set.seed(37);
simul = function(N=100, arrival_rate=.2, processing_rate=1, debug=FALSE) {
Arrival = cumsum(rexp(n=N, rate=arrival_rate));
Service = rexp(n=N, rate =processing_rate); # rep(N,x=1); rgamma(N, shape=.1,rate=.1)
Remaining = rep(N, x=NA);
Completion = rep(N, x=NA);
t = 0;
Working = 0;
CurrentTask = NA;
NextArrival = 1;
while (TRUE) {
if(debug) print(t)
if(debug) print(Arrival);
if(debug) print(Service);
if(debug) print(Remaining);
dtA = NA;
dtC = NA;
if(length(Arrival[Arrival>t])>0) {
NA
}
if(!is.na(CurrentTask)) {
NA
}
if(is.na(dtA) & is.na(dtC)) {
break;
}
dt = min(dtA,dtC,na.rm=T)
NA
# la date
t = t + dt;
NA
if((NextArrival <=N) & (Arrival[NextArrival] <= t)) { ## je met un <= et pas un == car 3-2.9!=0.1 ...
Remaining[NextArrival] = Service[NextArrival];
NextArrival = NextArrival + 1;
}
# le remaining
if(!is.na(CurrentTask)) {
Remaining[CurrentTask] = Remaining[CurrentTask] - dt ;
if(Remaining[CurrentTask] <= 0) {
Completion[CurrentTask] = t;
Remaining[CurrentTask] = NA;
}
CurrentTask = NA;
Working = Working + dt
}
# et currentTask (politique d'ordonnancement: FIFO)
WaitingList=(1:N)[!is.na(Remaining)];
if(length(WaitingList)>0) {
CurrentTask = head(WaitingList,n=1);
}
}
if(debug) print(Completion)
return(data.frame(
Arrival_rate=arrival_rate,
Processing_rate=processing_rate,
Arrival = Arrival,
Service = Service,
Completion = Completion,
Notworking = tail(Completion,1)-Working
))
}#Question1.Comparaisondelaperformancede S1 etde S2 NA
NA
#+begin_src R :results output :session *R* :exports both
dfs1 = data.frame()
for (r in seq(from=.1, to=.9, by=.1)) {
dfs1 = rbind(dfs1,simul(N=1000, arrival_rate=r, processing_rate=1, debug=FALSE));
}
#+end_src
#+begin_src R :results output :session *R* :exports both
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, uniondfs12 = dfs1 %>% group_by(Arrival_rate, Processing_rate) %>%
summarize(Response = mean(Completion - Arrival),
Response_se = sd(Completion - Arrival)/sqrt(n()))
#+end_src
dfs2 = data.frame()
for (r in seq(from=.1, to=.9, by=.1)) {
dfs2 = rbind(dfs2,simul(N=1000, arrival_rate=r, processing_rate=2, debug=FALSE));
}
#+end_src
#+begin_src R :results output :session *R* :exports both
dfs22 = dfs2 %>% group_by(Arrival_rate, Processing_rate) %>%
summarize(Response = mean(Completion - Arrival),
Response_se = sd(Completion - Arrival)/sqrt(n()))
#+end_src
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
library(ggplot2);
ggplot(data = dfs12, aes(x=Arrival_rate, y=Response)) + geom_line() +
geom_errorbar(data = dfs12, aes(ymin = Response - 2*Response_se,
ymax = Response + 2*Response_se)) +
geom_errorbar(data = dfs22, aes(ymin = Response - 2*Response_se,
ymax = Response + 2*Response_se))
#+end_srcNA
#+begin_src R :results output :session *R* :exports both
dfs1 = data.frame()
for (r in seq(from=.1, to=.9, by=.1)) {
dfs1 = rbind(dfs1,simul(N=1000, arrival_rate = r, processing_rate=1, debug=FALSE));
}
#+begin_src R :results output :session *R* :exports both
dfs12 = dfs1 %>% group_by(Arrival_rate, Processing_rate) %>%
summarize(Response = mean(Service+ Notworking * 0.5),
Response_se = sd(Service+Notworking * 0.5)/sqrt(n()))
#+end_src
dfs2 = data.frame()
for (r in seq(from=.1, to=.9, by=.1)) {
