Nothing
R/ETEall.R
In endtoend: Transmissions and Receptions in an End to End Network
globalVariables(c("..count..","..density..","ind", "values",
"Success Probability", "Expected Data Transmissions",
"Expected ACK Transmissions", "Expected Total Transmissions",
"Expected Data Receptions", "Expected ACK Receptions",
"Expected Total Receptions"))
####################################################################################
#THEORETICAL
####################################################################################
ETE <- function(p1,p2,L,N)
{
if(p1 >= 1 | p1 <= 0) stop("p1 must be a real number in (0,1)")
if(p2 >= 1 | p2 <= 0) stop("p2 must be a real number in (0,1)")
if(L != Inf && (L%%1!=0 | L<0)) stop("L must be a positive integer")
if(N%%1!=0 | N<1) stop("N must be a positive integer")
cat(" ","\n")
cat("###########################################","\n")
cat("END TO END - THEORETICAL RESULTS","\n")
cat("###########################################","\n")
cat(" ","\n")
cat(paste("Data success probability p1 = ",p1),"\n")
cat(paste("ACK success probability p2 = ",p2),"\n")
cat(paste("Maximum number of transmissions L = ",L),"\n")
cat(paste("Number of Hops N = ",N),"\n")
cat(" ","\n")
pp = p1*p2
if(L==Inf)
{
ETData = ((1 - p1^N)/(1-p1)) * ((1)/(p1*p2)^N)
ETACK = ((p1^N)*((1 - p2^N)/(1-p2))) * ((1)/(p1*p2)^N)
ETS = ETData + ETACK
# ETDataV = diff(c(0,((1 - p1^seq(1,N))/(1-p1)) * ((1)/(p1*p2)^seq(1,N))))
# ETACKV = diff(c(0,((p1^seq(1,N))*((1 - p2^seq(1,N))/(1-p2))) * ((1)/(p1*p2)^seq(1,N))))
# ETSV = ETDataT + ETACKT
REC_ETData = p1*((1 - p1^N)/(1-p1)) * ((1)/(p1*p2)^N)
REC_ETACK = p2 * ((p1^N)*((1 - p2^N)/(1-p2))) * ((1)/(p1*p2)^N)
REC_ETS = REC_ETData + REC_ETACK
# REC_ETDataV = diff(c(0,p1*((1 - p1^seq(1,N))/(1-p1)) * ((1)/(p1*p2)^seq(1,N))))
# REC_ETACKV = diff(c(0,p2 * ((p1^seq(1,N))*((1 - p2^seq(1,N))/(1-p2))) * ((1)/(p1*p2)^seq(1,N))))
# REC_ETSV = REC_ETDataV + REC_ETACKV
}else
{
if((p1*p2)<0.05)
{
ETData = L/(1-p1)
ETACK = 0
ETS = ETData + ETACK
REC_ETData = (p1*L)/(1-p1)
REC_ETACK = 0
REC_ETS = (p1*L)/(1-p1)
}else{
ETData = ((1 - p1^N)/(1-p1)) * ((1 - (1-(p1*p2)^N)^L)/(p1*p2)^N)
ETACK = ((p1^N)*((1 - p2^N)/(1-p2))) * ((1 - (1-(p1*p2)^N)^L)/(p1*p2)^N)
ETS = ETData + ETACK
# ETDataV = diff(c(0,((1 - p1^seq(1,N))/(1-p1)) * ((1 - (1-(p1*p2)^seq(1,N))^L)/(p1*p2)^seq(1,N))))
# ETACKV = diff(c(0,((p1^seq(1,N))*((1 - p2^seq(1,N))/(1-p2))) * ((1 - (1-(p1*p2)^seq(1,N))^L)/(p1*p2)^seq(1,N))))
# ETSV = ETDataT + ETACKT
REC_ETData = p1*((1 - p1^N)/(1-p1)) * ((1 - (1-(p1*p2)^N)^L)/(p1*p2)^N)
REC_ETACK = p2 * ((p1^N)*((1 - p2^N)/(1-p2))) * ((1 - (1-(p1*p2)^N)^L)/(p1*p2)^N)
REC_ETS = REC_ETData + REC_ETACK
# REC_ETDataV = diff(c(0,p1*((1 - p1^seq(1,N))/(1-p1)) * ((1 - (1-(p1*p2)^seq(1,N))^L)/(p1*p2)^seq(1,N))))
# REC_ETACKV = diff(c(0,p2 * ((p1^seq(1,N))*((1 - p2^seq(1,N))/(1-p2))) * ((1 - (1-(p1*p2)^seq(1,N))^L)/(p1*p2)^seq(1,N))))
# REC_ETSV = REC_ETDataV + REC_ETACKV
}
}
# Pr1 = 1-(1-p1)^L
PrS = 1-(1-p1^N)^L
# PrSV = 1-(1-p1^seq(1,N))^L
res = round(matrix(data = c(c(PrS),c(ETData),c(ETACK),c(ETS),c(REC_ETData),c(REC_ETACK),c(REC_ETS)),nrow = 7,ncol = 1,byrow = T),4)
rownames(res)=c("Success Probability",
"Expected Data Transmissions",
"Expected ACK Transmissions",
"Expected Total Transmissions",
"Expected Data Receptions",
"Expected ACK Receptions","Expected Total Receptions")
colnames(res)= c("Total")
return(res)
}
# ETE(p1 = 0.3,p2 = 0.4,L = Inf,N = 3)
# ETE(p1 = 0.3,p2 = 0.4,L = 4,N = 3)
####################################################################################
#MONTE CARLO
####################################################################################
MCETE = function(p1,p2,L,N,M=5000)
{
if(p1 >= 1 | p1 <= 0) stop("p1 must be a real number in (0,1)")
if(p2 >= 1 | p2 <= 0) stop("p2 must be a real number in (0,1)")
