  print(diffLoadLevel_Overall[levelNb])
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    print(diff)
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1}
+  }
+}
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 24),
+        axis.text.x = element_text(size = 24),
+        axis.title.y = element_text(size = 24),
+        axis.text.y = element_text(size = 24),
+        legend.text=element_text(size = 24),
+        legend.title=element_text(size = 24))
+####End
+
+### NORMALLY DISTRIBUTED LOAD (2 function instances/replicas) Std 10 - RANDOM BEGINNING DEVICE
+
+#Graphs for the categorization of placements and the relative difference in overall/marginal energy
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./RandomBeginningDevice/Std10/resultsParsed_40rep_DeviceOnlyVar_2replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+
+##Working on visualizing the difference
+#Calculate the difference - for Overall Energy
+diffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy - loadLevel0_Overall$OverallEnergy
+diffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy - loadLevel1_Overall$OverallEnergy
+diffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy - loadLevel2_Overall$OverallEnergy
+diffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy - loadLevel3_Overall$OverallEnergy
+diffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy - loadLevel4_Overall$OverallEnergy
+diffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy - loadLevel5_Overall$OverallEnergy
+diffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy - loadLevel6_Overall$OverallEnergy
+diffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy - loadLevel7_Overall$OverallEnergy
+diffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy - loadLevel8_Overall$OverallEnergy
+diffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy - loadLevel9_Overall$OverallEnergy
+diffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy - loadLevel10_Overall$OverallEnergy
+diffLoadLevel_Overall = list(diffLoadLevel0_Overall,diffLoadLevel1_Overall,diffLoadLevel2_Overall,
+                             diffLoadLevel3_Overall,diffLoadLevel4_Overall,diffLoadLevel5_Overall,
+                             diffLoadLevel6_Overall,diffLoadLevel7_Overall,diffLoadLevel8_Overall,
+                             diffLoadLevel9_Overall,diffLoadLevel10_Overall)
+#Calculate the relative difference - for Overall Energy
+reldiffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy / loadLevel0_Overall$OverallEnergy
+reldiffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy / loadLevel1_Overall$OverallEnergy
+reldiffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy / loadLevel2_Overall$OverallEnergy
+reldiffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy / loadLevel3_Overall$OverallEnergy
+reldiffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy / loadLevel4_Overall$OverallEnergy
+reldiffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy / loadLevel5_Overall$OverallEnergy
+reldiffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy / loadLevel6_Overall$OverallEnergy
+reldiffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy / loadLevel7_Overall$OverallEnergy
+reldiffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy / loadLevel8_Overall$OverallEnergy
+reldiffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy / loadLevel9_Overall$OverallEnergy
+reldiffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy / loadLevel10_Overall$OverallEnergy
+reldiffLoadLevel_Overall = list(reldiffLoadLevel0_Overall,reldiffLoadLevel1_Overall,reldiffLoadLevel2_Overall,
+                                reldiffLoadLevel3_Overall,reldiffLoadLevel4_Overall,reldiffLoadLevel5_Overall,
+                                reldiffLoadLevel6_Overall,reldiffLoadLevel7_Overall,reldiffLoadLevel8_Overall,
+                                reldiffLoadLevel9_Overall,reldiffLoadLevel10_Overall)
+#Calculate the relative difference - for Marginal Energy
+reldiffLoadLevel0_Marginal <- loadLevel0_Overall$MarginalEnergy / loadLevel0_Marginal$MarginalEnergy
+reldiffLoadLevel1_Marginal <- loadLevel1_Overall$MarginalEnergy / loadLevel1_Marginal$MarginalEnergy
+reldiffLoadLevel2_Marginal <- loadLevel2_Overall$MarginalEnergy / loadLevel2_Marginal$MarginalEnergy
+reldiffLoadLevel3_Marginal <- loadLevel3_Overall$MarginalEnergy / loadLevel3_Marginal$MarginalEnergy
+reldiffLoadLevel4_Marginal <- loadLevel4_Overall$MarginalEnergy / loadLevel4_Marginal$MarginalEnergy
+reldiffLoadLevel5_Marginal <- loadLevel5_Overall$MarginalEnergy / loadLevel5_Marginal$MarginalEnergy
+reldiffLoadLevel6_Marginal <- loadLevel6_Overall$MarginalEnergy / loadLevel6_Marginal$MarginalEnergy
+reldiffLoadLevel7_Marginal <- loadLevel7_Overall$MarginalEnergy / loadLevel7_Marginal$MarginalEnergy
+reldiffLoadLevel8_Marginal <- loadLevel8_Overall$MarginalEnergy / loadLevel8_Marginal$MarginalEnergy
+reldiffLoadLevel9_Marginal <- loadLevel9_Overall$MarginalEnergy / loadLevel9_Marginal$MarginalEnergy
+reldiffLoadLevel10_Marginal <- loadLevel10_Overall$MarginalEnergy / loadLevel10_Marginal$MarginalEnergy
+reldiffLoadLevel_Marginal = list(reldiffLoadLevel0_Marginal,reldiffLoadLevel1_Marginal,reldiffLoadLevel2_Marginal,
+                                 reldiffLoadLevel3_Marginal,reldiffLoadLevel4_Marginal,reldiffLoadLevel5_Marginal,