dfs2 = rbind(dfs2,simul(N=1000, arrival_rate=r, processing_rate=2, debug=FALSE));
}
#+end_src
#+begin_src R :results output :session *R* :exports both
dfs22 = dfs2 %>% group_by(Arrival_rate, Processing_rate) %>%
summarize(Response = mean(Service*4 + Notworking * 0.25),
Response_se = sd(Service*4+ Notworking * 0.25)/sqrt(n()))
#+begin_src R :results output graphics :file (org-babel-temp-file "figure" ".png") :exports both :width 600 :height 400 :session *R*
ggplot(dfs12, aes(x=Arrival_rate, y=Response)) + geom_line(data = dfs12) +
geom_errorbar(data = dfs12, aes(ymin = Response - 2*Response_se,
ymax = Response + 2*Response_se)) + geom_line(data = dfs22) +
geom_errorbar(data = dfs22, aes(ymin = Response - 2*Response_se,
ymax = Response + 2*Response_se))
#+end_srcNA
NA
NA NA
NA
simul2 = function(N=100, arrival_rate=0.2) {
Arrival = cumsum(rexp(n=N, rate=arrival_rate))
Service1 = rexp(n=N, rate =1)
Service2 = rexp(n=N, rate =2)
Remaining = rep(N, x=NA)
Completion = rep(N, x=NA)
t = 0
CurrentTask1 = NA
CurrentTask2= NA
NextArrival = 1
Temp1 = 0
Temp2 = 0
while (TRUE) {
dtA = NA
dtC = NA
if(length(Arrival[Arrival>t])>0) {
NA
}
if(!is.na(CurrentTask1) || (!is.na(CurrentTask2))) {
NA
}
if(is.na(dtA) & is.na(dtC)) {
break
}
dt = min(dtA,dtC,na.rm=T)
NA
# la date
t = t + dt
NA
if((NextArrival <=N) & (Arrival[NextArrival] <= t)) { ## je met un <= et pas un == car 3-2.9!=0.1 ...
NA
NextArrival = NextArrival + 1
}
# le remaining du serveur 1
if(!is.na(CurrentTask1)) {
Remaining[CurrentTask1] = Remaining[CurrentTask1] - dt
if(Remaining[CurrentTask1] <= 0) {
Completion[CurrentTask1] = t
Remaining[CurrentTask1] = NA
CurrentTask1=NA
}
Temp1 = Temp1 + dt
}
# le remaining du serveur 2
if(!is.na(CurrentTask2)) {
Remaining[CurrentTask2] = Remaining[CurrentTask2] - dt
if(Remaining[CurrentTask2] <= 0) {
Completion[CurrentTask2] = t
Remaining[CurrentTask2] = NA
CurrentTask2=NA
}
Temp2 = Temp2 + dt
}
# et currentTask (politique d'ordonnancement: FIFO), sur les deux serveurs
WaitingList=(1:N)[!is.na(Remaining)]
if(length(WaitingList)>0) {
if (is.na(CurrentTask1)) {
if(!is.na(CurrentTask2)) {
CurrentTask1 = WaitingList[2]
} else {
CurrentTask1 = head(WaitingList,n=1)
}
Remaining[CurrentTask1] = Service1[CurrentTask1]
}
if (is.na(CurrentTask2)) {
if(!is.na(CurrentTask1)){
CurrentTask2 = WaitingList[2]
} else {
CurrentTask2 = head(WaitingList,n=1)
}
Remaining[CurrentTask2] = Service2[CurrentTask2]
}
}
}
Energy = Temp1*1 + (tail(Completion,1)-Temp1)*.5 + Temp2*4 + (tail(Completion,1)-Temp2)*0.25
return(data.frame(
Arrival_rate=arrival_rate,
Arrival = Arrival,
Completion = Completion,
Energy = Energy
))
}
dfs3 = data.frame();
for (r in seq(from=.1, to=.9, by=.1)) {
dfs3 = rbind(dfs3,simul2(N=1000, arrival_rate=r));
}
#+end_src
#+begin_src R :results output :session *R* :exports both
dfs32 = dfs3 %>% group_by(Arrival_rate) %>%
summarize(Response = mean(Completion - Arrival),
Response_se = sd(Completion - Arrival)/sqrt(n()))
#+end_src
ggplot(data = dfs32, aes(x=Arrival_rate, y=Response)) + geom_line() +
geom_errorbar(aes(ymin = Response - 2*Response_se,
ymax = Response + 2*Response_se))
ggplot(dfs3, aes(x=Arrival_rate, y=Energy))+geom_line();
NA
NA
NA