if(L != Inf && (L%%1!=0 | L<0)) stop("L must be a positive integer")
if(N%%1!=0 | N<1) stop("N must be a positive integer")
if(M%%1!=0 | M<1) stop("N must be a positive integer")
cat(" ","\n")
cat("###########################################","\n")
cat("END TO END - MONTE CARLO SIMULATION RESULTS","\n")
cat("###########################################","\n")
cat(" ","\n")
cat(paste("Data success probability p1 = ",p1),"\n")
cat(paste("ACK success probability p2 = ",p2),"\n")
cat(paste("Maximum number of transmissions L = ",L),"\n")
cat(paste("Number of Hops N = ",N),"\n")
cat(paste("Monte Carlo Simulations M = ",M),"\n")
cat(" ","\n")
prog2 = function(p1,p2,L,N)
{
pos = 1
trans = 0
ack = 0
maxpos = 1
ok = FALSE
okACK = FALSE
arr = 0
abj = 0
failUP = 0
failACK = 0
failT = 0
chegou = 0
#mientras hayan intentos y mientas no haya llegado
while(failT < L && okACK == FALSE)
{
#mientas np se llegue al final y hayan intentos
back = FALSE
while(pos<=N && failT < L)
{
maxpos = max(maxpos,pos)
u1 = runif(1)
trans = trans +1
if(u1<p1){arr = arr + 1;pos = pos + 1}else{pos = 1;failUP = failUP + 1;failT = failT + 1}
}
if(pos == N+1)
{
maxpos = N+1
posACK = pos
ok = TRUE
chegou=1
while(posACK >1 && back == FALSE)
{
u2 = runif(1)
ack = ack +1
if(u2<p2){abj = abj + 1;posACK = posACK - 1}else{back = TRUE;pos = 1;failACK = failACK + 1;failT = failT + 1}
if(posACK == 1){okACK = TRUE}
}
}
}
return(list(pos=pos,tDATA = trans,tACK = ack,
trans = trans+ack,RDATA = arr,
RACK = abj,Rtrans = arr+abj,ok=chegou))
cat(" ","\n")
}
resul = matrix(data = NA,nrow = M,ncol = 8)
pb <- txtProgressBar(min = 0, max = M, style = 3)
for(k in 1:M)
{
run = prog2(p1,p2,L,N)
resul[k,1]=run$pos
resul[k,2]=run$tDATA
resul[k,3]=run$tACK
resul[k,4]=run$trans
resul[k,5]=run$RDATA
resul[k,6]=run$RACK
resul[k,7]=run$Rtrans
resul[k,8]=run$ok
setTxtProgressBar(pb, k)
}
close(pb)
success = sum(resul[,8])/M
tarr = mean(resul[,2])
tabj = mean(resul[,3])
tt = tarr + tabj
rarr = mean(resul[,5])
rabj = mean(resul[,6])
rt = rarr + rabj
table = round(rbind(success,tarr,tabj,tt,rarr,rabj,rt),4)
rownames(table)=c("MC Success Probability","MC Mean Data Transmissions","MC Mean ACK Transmissions","MC Mean Total Transmissions","MC Mean Data Receptions","MC Mean ACK Receptions","MC Mean Total Receptions")
colnames(table)= c("Total")
return(table)
cat(" ","\n")
}
####################################################################################
#no output
####################################################################################
ETE0 = function (p1, p2, L, N){
pp = p1 * p2
if (L == Inf) {
ETData = ((1 - p1^N)/(1 - p1)) * ((1)/(p1 * p2)^N)
ETACK = ((p1^N) * ((1 - p2^N)/(1 - p2))) * ((1)/(p1 *
p2)^N)
ETS = ETData + ETACK
REC_ETData = p1 * ((1 - p1^N)/(1 - p1)) * ((1)/(p1 *
p2)^N)
REC_ETACK = p2 * ((p1^N) * ((1 - p2^N)/(1 - p2))) * ((1)/(p1 *
p2)^N)
REC_ETS = REC_ETData + REC_ETACK
}else {
if ((p1 * p2) < 0.05) {
ETData = L/(1 - p1)
ETACK = 0
ETS = ETData + ETACK
REC_ETData = (p1 * L)/(1 - p1)
REC_ETACK = 0
REC_ETS = (p1 * L)/(1 - p1)
}else {
ETData = ((1 - p1^N)/(1 - p1)) * ((1 - (1 - (p1 *
p2)^N)^L)/(p1 * p2)^N)
ETACK = ((p1^N) * ((1 - p2^N)/(1 - p2))) * ((1 -
(1 - (p1 * p2)^N)^L)/(p1 * p2)^N)
ETS = ETData + ETACK
REC_ETData = p1 * ((1 - p1^N)/(1 - p1)) * ((1 - (1 -
(p1 * p2)^N)^L)/(p1 * p2)^N)
REC_ETACK = p2 * ((p1^N) * ((1 - p2^N)/(1 - p2))) *
((1 - (1 - (p1 * p2)^N)^L)/(p1 * p2)^N)
REC_ETS = REC_ETData + REC_ETACK
}
}
PrS = 1 - (1 - p1^N)^L
res = round(matrix(data = c(c(PrS), c(ETData), c(ETACK),
c(ETS), c(REC_ETData), c(REC_ETACK), c(REC_ETS)), nrow = 7,
ncol = 1, byrow = T), 4)
# rownames(res) = c("Success Probability", "Expected Data Transmissions",
# "Expected ACK Transmissions", "Expected Total Transmissions",
# "Expected Data Receptions", "Expected ACK Receptions",
# "Expected Total Receptions")
# colnames(res) = c("Total")
return(res)