+                                 reldiffLoadLevel6_Marginal,reldiffLoadLevel7_Marginal,reldiffLoadLevel8_Marginal,
+                                 reldiffLoadLevel9_Marginal,reldiffLoadLevel10_Marginal)
+
+#Calculating how many are same, different and infeasible, also storing the data about the difference
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+datadiff=vector()
+datareldiff=vector()
+datareldiff_m=vector()
+datadiffloc=vector()
+for (levelNb in seq(1,11)){
+  difference=vector()
+  reldifference=vector()
+  reldifference_m=vector()
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1
+    difference=append(difference,diff)}
+  }
+  for(diff in reldiffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference=append(reldifference,diff)}
+  }
+  datadiffloc=append(datadiffloc,rep((levelNb-1)*10,length(difference)))
+  datadiff=append(datadiff,difference)
+  datareldiff=append(datareldiff,reldifference)
+  for(diff in reldiffLoadLevel_Marginal[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference_m=append(reldifference_m,diff)}
+  }
+  datareldiff_m=append(datareldiff_m,reldifference_m)
+}
+
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 24),
+        axis.text.x = element_text(size = 24),
+        axis.title.y = element_text(size = 24),
+        axis.text.y = element_text(size = 24),
+        legend.text=element_text(size = 24),
+        legend.title=element_text(size = 24))
+
+##Create the dataframe for statistics about the difference - OVERALL ENERGY
+statisticsPlacement=data.frame(datadiffloc,datadiff,datareldiff)
+
+#Get numbers for the text
+quantile(statisticsPlacement$datareldiff,0.10)
+quantile(statisticsPlacement$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement, aes(x=factor(datadiffloc), y=datareldiff)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in overall energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+
+##Create the dataframe for statistics about the difference - MARGINAL ENERGY
+statisticsPlacement_m=data.frame(datadiffloc,datareldiff_m)
+
+#Get numbers for the text
+quantile(statisticsPlacement_m$datareldiff,0.10)
+quantile(statisticsPlacement_m$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement_m, aes(x=factor(datadiffloc), y=datareldiff_m)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in marginal energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Average included device utilization data graph
+####Begin
+### Getting the data - different placements ONLY
+result_data_csv <- read.csv(file="./RandomBeginningDevice/Std10/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_2replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10
+
+#Create a dataframe with only the device utilization information
+utilization=data.frame(result_data_csv$Device0,result_data_csv$Device1,result_data_csv$Device2,result_data_csv$Device3,
+                       result_data_csv$Device4,result_data_csv$Device5,result_data_csv$Device6,result_data_csv$Device7,
+                       result_data_csv$Device8,result_data_csv$Device9,result_data_csv$Device10)
+
+#Calculating the mean utilization for each data line
+meanUt=rowMeans(utilization,na.rm=TRUE)
+
+#Create data frame for plotting
+mean_data_utilization= data.frame(result_data_csv$LoadLevel,result_data_csv$Alternative,meanUt)
+
+###Plot - Statistics about the utilization, violin plot
+ggplot(data=mean_data_utilization, aes(x=factor(result_data_csv$LoadLevel), y=meanUt, fill=result_data_csv$Alternative)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Mean device utilization when placements are different (%)")+
+  xlab("Average load level in %")+
+  labs(fill = "Optimization objective")+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Completion Time graph for different placements
+####Begin
+## Getting the data - different placements ONLY
+result_data_csv_ut_DifferentOnly <- read.csv(file="./RandomBeginningDevice/Std10/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_2replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+## Getting the data - all placements
+result_data_csv_ev_All <- read.csv(file="./RandomBeginningDevice/Std10/resultsParsed_40rep_DeviceOnlyVar_2replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+result_data_csv_ev_All$LoadLevel <- result_data_csv_ev_All$Scenario*10 
+
+##Adding a column for the combination Repetition_Scenario to be able to filter
+result_data_csv_ut_DifferentOnly$id <- paste(result_data_csv_ut_DifferentOnly$Repetition,result_data_csv_ut_DifferentOnly$Scenario,sep = "_")
+result_data_csv_ev_All$id <- paste(result_data_csv_ev_All$Repetition,result_data_csv_ev_All$Scenario,sep = "_")
+
+##Filter the all data from the combination Repetition/Scenario/Alternative? to get only the info when placements are different
+library(dplyr)
+result_data_csv_ev_DifferentOnly = result_data_csv_ev_All %>% filter(id %in% result_data_csv_ut_DifferentOnly$id)
+
+#Boxplot
+ggplot(data=result_data_csv_ev_DifferentOnly, aes(x=factor(LoadLevel), y=CompletionTime,
+                                                  fill=Alternative)) +
+  geom_boxplot()+
+  theme_minimal()+
+  ylab("Request completion time when placements are different (ms)")+
+  xlab("Average load level in %")+
+  ylim(0,100)+
+  labs(fill = "Optimization objective")+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+## NORMALLY DISTRIBUTED LOAD - STD 30 (2 function instances/replicas) - RANDOM BEGINNING DEVICE
+
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./RandomBeginningDevice/Std30/resultsParsed_40rep_DeviceOnlyVar_2replicas_Std30_RequestDeviceRandom.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+
+#Calculating how many are same, different and infeasible, also storing the data about the difference
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+datadiff=vector()
+datareldiff=vector()
+datareldiff_m=vector()
+datadiffloc=vector()
+for (levelNb in seq(1,11)){
+  difference=vector()
+  reldifference=vector()
+  reldifference_m=vector()
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1
+    difference=append(difference,diff)}
+  }
+  for(diff in reldiffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference=append(reldifference,diff)}
+  }
+  datadiffloc=append(datadiffloc,rep((levelNb-1)*10,length(difference)))
+  datadiff=append(datadiff,difference)
+  datareldiff=append(datareldiff,reldifference)
+  for(diff in reldiffLoadLevel_Marginal[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference_m=append(reldifference_m,diff)}
+  }
+  datareldiff_m=append(datareldiff_m,reldifference_m)
+}
+
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 24),
+        axis.text.x = element_text(size = 24),
+        axis.title.y = element_text(size = 24),
+        axis.text.y = element_text(size = 24),
+        legend.text=element_text(size = 24),
+        legend.title=element_text(size = 24))
+####End
+
+## NORMALLY DISTRIBUTED LOAD - STD 10 (4 function instances/replicas) - RANDOM BEGINNING DEVICE
+
+#Graphs for the categorization of placements and the relative difference in overall/marginal energy
+####Begin
+### Getting the data
+result_data_csv <- read.csv(file="./RandomBeginningDevice/4fi/resultsParsed_40rep_DeviceOnlyVar_4replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+
+##Working on visualizing the difference
+#Calculate the difference - for Overall Energy
+diffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy - loadLevel0_Overall$OverallEnergy
+diffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy - loadLevel1_Overall$OverallEnergy
+diffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy - loadLevel2_Overall$OverallEnergy
+diffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy - loadLevel3_Overall$OverallEnergy
+diffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy - loadLevel4_Overall$OverallEnergy
+diffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy - loadLevel5_Overall$OverallEnergy
+diffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy - loadLevel6_Overall$OverallEnergy
+diffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy - loadLevel7_Overall$OverallEnergy
+diffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy - loadLevel8_Overall$OverallEnergy
+diffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy - loadLevel9_Overall$OverallEnergy
+diffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy - loadLevel10_Overall$OverallEnergy
+diffLoadLevel_Overall = list(diffLoadLevel0_Overall,diffLoadLevel1_Overall,diffLoadLevel2_Overall,
+                             diffLoadLevel3_Overall,diffLoadLevel4_Overall,diffLoadLevel5_Overall,
+                             diffLoadLevel6_Overall,diffLoadLevel7_Overall,diffLoadLevel8_Overall,
+                             diffLoadLevel9_Overall,diffLoadLevel10_Overall)
+#Calculate the relative difference - for Overall Energy
+reldiffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy / loadLevel0_Overall$OverallEnergy
+reldiffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy / loadLevel1_Overall$OverallEnergy
+reldiffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy / loadLevel2_Overall$OverallEnergy
+reldiffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy / loadLevel3_Overall$OverallEnergy
+reldiffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy / loadLevel4_Overall$OverallEnergy
+reldiffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy / loadLevel5_Overall$OverallEnergy
+reldiffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy / loadLevel6_Overall$OverallEnergy
+reldiffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy / loadLevel7_Overall$OverallEnergy
+reldiffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy / loadLevel8_Overall$OverallEnergy
+reldiffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy / loadLevel9_Overall$OverallEnergy
+reldiffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy / loadLevel10_Overall$OverallEnergy
+reldiffLoadLevel_Overall = list(reldiffLoadLevel0_Overall,reldiffLoadLevel1_Overall,reldiffLoadLevel2_Overall,
+                                reldiffLoadLevel3_Overall,reldiffLoadLevel4_Overall,reldiffLoadLevel5_Overall,
+                                reldiffLoadLevel6_Overall,reldiffLoadLevel7_Overall,reldiffLoadLevel8_Overall,
+                                reldiffLoadLevel9_Overall,reldiffLoadLevel10_Overall)
+#Calculate the relative difference - for Marginal Energy
+reldiffLoadLevel0_Marginal <- loadLevel0_Overall$MarginalEnergy / loadLevel0_Marginal$MarginalEnergy