}
stochastic_ETE = function(dist1,p11,p12,dist2,p21,p22,L,N,M=10^5,printout=TRUE,plotspdf=TRUE){
if(L != Inf && (L%%1!=0 | L<0)) stop("L must be a positive integer")
if(N%%1!=0 | N<1) stop("N must be a positive integer")
if(dist1 == "uniform"){
p1 = runif(M,p11,p12)
}else{
if(dist1 == "beta"){
p1 = rbeta(M,p11,p12)
}else{
stop("p1 distribution must be either 'uniform' or 'beta'.")
}
}
if(dist2 == "uniform"){
p2 = runif(M,p21,p22)
}else{
if(dist2 == "beta"){
p2 = rbeta(M,p21,p22)
}else{
stop("p1 distribution must be either 'uniform' or 'beta'.")
}
}
out = apply(X = cbind(p1,p2),MARGIN = 1, function(x) ETE0(x[1], x[2], L, N))
outsum = matrix(apply(out,1,mean),7,1)
rownames(outsum) = c("Success Probability", "Expected Data Transmissions",
"Expected ACK Transmissions", "Expected Total Transmissions",
"Expected Data Receptions", "Expected ACK Receptions",
"Expected Total Receptions")
colnames(outsum) = c("Total")
df = data.frame(p1,p2,t(out))
colnames(df) = c("p1","p2",rownames(outsum))
#print(summary(df))
#install.packages("pastecs")
#library(pastecs)
stats = as.data.frame(t(stat.desc(df))[,-c(1:3)])
p1 = ggplot(df,aes(p1)) +
geom_histogram(aes(y=..density.., fill = "p1"),alpha = 0.4,color="gray40",breaks = seq(min(p1),max(p1),length.out = round(diff(range(p1))/0.0625)+1)) +
geom_histogram(aes(x = p2, y = ..density..,fill = "p2"),alpha = 0.4,color="gray40",breaks = seq(min(p2),max(p2),length.out = round(diff(range(p2))/0.0625)+1))+
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
labs(fill = "")+
xlab("probability") +
ylab("density") +
ggtitle("Data and ACK Success Probabilities") +
xlim(0,1) +
theme_classic()
p2 = ggplot(df,aes(x=`Success Probability`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 1,
breaks = seq(min(df$`Success Probability`),max(df$`Success Probability`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank())+
geom_vline(xintercept = outsum[1],color="gray40",lwd=1.2) +
ggtitle(paste("Success Probability (mean = ",round(outsum[1],3),")",sep = "")) +
ylab("relative frequency")+ theme_classic()
p3 = ggplot(df,aes(x=`Expected Data Transmissions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 2,
breaks = seq(min(df$`Expected Data Transmissions`),max(df$`Expected Data Transmissions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[2],color="gray40",lwd=1.2) +
ggtitle(paste("Expected Data Transmissions (mean = ",round(outsum[2],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
p4 = ggplot(df,aes(x=`Expected ACK Transmissions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 3,
breaks = seq(min(df$`Expected ACK Transmissions`),max(df$`Expected ACK Transmissions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[3],color="gray40",lwd=1.2) +
ggtitle(paste("Expected ACK Transmissions (mean = ",round(outsum[3],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
p5 = ggplot(df,aes(x=`Expected Total Transmissions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 4,
breaks = seq(min(df$`Expected Total Transmissions`),max(df$`Expected Total Transmissions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[4],color="gray40",lwd=1.2) +
ggtitle(paste("Expected Total Transmissions (mean = ",round(outsum[4],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
p6 = ggplot(df,aes(x=`Expected Data Receptions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 5,
breaks = seq(min(df$`Expected Data Receptions`),max(df$`Expected Data Receptions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[5],color="gray40",lwd=1.2) +
ggtitle(paste("Expected Data Receptions (mean = ",round(outsum[5],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
p7 = ggplot(df,aes(x=`Expected ACK Receptions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 6,