+reldiffLoadLevel1_Marginal <- loadLevel1_Overall$MarginalEnergy / loadLevel1_Marginal$MarginalEnergy
+reldiffLoadLevel2_Marginal <- loadLevel2_Overall$MarginalEnergy / loadLevel2_Marginal$MarginalEnergy
+reldiffLoadLevel3_Marginal <- loadLevel3_Overall$MarginalEnergy / loadLevel3_Marginal$MarginalEnergy
+reldiffLoadLevel4_Marginal <- loadLevel4_Overall$MarginalEnergy / loadLevel4_Marginal$MarginalEnergy
+reldiffLoadLevel5_Marginal <- loadLevel5_Overall$MarginalEnergy / loadLevel5_Marginal$MarginalEnergy
+reldiffLoadLevel6_Marginal <- loadLevel6_Overall$MarginalEnergy / loadLevel6_Marginal$MarginalEnergy
+reldiffLoadLevel7_Marginal <- loadLevel7_Overall$MarginalEnergy / loadLevel7_Marginal$MarginalEnergy
+reldiffLoadLevel8_Marginal <- loadLevel8_Overall$MarginalEnergy / loadLevel8_Marginal$MarginalEnergy
+reldiffLoadLevel9_Marginal <- loadLevel9_Overall$MarginalEnergy / loadLevel9_Marginal$MarginalEnergy
+reldiffLoadLevel10_Marginal <- loadLevel10_Overall$MarginalEnergy / loadLevel10_Marginal$MarginalEnergy
+reldiffLoadLevel_Marginal = list(reldiffLoadLevel0_Marginal,reldiffLoadLevel1_Marginal,reldiffLoadLevel2_Marginal,
+                                 reldiffLoadLevel3_Marginal,reldiffLoadLevel4_Marginal,reldiffLoadLevel5_Marginal,
+                                 reldiffLoadLevel6_Marginal,reldiffLoadLevel7_Marginal,reldiffLoadLevel8_Marginal,
+                                 reldiffLoadLevel9_Marginal,reldiffLoadLevel10_Marginal)
+
+#Calculating how many are same, different and infeasible, also storing the data about the difference
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+datadiff=vector()
+datareldiff=vector()
+datareldiff_m=vector()
+datadiffloc=vector()
+for (levelNb in seq(1,11)){
+  difference=vector()
+  reldifference=vector()
+  reldifference_m=vector()
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1
+    difference=append(difference,diff)}
+  }
+  for(diff in reldiffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference=append(reldifference,diff)}
+  }
+  datadiffloc=append(datadiffloc,rep((levelNb-1)*10,length(difference)))
+  datadiff=append(datadiff,difference)
+  datareldiff=append(datareldiff,reldifference)
+  for(diff in reldiffLoadLevel_Marginal[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference_m=append(reldifference_m,diff)}
+  }
+  datareldiff_m=append(datareldiff_m,reldifference_m)
+}
+
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 24),
+        axis.text.x = element_text(size = 24),
+        axis.title.y = element_text(size = 24),
+        axis.text.y = element_text(size = 24),
+        legend.text=element_text(size = 24),
+        legend.title=element_text(size = 24))
+
+##Create the dataframe for statistics about the difference - OVERALL ENERGY
+statisticsPlacement=data.frame(datadiffloc,datadiff,datareldiff)
+
+#Get numbers for the text
+quantile(statisticsPlacement$datareldiff,0.10)
+quantile(statisticsPlacement$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement, aes(x=factor(datadiffloc), y=datareldiff)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in overall energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+
+##Create the dataframe for statistics about the difference - MARGINAL ENERGY
+statisticsPlacement_m=data.frame(datadiffloc,datareldiff_m)
+
+#Get numbers for the text
+quantile(statisticsPlacement_m$datareldiff,0.10)
+quantile(statisticsPlacement_m$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement_m, aes(x=factor(datadiffloc), y=datareldiff_m)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in marginal energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Average included device utilization data graph
+####Begin
+### Getting the data - different placements ONLY
+result_data_csv <- read.csv(file="./RandomBeginningDevice/4fi/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_4replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10
+
+#Create a dataframe with only the device utilization information
+utilization=data.frame(result_data_csv$Device0,result_data_csv$Device1,result_data_csv$Device2,result_data_csv$Device3,
+                       result_data_csv$Device4,result_data_csv$Device5,result_data_csv$Device6,result_data_csv$Device7,
+                       result_data_csv$Device8,result_data_csv$Device9,result_data_csv$Device10)
+
+#Calculating the mean utilization for each data line
+meanUt=rowMeans(utilization,na.rm=TRUE)
+
+#Create data frame for plotting
+mean_data_utilization= data.frame(result_data_csv$LoadLevel,result_data_csv$Alternative,meanUt)
+
+###Plot - Statistics about the utilization, violin plot
+ggplot(data=mean_data_utilization, aes(x=factor(result_data_csv$LoadLevel), y=meanUt, fill=result_data_csv$Alternative)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Mean device utilization when placements are different (%)")+
+  xlab("Average load level in %")+
+  labs(fill = "Optimization objective")+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Completion Time graph for different placements 
+####Begin
+## Getting the data - different placements ONLY
+result_data_csv_ut_DifferentOnly <- read.csv(file="./4fi/RandomBeginningDevice/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_4replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+## Getting the data - all placements
+result_data_csv_ev_All <- read.csv(file="./RandomBeginningDevice/4fi/resultsParsed_40rep_DeviceOnlyVar_4replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+result_data_csv_ev_All$LoadLevel <- result_data_csv_ev_All$Scenario*10 
+
+##Adding a column for the combination Repetition_Scenario to be able to filter
+result_data_csv_ut_DifferentOnly$id <- paste(result_data_csv_ut_DifferentOnly$Repetition,result_data_csv_ut_DifferentOnly$Scenario,sep = "_")
+result_data_csv_ev_All$id <- paste(result_data_csv_ev_All$Repetition,result_data_csv_ev_All$Scenario,sep = "_")
+
+##Filter the all data from the combination Repetition/Scenario/Alternative? to get only the info when placements are different
+library(dplyr)
+result_data_csv_ev_DifferentOnly = result_data_csv_ev_All %>% filter(id %in% result_data_csv_ut_DifferentOnly$id)
+
+#Boxplot
+ggplot(data=result_data_csv_ev_DifferentOnly, aes(x=factor(LoadLevel), y=CompletionTime,
+                                                  fill=Alternative)) +
+  geom_boxplot()+
+  theme_minimal()+
+  ylab("Request completion time when placements are different (ms)")+
+  xlab("Average load level in %")+
+  ylim(0,100)+
+  labs(fill = "Optimization objective")+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+
+### NORMALLY DISTRIBUTED LOAD - STD 10 (6 function instances/replicas) - RANDOM BEGINNING DEVICE
+
+#Graphs for the categorization of placements and the relative difference in overall/marginal energy
+#### Begin
+### Getting the data
+result_data_csv <- read.csv(file="./RandomBeginningDevice/6fi/resultsParsed_40rep_DeviceOnlyVar_6replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10 
+
+###Filter per loadLevel
+loadLevel0_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Overall"),]
+loadLevel0_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 0 & result_data_csv$Alternative=="Marginal"),]
+loadLevel1_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Overall"),]
+loadLevel1_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 10 & result_data_csv$Alternative=="Marginal"),]
+loadLevel2_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Overall"),]
+loadLevel2_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 20 & result_data_csv$Alternative=="Marginal"),]
+loadLevel3_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Overall"),]
+loadLevel3_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 30 & result_data_csv$Alternative=="Marginal"),]
+loadLevel4_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Overall"),]
+loadLevel4_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 40 & result_data_csv$Alternative=="Marginal"),]
+loadLevel5_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Overall"),]
+loadLevel5_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 50 & result_data_csv$Alternative=="Marginal"),]
+loadLevel6_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Overall"),]
+loadLevel6_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 60 & result_data_csv$Alternative=="Marginal"),]
+loadLevel7_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Overall"),]
+loadLevel7_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 70 & result_data_csv$Alternative=="Marginal"),]
+loadLevel8_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Overall"),]
+loadLevel8_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 80 & result_data_csv$Alternative=="Marginal"),]
+loadLevel9_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Overall"),]
+loadLevel9_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 90 & result_data_csv$Alternative=="Marginal"),]
+loadLevel10_Overall <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Overall"),]
+loadLevel10_Marginal <- result_data_csv[which(result_data_csv$LoadLevel == 100 & result_data_csv$Alternative=="Marginal"),]
+
+
+##Working on visualizing the difference
+#Calculate the difference - for Overall Energy
+diffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy - loadLevel0_Overall$OverallEnergy
+diffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy - loadLevel1_Overall$OverallEnergy
+diffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy - loadLevel2_Overall$OverallEnergy
+diffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy - loadLevel3_Overall$OverallEnergy
+diffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy - loadLevel4_Overall$OverallEnergy
+diffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy - loadLevel5_Overall$OverallEnergy
+diffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy - loadLevel6_Overall$OverallEnergy
+diffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy - loadLevel7_Overall$OverallEnergy
+diffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy - loadLevel8_Overall$OverallEnergy
+diffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy - loadLevel9_Overall$OverallEnergy
+diffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy - loadLevel10_Overall$OverallEnergy
+diffLoadLevel_Overall = list(diffLoadLevel0_Overall,diffLoadLevel1_Overall,diffLoadLevel2_Overall,
+                             diffLoadLevel3_Overall,diffLoadLevel4_Overall,diffLoadLevel5_Overall,
+                             diffLoadLevel6_Overall,diffLoadLevel7_Overall,diffLoadLevel8_Overall,
+                             diffLoadLevel9_Overall,diffLoadLevel10_Overall)