breaks = seq(min(df$`Expected ACK Receptions`),max(df$`Expected ACK Receptions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[6],color="gray40",lwd=1.2) +
ggtitle(paste("Expected ACK Receptions (mean = ",round(outsum[6],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
p8 = ggplot(df,aes(x=`Expected Total Receptions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 7,
breaks = seq(min(df$`Expected Total Receptions`),max(df$`Expected Total Receptions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[7],color="gray40",lwd=1.2) +
ggtitle(paste("Expected Total Receptions (mean = ",round(outsum[7],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
df2 = stack(df[,c(4:9)])
p9 = ggplot(df2, aes(x = ind, y = values)) +
geom_boxplot(fill = rev(2:7),alpha = 0.2,color="gray40") +
coord_flip() +
#scale_y_continuous(trans='sqrt') +
xlab("") +
scale_x_discrete(limits = rev(levels(df2$ind))) +
theme_classic()
if(isTRUE(printout)){
cat(paste("Monte Carlo simulations M = ", M), "\n")
cat(paste("Maximum number of transmissions L = ", L), "\n")
cat(paste("Number of Hops N = ", N), "\n")
print(stats)
print(p1)
print(p2)
print(p3)
print(p4)
print(p5)
print(p6)
print(p7)
print(p8)
print(p9)
}
if(isTRUE(plotspdf)){
plotsPath = paste("ETE",format(Sys.time(),"%d%m%y_%H%M%S"),".pdf",sep="")
pdf(file=plotsPath,width = 8.27,height = 5.83)
print(p1)
print(p2)
print(p3)
print(p4)
print(p5)
print(p6)
print(p7)
print(p8)
print(p9)
dev.off()
print(paste("Plots file ",plotsPath," saved in working directory ",getwd(),".",sep = ""))
}
return(list(data=df,stats = stats))
}
#RUN
#Theoretical
# ETE(p1=0.10,p2=0.10,L=17,N=10)
# #MonteCarlo Simulations
# MCETE(p1=0.10,p2=0.10,L=17,N=10,M=5000)
# 1-(0.15^2)^10
# 17/(1-0.15)
# N=10
# pseq = seq(from = 0.1,to = 0.9,by = 0.1)
# Lseq = c(27,13,8,6,5,4,3,2,2)
#
# SIM = matrix(data = NA,nrow = 9,ncol = 13,byrow = TRUE)
#
# for(i in 1:9)
# {
# p1 = p2 = pseq[i]
# L = Lseq[i]
# SIM[i,] = c(ETE(p1=p1,p2=p2,L=L,N=10),MCETE(p1=p1,p2=p2,L,N=10,M=10^6)[2:7])
# }
#
# SIM[,2:7]-SIM[,8:13]
#
# TABLE = cbind(pseq,Lseq,SIM)
# library(xtable)
# xtable(TABLE)
# N=5
# pseq = seq(from = 0.1,to = 0.9,by = 0.1)
# Lseq = c(27,13,8,6,5,4,3,2,2)
#
# SIM2 = matrix(data = NA,nrow = 9,ncol = 13,byrow = TRUE)
#
# for(i in 1:9)
# {
# p1 = p2 = pseq[i]
# L = Lseq[i]
# SIM2[i,] = c(ETE(p1=p1,p2=p2,L=L,N=5),MCETE(p1=p1,p2=p2,L,N=5,M=10^6)[2:7])
# }
#
# SIM2[,2:7]-SIM2[,8:13]
#
# TABLE2 = cbind(pseq,Lseq,SIM2)
# library(xtable)
# xtable(TABLE2)
#
#
#
#
# N=7
# pseq = seq(from = 0.1,to = 0.9,by = 0.1)
# Lseq = c(27,13,8,6,5,4,3,2,2)
#
# SIM3 = matrix(data = NA,nrow = 9,ncol = 13,byrow = TRUE)
#
# for(i in 1:9)
# {
# p1 = p2 = pseq[i]
# L = Lseq[i]
# SIM3[i,] = c(ETE(p1=p1,p2=p2,L=L,N=7),MCETE(p1=p1,p2=p2,L,N=7,M=10^6)[2:7])
# }
#
# SIM3[,2:7]-SIM3[,8:13]
#
# TABLE3 = cbind(pseq,Lseq,SIM3)
# library(xtable)
# xtable(TABLE3)
# N=7
# pseq = seq(from = 0.1,to = 0.9,by = 0.1)
# Lseq = c(27,13,8,6,5,4,3,2,2)
#
# SIM4 = matrix(data = NA,nrow = 9,ncol = 13,byrow = TRUE)
#
# for(i in 1:9)
# {
# p1 = p2 = pseq[i]
# L = Lseq[i]
# SIM4[i,] = c(ETE(p1=p1,p2=p2,L=L,N=7),MCETE(p1=p1,p2=p2,L,N=7,M=10^6)[2:7])
# }
# SIM4[,1]
#
# ERROR4 = (abs(SIM4[,2:7]-SIM4[,8:13]))
#
#
# boxplot(abs(SIM4[,2:7]-SIM4[,8:13]))
#
#
# TABLE4 = cbind(pseq,Lseq,SIM4)
# library(xtable)
# xtable(TABLE4,digits = 4)
#
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globalVariables(c("..count..","..density..","ind", "values",
"Success Probability", "Expected Data Transmissions",
"Expected ACK Transmissions", "Expected Total Transmissions",
"Expected Data Receptions", "Expected ACK Receptions",
"Expected Total Receptions"))
####################################################################################
#THEORETICAL