+#Calculate the relative difference - for Overall Energy
+reldiffLoadLevel0_Overall <- loadLevel0_Marginal$OverallEnergy / loadLevel0_Overall$OverallEnergy
+reldiffLoadLevel1_Overall <- loadLevel1_Marginal$OverallEnergy / loadLevel1_Overall$OverallEnergy
+reldiffLoadLevel2_Overall <- loadLevel2_Marginal$OverallEnergy / loadLevel2_Overall$OverallEnergy
+reldiffLoadLevel3_Overall <- loadLevel3_Marginal$OverallEnergy / loadLevel3_Overall$OverallEnergy
+reldiffLoadLevel4_Overall <- loadLevel4_Marginal$OverallEnergy / loadLevel4_Overall$OverallEnergy
+reldiffLoadLevel5_Overall <- loadLevel5_Marginal$OverallEnergy / loadLevel5_Overall$OverallEnergy
+reldiffLoadLevel6_Overall <- loadLevel6_Marginal$OverallEnergy / loadLevel6_Overall$OverallEnergy
+reldiffLoadLevel7_Overall <- loadLevel7_Marginal$OverallEnergy / loadLevel7_Overall$OverallEnergy
+reldiffLoadLevel8_Overall <- loadLevel8_Marginal$OverallEnergy / loadLevel8_Overall$OverallEnergy
+reldiffLoadLevel9_Overall <- loadLevel9_Marginal$OverallEnergy / loadLevel9_Overall$OverallEnergy
+reldiffLoadLevel10_Overall <- loadLevel10_Marginal$OverallEnergy / loadLevel10_Overall$OverallEnergy
+reldiffLoadLevel_Overall = list(reldiffLoadLevel0_Overall,reldiffLoadLevel1_Overall,reldiffLoadLevel2_Overall,
+                                reldiffLoadLevel3_Overall,reldiffLoadLevel4_Overall,reldiffLoadLevel5_Overall,
+                                reldiffLoadLevel6_Overall,reldiffLoadLevel7_Overall,reldiffLoadLevel8_Overall,
+                                reldiffLoadLevel9_Overall,reldiffLoadLevel10_Overall)
+#Calculate the relative difference - for Marginal Energy
+reldiffLoadLevel0_Marginal <- loadLevel0_Overall$MarginalEnergy / loadLevel0_Marginal$MarginalEnergy
+reldiffLoadLevel1_Marginal <- loadLevel1_Overall$MarginalEnergy / loadLevel1_Marginal$MarginalEnergy
+reldiffLoadLevel2_Marginal <- loadLevel2_Overall$MarginalEnergy / loadLevel2_Marginal$MarginalEnergy
+reldiffLoadLevel3_Marginal <- loadLevel3_Overall$MarginalEnergy / loadLevel3_Marginal$MarginalEnergy
+reldiffLoadLevel4_Marginal <- loadLevel4_Overall$MarginalEnergy / loadLevel4_Marginal$MarginalEnergy
+reldiffLoadLevel5_Marginal <- loadLevel5_Overall$MarginalEnergy / loadLevel5_Marginal$MarginalEnergy
+reldiffLoadLevel6_Marginal <- loadLevel6_Overall$MarginalEnergy / loadLevel6_Marginal$MarginalEnergy
+reldiffLoadLevel7_Marginal <- loadLevel7_Overall$MarginalEnergy / loadLevel7_Marginal$MarginalEnergy
+reldiffLoadLevel8_Marginal <- loadLevel8_Overall$MarginalEnergy / loadLevel8_Marginal$MarginalEnergy
+reldiffLoadLevel9_Marginal <- loadLevel9_Overall$MarginalEnergy / loadLevel9_Marginal$MarginalEnergy
+reldiffLoadLevel10_Marginal <- loadLevel10_Overall$MarginalEnergy / loadLevel10_Marginal$MarginalEnergy
+reldiffLoadLevel_Marginal = list(reldiffLoadLevel0_Marginal,reldiffLoadLevel1_Marginal,reldiffLoadLevel2_Marginal,
+                                 reldiffLoadLevel3_Marginal,reldiffLoadLevel4_Marginal,reldiffLoadLevel5_Marginal,
+                                 reldiffLoadLevel6_Marginal,reldiffLoadLevel7_Marginal,reldiffLoadLevel8_Marginal,
+                                 reldiffLoadLevel9_Marginal,reldiffLoadLevel10_Marginal)
+
+#Calculating how many are same, different and infeasible, also storing the data about the difference
+same=rep(0,11)
+different=rep(0,11)
+infeasible=rep(0,11)
+datadiff=vector()
+datareldiff=vector()
+datareldiff_m=vector()
+datadiffloc=vector()
+for (levelNb in seq(1,11)){
+  difference=vector()
+  reldifference=vector()
+  reldifference_m=vector()
+  for(diff in diffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){infeasible[levelNb]=infeasible[levelNb]+1}
+    else if (diff==0){same[levelNb]=same[levelNb]+1}
+    else if (diff>0){different[levelNb]=different[levelNb]+1
+    difference=append(difference,diff)}
+  }
+  for(diff in reldiffLoadLevel_Overall[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference=append(reldifference,diff)}
+  }
+  datadiffloc=append(datadiffloc,rep((levelNb-1)*10,length(difference)))
+  datadiff=append(datadiff,difference)
+  datareldiff=append(datareldiff,reldifference)
+  for(diff in reldiffLoadLevel_Marginal[[levelNb]]){
+    if (is.na(diff)){}
+    else if (diff>1){reldifference_m=append(reldifference_m,diff)}
+  }
+  datareldiff_m=append(datareldiff_m,reldifference_m)
+}
+
+
+##Create the dataframe for plotting the difference
+LoadLevel= rep(seq(0,100,10),3)
+Outcome=c(rep("Same",11),rep("Different",11),rep("Infeasible",11))
+NbPlacements=c(same,different,infeasible)
+nbDifferentPlacements =data.frame(LoadLevel,Outcome,NbPlacements)
+
+### Plot - Nb of different placement
+ggplot(data=nbDifferentPlacements, aes(x=LoadLevel, y=NbPlacements, fill=Outcome)) +
+  geom_bar(stat="identity", position = position_stack())+
+  theme_minimal()+
+  ylab("# obtained placements")+
+  xlab("Average load level in %")+
+  labs(fill = "Overall and Marginal placements are")+
+  scale_fill_manual(values=c("#A95AA1","#F5793A","#85C0F9"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 24),
+        axis.text.x = element_text(size = 24),
+        axis.title.y = element_text(size = 24),
+        axis.text.y = element_text(size = 24),
+        legend.text=element_text(size = 24),
+        legend.title=element_text(size = 24))
+
+##Create the dataframe for statistics about the difference - OVERALL ENERGY
+statisticsPlacement=data.frame(datadiffloc,datadiff,datareldiff)
+
+#Get numbers for the text
+quantile(statisticsPlacement$datareldiff,0.10)
+quantile(statisticsPlacement$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement, aes(x=factor(datadiffloc), y=datareldiff)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in overall energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+
+##Create the dataframe for statistics about the difference - MARGINAL ENERGY
+statisticsPlacement_m=data.frame(datadiffloc,datareldiff_m)
+
+#Get numbers for the text
+quantile(statisticsPlacement_m$datareldiff,0.10)
+quantile(statisticsPlacement_m$datareldiff,0.90)
+
+###Plot - Statistics about the relative difference, violin plot
+ggplot(data=statisticsPlacement_m, aes(x=factor(datadiffloc), y=datareldiff_m)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Relative difference in marginal energy (J)")+
+  xlab("Average load level in %")+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Average included device utilization data graph
+####Begin
+### Getting the data - different placements ONLY
+result_data_csv <- read.csv(file="./RandomBeginningDevice/6fi/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_6replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+#Adding the load level column
+result_data_csv$LoadLevel <- result_data_csv$Scenario*10
+
+#Create a dataframe with only the device utilization information
+utilization=data.frame(result_data_csv$Device0,result_data_csv$Device1,result_data_csv$Device2,result_data_csv$Device3,
+                       result_data_csv$Device4,result_data_csv$Device5,result_data_csv$Device6,result_data_csv$Device7,
+                       result_data_csv$Device8,result_data_csv$Device9,result_data_csv$Device10)
+
+#Calculating the mean utilization for each data line
+meanUt=rowMeans(utilization,na.rm=TRUE)
+
+#Create data frame for plotting
+mean_data_utilization= data.frame(result_data_csv$LoadLevel,result_data_csv$Alternative,meanUt)
+
+###Plot - Statistics about the utilization, violin plot
+ggplot(data=mean_data_utilization, aes(x=factor(result_data_csv$LoadLevel), y=meanUt, fill=result_data_csv$Alternative)) +
+  geom_violin()+
+  theme_minimal()+
+  ylab("Mean device utilization when placements are different (%)")+
+  xlab("Average load level in %")+
+  labs(fill = "Optimization objective")+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))
+####End
+
+#Completion Time graph for different placements 
+#### Begin
+## Getting the data - different placements ONLY
+result_data_csv_ut_DifferentOnly <- read.csv(file="./RandomBeginningDevice/6fi/resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_6replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+## Getting the data - all placements
+result_data_csv_ev_All <- read.csv(file="./RandomBeginningDevice/6fi/resultsParsed_40rep_DeviceOnlyVar_6replicas_Std10_RequestDeviceRandom.csv", header=TRUE, sep=",")
+result_data_csv_ev_All$LoadLevel <- result_data_csv_ev_All$Scenario*10 
+
+##Adding a column for the combination Repetition_Scenario to be able to filter
+result_data_csv_ut_DifferentOnly$id <- paste(result_data_csv_ut_DifferentOnly$Repetition,result_data_csv_ut_DifferentOnly$Scenario,sep = "_")
+result_data_csv_ev_All$id <- paste(result_data_csv_ev_All$Repetition,result_data_csv_ev_All$Scenario,sep = "_")
+
+##Filter the all data from the combination Repetition/Scenario/Alternative? to get only the info when placements are different
+library(dplyr)
+result_data_csv_ev_DifferentOnly = result_data_csv_ev_All %>% filter(id %in% result_data_csv_ut_DifferentOnly$id)
+
+#Boxplot
+ggplot(data=result_data_csv_ev_DifferentOnly, aes(x=factor(LoadLevel), y=CompletionTime,
+                                                  fill=Alternative)) +
+  geom_boxplot()+
+  theme_minimal()+
+  ylab("Request completion time when placements are different (ms)")+
+  xlab("Average load level in %")+
+  labs(fill = "Optimization objective")+
+  ylim(0,100)+
+  scale_fill_manual(values=c("#F0E442","#0072B2"))+
+  theme(legend.position = "top",axis.title.x = element_text(size = 18),
+        axis.text.x = element_text(size = 18),
+        axis.title.y = element_text(size = 18),
+        axis.text.y = element_text(size = 18),
+        legend.text=element_text(size = 18),
+        legend.title=element_text(size = 18))

Analysis/resultLogParsing.py

+import csv
+import re
+
+# open the file in the write mode
+f = open('resultsParsed_40rep_DeviceOnlyVar_2replicas_Std30_RequestDeviceRandom.csv', 'w',newline='')
+
+# create the csv writer
+writer = csv.writer(f)
+# Header
+writer.writerow(['Repetition','Scenario','Alternative','ExecutionTime','CompletionTime','OverallEnergy','MarginalEnergy','CompletionTimeLink','CompletionTimeDevice', 'EnergyOverallLink','EnergyOverallDevice','EnergyMarginalLink','EnergyMarginalDevice'])
+
+nextline= False
+
+with open("40rep_DeviceOnlyVar_2replicas_Std30_RequestDeviceRandom.txt","r") as fi:
+	for ln in fi:
+	
+		if ln.startswith("Repetition"):
+			# Get the repetition number
+			repetition =[s for s in re.findall(r'\b\d+\b', ln)]
+	
+		if ln.startswith("Utilization scenario"):
+			# Get the scenario number