####################################################################################
ETE <- function(p1,p2,L,N)
{
if(p1 >= 1 | p1 <= 0) stop("p1 must be a real number in (0,1)")
if(p2 >= 1 | p2 <= 0) stop("p2 must be a real number in (0,1)")
if(L != Inf && (L%%1!=0 | L<0)) stop("L must be a positive integer")
if(N%%1!=0 | N<1) stop("N must be a positive integer")
cat(" ","\n")
cat("###########################################","\n")
cat("END TO END - THEORETICAL RESULTS","\n")
cat("###########################################","\n")
cat(" ","\n")
cat(paste("Data success probability p1 = ",p1),"\n")
cat(paste("ACK success probability p2 = ",p2),"\n")
cat(paste("Maximum number of transmissions L = ",L),"\n")
cat(paste("Number of Hops N = ",N),"\n")
cat(" ","\n")
pp = p1*p2
if(L==Inf)
{
ETData = ((1 - p1^N)/(1-p1)) * ((1)/(p1*p2)^N)
ETACK = ((p1^N)*((1 - p2^N)/(1-p2))) * ((1)/(p1*p2)^N)
ETS = ETData + ETACK
# ETDataV = diff(c(0,((1 - p1^seq(1,N))/(1-p1)) * ((1)/(p1*p2)^seq(1,N))))
# ETACKV = diff(c(0,((p1^seq(1,N))*((1 - p2^seq(1,N))/(1-p2))) * ((1)/(p1*p2)^seq(1,N))))
# ETSV = ETDataT + ETACKT
REC_ETData = p1*((1 - p1^N)/(1-p1)) * ((1)/(p1*p2)^N)
REC_ETACK = p2 * ((p1^N)*((1 - p2^N)/(1-p2))) * ((1)/(p1*p2)^N)
REC_ETS = REC_ETData + REC_ETACK
# REC_ETDataV = diff(c(0,p1*((1 - p1^seq(1,N))/(1-p1)) * ((1)/(p1*p2)^seq(1,N))))
# REC_ETACKV = diff(c(0,p2 * ((p1^seq(1,N))*((1 - p2^seq(1,N))/(1-p2))) * ((1)/(p1*p2)^seq(1,N))))
# REC_ETSV = REC_ETDataV + REC_ETACKV
}else
{
if((p1*p2)<0.05)
{
ETData = L/(1-p1)
ETACK = 0
ETS = ETData + ETACK
REC_ETData = (p1*L)/(1-p1)
REC_ETACK = 0
REC_ETS = (p1*L)/(1-p1)
}else{
ETData = ((1 - p1^N)/(1-p1)) * ((1 - (1-(p1*p2)^N)^L)/(p1*p2)^N)
ETACK = ((p1^N)*((1 - p2^N)/(1-p2))) * ((1 - (1-(p1*p2)^N)^L)/(p1*p2)^N)
ETS = ETData + ETACK
# ETDataV = diff(c(0,((1 - p1^seq(1,N))/(1-p1)) * ((1 - (1-(p1*p2)^seq(1,N))^L)/(p1*p2)^seq(1,N))))
# ETACKV = diff(c(0,((p1^seq(1,N))*((1 - p2^seq(1,N))/(1-p2))) * ((1 - (1-(p1*p2)^seq(1,N))^L)/(p1*p2)^seq(1,N))))
# ETSV = ETDataT + ETACKT
REC_ETData = p1*((1 - p1^N)/(1-p1)) * ((1 - (1-(p1*p2)^N)^L)/(p1*p2)^N)
REC_ETACK = p2 * ((p1^N)*((1 - p2^N)/(1-p2))) * ((1 - (1-(p1*p2)^N)^L)/(p1*p2)^N)
REC_ETS = REC_ETData + REC_ETACK
# REC_ETDataV = diff(c(0,p1*((1 - p1^seq(1,N))/(1-p1)) * ((1 - (1-(p1*p2)^seq(1,N))^L)/(p1*p2)^seq(1,N))))
# REC_ETACKV = diff(c(0,p2 * ((p1^seq(1,N))*((1 - p2^seq(1,N))/(1-p2))) * ((1 - (1-(p1*p2)^seq(1,N))^L)/(p1*p2)^seq(1,N))))
# REC_ETSV = REC_ETDataV + REC_ETACKV
}
}
# Pr1 = 1-(1-p1)^L
PrS = 1-(1-p1^N)^L
# PrSV = 1-(1-p1^seq(1,N))^L
res = round(matrix(data = c(c(PrS),c(ETData),c(ETACK),c(ETS),c(REC_ETData),c(REC_ETACK),c(REC_ETS)),nrow = 7,ncol = 1,byrow = T),4)
rownames(res)=c("Success Probability",
"Expected Data Transmissions",
"Expected ACK Transmissions",
"Expected Total Transmissions",
"Expected Data Receptions",
"Expected ACK Receptions","Expected Total Receptions")
colnames(res)= c("Total")
return(res)
}
# ETE(p1 = 0.3,p2 = 0.4,L = Inf,N = 3)
# ETE(p1 = 0.3,p2 = 0.4,L = 4,N = 3)
####################################################################################
#MONTE CARLO
####################################################################################
MCETE = function(p1,p2,L,N,M=5000)
{
if(p1 >= 1 | p1 <= 0) stop("p1 must be a real number in (0,1)")
if(p2 >= 1 | p2 <= 0) stop("p2 must be a real number in (0,1)")
if(L != Inf && (L%%1!=0 | L<0)) stop("L must be a positive integer")
if(N%%1!=0 | N<1) stop("N must be a positive integer")
if(M%%1!=0 | M<1) stop("N must be a positive integer")
cat(" ","\n")
cat("###########################################","\n")
cat("END TO END - MONTE CARLO SIMULATION RESULTS","\n")
cat("###########################################","\n")
cat(" ","\n")
cat(paste("Data success probability p1 = ",p1),"\n")
cat(paste("ACK success probability p2 = ",p2),"\n")
cat(paste("Maximum number of transmissions L = ",L),"\n")
cat(paste("Number of Hops N = ",N),"\n")
cat(paste("Monte Carlo Simulations M = ",M),"\n")
cat(" ","\n")
prog2 = function(p1,p2,L,N)
{
pos = 1
trans = 0
ack = 0
maxpos = 1
ok = FALSE
okACK = FALSE
arr = 0
abj = 0
failUP = 0
failACK = 0
failT = 0
chegou = 0
#mientras hayan intentos y mientas no haya llegado
while(failT < L && okACK == FALSE)
{
#mientas np se llegue al final y hayan intentos
back = FALSE
while(pos<=N && failT < L)
{
maxpos = max(maxpos,pos)
u1 = runif(1)
trans = trans +1
if(u1<p1){arr = arr + 1;pos = pos + 1}else{pos = 1;failUP = failUP + 1;failT = failT + 1}
}
if(pos == N+1)
{
maxpos = N+1
posACK = pos
ok = TRUE
chegou=1
while(posACK >1 && back == FALSE)
{
u2 = runif(1)
ack = ack +1
if(u2<p2){abj = abj + 1;posACK = posACK - 1}else{back = TRUE;pos = 1;failACK = failACK + 1;failT = failT + 1}
if(posACK == 1){okACK = TRUE}
}
}
}
return(list(pos=pos,tDATA = trans,tACK = ack,
trans = trans+ack,RDATA = arr,
RACK = abj,Rtrans = arr+abj,ok=chegou))
cat(" ","\n")
}
resul = matrix(data = NA,nrow = M,ncol = 8)
pb <- txtProgressBar(min = 0, max = M, style = 3)
for(k in 1:M)
{
run = prog2(p1,p2,L,N)
resul[k,1]=run$pos
resul[k,2]=run$tDATA
resul[k,3]=run$tACK
resul[k,4]=run$trans
resul[k,5]=run$RDATA
resul[k,6]=run$RACK
resul[k,7]=run$Rtrans
resul[k,8]=run$ok
setTxtProgressBar(pb, k)
}
close(pb)
success = sum(resul[,8])/M
tarr = mean(resul[,2])
tabj = mean(resul[,3])
tt = tarr + tabj
rarr = mean(resul[,5])
rabj = mean(resul[,6])
rt = rarr + rabj
table = round(rbind(success,tarr,tabj,tt,rarr,rabj,rt),4)
rownames(table)=c("MC Success Probability","MC Mean Data Transmissions","MC Mean ACK Transmissions","MC Mean Total Transmissions","MC Mean Data Receptions","MC Mean ACK Receptions","MC Mean Total Receptions")
colnames(table)= c("Total")
return(table)
cat(" ","\n")
}
####################################################################################
#no output
####################################################################################
ETE0 = function (p1, p2, L, N){
pp = p1 * p2
if (L == Inf) {
ETData = ((1 - p1^N)/(1 - p1)) * ((1)/(p1 * p2)^N)
ETACK = ((p1^N) * ((1 - p2^N)/(1 - p2))) * ((1)/(p1 *
p2)^N)
ETS = ETData + ETACK
REC_ETData = p1 * ((1 - p1^N)/(1 - p1)) * ((1)/(p1 *
p2)^N)
REC_ETACK = p2 * ((p1^N) * ((1 - p2^N)/(1 - p2))) * ((1)/(p1 *
p2)^N)
REC_ETS = REC_ETData + REC_ETACK
}else {
if ((p1 * p2) < 0.05) {
ETData = L/(1 - p1)
ETACK = 0
ETS = ETData + ETACK
REC_ETData = (p1 * L)/(1 - p1)
REC_ETACK = 0
REC_ETS = (p1 * L)/(1 - p1)
}else {
ETData = ((1 - p1^N)/(1 - p1)) * ((1 - (1 - (p1 *
p2)^N)^L)/(p1 * p2)^N)
ETACK = ((p1^N) * ((1 - p2^N)/(1 - p2))) * ((1 -
(1 - (p1 * p2)^N)^L)/(p1 * p2)^N)
ETS = ETData + ETACK
REC_ETData = p1 * ((1 - p1^N)/(1 - p1)) * ((1 - (1 -
(p1 * p2)^N)^L)/(p1 * p2)^N)
REC_ETACK = p2 * ((p1^N) * ((1 - p2^N)/(1 - p2))) *
((1 - (1 - (p1 * p2)^N)^L)/(p1 * p2)^N)
REC_ETS = REC_ETData + REC_ETACK
}
}
PrS = 1 - (1 - p1^N)^L
res = round(matrix(data = c(c(PrS), c(ETData), c(ETACK),
c(ETS), c(REC_ETData), c(REC_ETACK), c(REC_ETS)), nrow = 7,
ncol = 1, byrow = T), 4)
# rownames(res) = c("Success Probability", "Expected Data Transmissions",
# "Expected ACK Transmissions", "Expected Total Transmissions",
# "Expected Data Receptions", "Expected ACK Receptions",
# "Expected Total Receptions")
# colnames(res) = c("Total")
return(res)
}
stochastic_ETE = function(dist1,p11,p12,dist2,p21,p22,L,N,M=10^5,printout=TRUE,plotspdf=TRUE){
if(L != Inf && (L%%1!=0 | L<0)) stop("L must be a positive integer")
if(N%%1!=0 | N<1) stop("N must be a positive integer")
if(dist1 == "uniform"){
p1 = runif(M,p11,p12)
}else{
if(dist1 == "beta"){
p1 = rbeta(M,p11,p12)
}else{
stop("p1 distribution must be either 'uniform' or 'beta'.")