+			number =[s for s in re.findall(r'\b\d+\b', ln)]
+	
+		if nextline:
+			#This is a line with the results for the placement evaluation
+			# The results should be in the following order: CompletionTime, OverallEnergy, MarginalEnergy, CompletionTimeLink, CompletionTimeDevice, EnergyOverallLink, EnergyOverallDevice, EnergyMarginalLink, EnergyMarginalDevice
+			results=[s for s in re.findall(r'\d+\.\d+', ln)]
+			
+			if (results):
+				
+				# Write to the CSV file
+				writer.writerow([repetition[0],number[0],alternative,executionTime[0],results[0],results[1],results[2],results[3],results[4],results[5],results[6],results[7],results[8]])
+			else:
+				# No results because infeasible
+				# Write to the CSV file
+				writer.writerow([repetition[0],number[0],alternative,executionTime[0],'NA','NA','NA','NA','NA','NA','NA','NA','NA'])
+			
+			# Reset
+			nextline= False
+		
+		
+		if ln.startswith("OVERALL OPT"):
+			# Get the scenario number
+			alternative ="Overall"
+			# Get the value for the execution time
+			executionTime=[s for s in re.findall(r'\d+', ln)]
+			# Get to the nextline
+			nextline=True
+		else:
+			if ln.startswith("MARGINAL OPT"):
+				# Get the scenario number
+				alternative ="Marginal"
+				# Get the value for the execution time
+				executionTime=[s for s in re.findall(r'\d+', ln)]
+				# Get to the nextline
+				nextline=True
+		
+
+# close the file
+f.close()
\ No newline at end of file

Analysis/resultLogParsing_UtilizationDifferent.py

+import csv
+import re
+
+# open the file in the write mode
+f = open('resultsParsed_UtilizationDifferent_40rep_DeviceOnlyVar_2replicas_Std30_RequestDeviceRandom.csv', 'w',newline='')
+
+# create the csv writer
+writer = csv.writer(f)
+# Header
+writer.writerow(['Repetition','Scenario','Alternative','Device0','Device1','Device2','Device3','Device4','Device5', 'Device6','Device7','Device8','Device9','Device10'])
+
+nextline= False
+nextlineUtilization = False
+i=0
+saveDevicePlacement = True
+
+with open("40rep_DeviceOnlyVar_2replicas_Std30_RequestDeviceRandom.txt","r") as fi:
+	for ln in fi:
+		
+		if nextlineUtilization:
+			#This is a line with the data for the utilization scenario
+			gatewayList=[s for s in re.findall(r'[\s\{]gateway_(\d+)=(\d+.\d+)', ln)]
+			utilizationInfo=[0.0]*11
+			for infoPair in gatewayList: #A pair has the form (deviceNumber,utilizationValue)
+				utilizationInfo[int(infoPair[0])]=infoPair[1]
+			#print(utilizationInfo)
+			
+			# Reset
+			nextlineUtilization= False
+	
+		if ln.startswith("Repetition"):
+			# Get the repetition number
+			repetition =[s for s in re.findall(r'\b\d+\b', ln)]
+	
+		if ln.startswith("Utilization scenario"):
+			# Get the scenario number
+			number =[s for s in re.findall(r'\b\d+\b', ln)]
+			nextlineUtilization=True          
+	
+		if nextline:
+			#This is a line with the name of the alternative
+			if ln.startswith("OVERALL OPT"):
+				# Get the scenario number
+				alternative ="Overall"
+				saveDevicePlacement=False
+                # The results indicate the utilization information only for the devices used in the placement - save temporarily overall results
+				results2=[]
+				for deviceNb in range(11):
+					if deviceNb in devicesUsedInPlacement:
+						results2.append(utilizationInfo[deviceNb])
+					else:
+						results2.append('NA')
+				#print(results)	
+			if ln.startswith("MARGINAL OPT"):
+				# Get the scenario number
+				alternative ="Marginal"
+                # Assuming Marginal is always second
+				saveDevicePlacement=True
+                
+				if not devicesUsedInPlacement==devicesUsedInPlacementSaved:
+					#Only save info when placement is different
+					print("Different placement, writing to CSV")
+					# The results indicate the utilization information only for the devices used in the placement
+					results=[]
+					for deviceNb in range(11):
+						if deviceNb in devicesUsedInPlacement:
+							results.append(utilizationInfo[deviceNb])
+						else:
+							results.append('NA')
+					#print(results)	
+					# Write to the CSV file - the two rows
+					writer.writerow([repetition[0],number[0],"Overall",results2[0],results2[1],results2[2],results2[3],results2[4],results2[5],results2[6],results2[7],results2[8],results2[9],results2[10]])
+					writer.writerow([repetition[0],number[0],alternative,results[0],results[1],results[2],results[3],results[4],results[5],results[6],results[7],results[8],results[9],results[10]])
+					i=i+2
+					print(i)
+			
+			# Reset
+			nextline= False
+			
+		if ln.startswith("Objective"):
+			# Get the devices that are part of the resulting placement
+			devicesUsedInPlacement=[int(s) for s in re.findall(r'yg(\d+)\w\w=1', ln)]
+			print(devicesUsedInPlacement)
+			if (saveDevicePlacement):
+				devicesUsedInPlacementSaved=devicesUsedInPlacement
+			# Get to the nextline - where the alternative is written
+			nextline=True
+		if ln.startswith("The request is infeasible"):
+			# Get the devices that are part of the resulting placement - none in this case
+			devicesUsedInPlacement=[]
+			print(devicesUsedInPlacement)
+			if (saveDevicePlacement):
+				devicesUsedInPlacementSaved=devicesUsedInPlacement
+			# Get to the nextline - where the alternative is written
+			nextline=True
+		
+
+# close the file
+f.close()
\ No newline at end of file