}
}
if(dist2 == "uniform"){
p2 = runif(M,p21,p22)
}else{
if(dist2 == "beta"){
p2 = rbeta(M,p21,p22)
}else{
stop("p1 distribution must be either 'uniform' or 'beta'.")
}
}
out = apply(X = cbind(p1,p2),MARGIN = 1, function(x) ETE0(x[1], x[2], L, N))
outsum = matrix(apply(out,1,mean),7,1)
rownames(outsum) = c("Success Probability", "Expected Data Transmissions",
"Expected ACK Transmissions", "Expected Total Transmissions",
"Expected Data Receptions", "Expected ACK Receptions",
"Expected Total Receptions")
colnames(outsum) = c("Total")
df = data.frame(p1,p2,t(out))
colnames(df) = c("p1","p2",rownames(outsum))
#print(summary(df))
#install.packages("pastecs")
#library(pastecs)
stats = as.data.frame(t(stat.desc(df))[,-c(1:3)])
p1 = ggplot(df,aes(p1)) +
geom_histogram(aes(y=..density.., fill = "p1"),alpha = 0.4,color="gray40",breaks = seq(min(p1),max(p1),length.out = round(diff(range(p1))/0.0625)+1)) +
geom_histogram(aes(x = p2, y = ..density..,fill = "p2"),alpha = 0.4,color="gray40",breaks = seq(min(p2),max(p2),length.out = round(diff(range(p2))/0.0625)+1))+
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
labs(fill = "")+
xlab("probability") +
ylab("density") +
ggtitle("Data and ACK Success Probabilities") +
xlim(0,1) +
theme_classic()
p2 = ggplot(df,aes(x=`Success Probability`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 1,
breaks = seq(min(df$`Success Probability`),max(df$`Success Probability`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank())+
geom_vline(xintercept = outsum[1],color="gray40",lwd=1.2) +
ggtitle(paste("Success Probability (mean = ",round(outsum[1],3),")",sep = "")) +
ylab("relative frequency")+ theme_classic()
p3 = ggplot(df,aes(x=`Expected Data Transmissions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 2,
breaks = seq(min(df$`Expected Data Transmissions`),max(df$`Expected Data Transmissions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[2],color="gray40",lwd=1.2) +
ggtitle(paste("Expected Data Transmissions (mean = ",round(outsum[2],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
p4 = ggplot(df,aes(x=`Expected ACK Transmissions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 3,
breaks = seq(min(df$`Expected ACK Transmissions`),max(df$`Expected ACK Transmissions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[3],color="gray40",lwd=1.2) +
ggtitle(paste("Expected ACK Transmissions (mean = ",round(outsum[3],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
p5 = ggplot(df,aes(x=`Expected Total Transmissions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 4,
breaks = seq(min(df$`Expected Total Transmissions`),max(df$`Expected Total Transmissions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[4],color="gray40",lwd=1.2) +
ggtitle(paste("Expected Total Transmissions (mean = ",round(outsum[4],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
p6 = ggplot(df,aes(x=`Expected Data Receptions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 5,
breaks = seq(min(df$`Expected Data Receptions`),max(df$`Expected Data Receptions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[5],color="gray40",lwd=1.2) +
ggtitle(paste("Expected Data Receptions (mean = ",round(outsum[5],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
p7 = ggplot(df,aes(x=`Expected ACK Receptions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 6,
breaks = seq(min(df$`Expected ACK Receptions`),max(df$`Expected ACK Receptions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[6],color="gray40",lwd=1.2) +
ggtitle(paste("Expected ACK Receptions (mean = ",round(outsum[6],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
p8 = ggplot(df,aes(x=`Expected Total Receptions`)) +
geom_histogram(aes(y = (..count..)/sum(..count..)),alpha = 0.2,color="gray40",fill = 7,
breaks = seq(min(df$`Expected Total Receptions`),max(df$`Expected Total Receptions`),length.out = 17)) +
theme(axis.title.x=element_blank(),
axis.ticks.x=element_blank()) +
geom_vline(xintercept = outsum[7],color="gray40",lwd=1.2) +
ggtitle(paste("Expected Total Receptions (mean = ",round(outsum[7],3),")",sep = "")) +
ylab("relative frequency") +
theme_classic()
df2 = stack(df[,c(4:9)])
p9 = ggplot(df2, aes(x = ind, y = values)) +
geom_boxplot(fill = rev(2:7),alpha = 0.2,color="gray40") +
coord_flip() +
#scale_y_continuous(trans='sqrt') +
xlab("") +
scale_x_discrete(limits = rev(levels(df2$ind))) +
theme_classic()
if(isTRUE(printout)){
cat(paste("Monte Carlo simulations M = ", M), "\n")
cat(paste("Maximum number of transmissions L = ", L), "\n")
cat(paste("Number of Hops N = ", N), "\n")
print(stats)
print(p1)
print(p2)
print(p3)
print(p4)
print(p5)
print(p6)
print(p7)
print(p8)
print(p9)
}
if(isTRUE(plotspdf)){
plotsPath = paste("ETE",format(Sys.time(),"%d%m%y_%H%M%S"),".pdf",sep="")
pdf(file=plotsPath,width = 8.27,height = 5.83)
print(p1)
print(p2)
print(p3)
print(p4)
print(p5)
print(p6)
print(p7)
print(p8)
print(p9)
dev.off()
print(paste("Plots file ",plotsPath," saved in working directory ",getwd(),".",sep = ""))
}
return(list(data=df,stats = stats))
}
#RUN
#Theoretical
# ETE(p1=0.10,p2=0.10,L=17,N=10)
# #MonteCarlo Simulations
# MCETE(p1=0.10,p2=0.10,L=17,N=10,M=5000)
# 1-(0.15^2)^10
# 17/(1-0.15)
# N=10
# pseq = seq(from = 0.1,to = 0.9,by = 0.1)
# Lseq = c(27,13,8,6,5,4,3,2,2)
#
# SIM = matrix(data = NA,nrow = 9,ncol = 13,byrow = TRUE)
#
# for(i in 1:9)
# {
# p1 = p2 = pseq[i]
# L = Lseq[i]
# SIM[i,] = c(ETE(p1=p1,p2=p2,L=L,N=10),MCETE(p1=p1,p2=p2,L,N=10,M=10^6)[2:7])
# }
#
# SIM[,2:7]-SIM[,8:13]
#
# TABLE = cbind(pseq,Lseq,SIM)
# library(xtable)
# xtable(TABLE)
# N=5
# pseq = seq(from = 0.1,to = 0.9,by = 0.1)
# Lseq = c(27,13,8,6,5,4,3,2,2)
#
# SIM2 = matrix(data = NA,nrow = 9,ncol = 13,byrow = TRUE)
#
# for(i in 1:9)
# {
# p1 = p2 = pseq[i]
# L = Lseq[i]
# SIM2[i,] = c(ETE(p1=p1,p2=p2,L=L,N=5),MCETE(p1=p1,p2=p2,L,N=5,M=10^6)[2:7])
# }
#
# SIM2[,2:7]-SIM2[,8:13]
#
# TABLE2 = cbind(pseq,Lseq,SIM2)
# library(xtable)
# xtable(TABLE2)
#
#
#
#
# N=7
# pseq = seq(from = 0.1,to = 0.9,by = 0.1)
# Lseq = c(27,13,8,6,5,4,3,2,2)
#
# SIM3 = matrix(data = NA,nrow = 9,ncol = 13,byrow = TRUE)
#
# for(i in 1:9)
# {
# p1 = p2 = pseq[i]
# L = Lseq[i]
# SIM3[i,] = c(ETE(p1=p1,p2=p2,L=L,N=7),MCETE(p1=p1,p2=p2,L,N=7,M=10^6)[2:7])
# }
#
# SIM3[,2:7]-SIM3[,8:13]
#
# TABLE3 = cbind(pseq,Lseq,SIM3)
# library(xtable)
# xtable(TABLE3)
# N=7
# pseq = seq(from = 0.1,to = 0.9,by = 0.1)
# Lseq = c(27,13,8,6,5,4,3,2,2)
#
# SIM4 = matrix(data = NA,nrow = 9,ncol = 13,byrow = TRUE)
#
# for(i in 1:9)
# {
# p1 = p2 = pseq[i]
# L = Lseq[i]
# SIM4[i,] = c(ETE(p1=p1,p2=p2,L=L,N=7),MCETE(p1=p1,p2=p2,L,N=7,M=10^6)[2:7])
# }
# SIM4[,1]
#
# ERROR4 = (abs(SIM4[,2:7]-SIM4[,8:13]))
#
#
# boxplot(abs(SIM4[,2:7]-SIM4[,8:13]))
#
#
# TABLE4 = cbind(pseq,Lseq,SIM4)
# library(xtable)
# xtable(TABLE4,digits = 4)
#
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