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sim.r
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sim.r
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serverSim <- function(duration, ns, lambda, mu, fP, nP, simType, showResults = FALSE){
# duration: Duration of the simulation
# lambda: Queries arrival rate
# mu: Queries service/departure rate
# fP: Fast queries queue proportion
# nP: Normal queries queue proportion
# nS: Number of servers
# simType : End of simulation return setting (busy time or lost queries)
# proportion of slow queries is 1 - (fP + nP)
# DEBUG
debug <- FALSE
# time vars
endTime = duration # duration of simulation
currentTime <- 0 # simulation time
# simulation parameters
# we will be using an exponential distribution for incoming and departing queries
queue <- 0 # query queue
fQ <- 0 # fast queue
nQ <- 0 # normal queue
sQ <- 0 # slow queue
N <- 150 # total query queue(s) capacity
nextArrival <- 0 # time for the next query arrival (reception)
nextDeparture <- endTime # time for the next query departure (service)
totalArrivals <- 0 # total number of received queries
totalFA <- 0 # total number of fast received queries
totalNA <- 0 # total number of normal received queries
totalSA <- 0 # total number of slow received queries
totalDepartures <- 0 # total number of serviced queries
totalFD <- 0 # total number of fast serviced queries
totalND <- 0 # total number of normal serviced queries
totalSD <- 0 # total number of slow serviced queries
busyTime <- 0 # total time servicing queries
timeStep <- 1
timeState <- 0
mQState <- 0
fQState <- 0
nQState <- 0
sQState <- 0
if(nS < 1){
return(cat("Le nombre de serveur ne peut pas être nul.\n"))
}
while (currentTime < endTime){
# Query arrival
if (nextArrival < nextDeparture || queue == 0){
if (debug){
print("[DEBUG] NEW QUERY ADDED [DEBUG]")
}
# Determining query type using proportions
queryType = runif(1)
if (queryType < fP){
fQ = fQ + 1
totalFA = totalFA + 1
} else if (queryType < fP + nP){
nQ = nQ + 1
totalNA = totalNA + 1
} else {
sQ = sQ + 1
totalSA = totalSA + 1
}
# Adding a new query, regardless of its type, and calculating its arrival time
queue = fQ + nQ + sQ
totalArrivals = totalArrivals + 1
currentTime = nextArrival
# Predermining the next query's arrival time
nextArrival = currentTime + rexp(1, lambda)
if (queue == 1){
# Only query in queue is directly serviced
if (debug){
print("[DEBUG] SERVICING ONLY QUERY IN QUEUE [DEBUG]")
}
nextDeparture = currentTime + rexp(1, mu)
lastBusyTime = currentTime
}
} else {
# Queue departure
# As long as there are more prioritised queries, those will be serviced before moving to the slow queue
servicedQueries = 1
while (servicedQueries <= nS && queue > 0){
# Servicing queries as long as there are any in queue and as many as the servers can handle (number of servers)
if (fQ > 0){
fQ = fQ - 1
} else if (nQ > 0){
nQ = nQ - 1
} else {
sQ = sQ - 1
}
queue = fQ + nQ + sQ
currentTime = nextDeparture
totalDepartures = totalDepartures + 1
servicedQueries = servicedQueries + 1
}
if (queue > 0 || servicedQueries > 0){
if (debug){
print("[DEBUG] SERVICING QUERY [DEBUG]")
}
while (servicedQueries > 0 && queue > 0){
furthestDeparture = currentTime + rexp(1, mu)
if (furthestDeparture > nextDeparture){
nextDeparture = furthestDeparture
}
servicedQueries = servicedQueries - 1
}
}
}
if (queue == 0) {
# Queue is empty, no more queries to service, next service time is moved to the end of the simulation
nextDeparture = endTime
busyTime = busyTime + currentTime - lastBusyTime
}
if(debug){
cat("busyTime : ", busyTime, "\n")
cat("lastBusyTime: ", lastBusyTime, "\n")
cat("Queue status: ", queue, "\n")
}
if(simType == "queue") { # Si on veut plotter
timeState[timeStep] = currentTime
mQState[timeStep] = queue # On combine les vecteurs (total)
fQState[timeStep] = fQ
nQState[timeStep] = nQ
sQState[timeStep] = sQ
timeStep = timeStep + 1
}
}
busyTime = busyTime + currentTime - lastBusyTime
if (nextDeparture>endTime){
if (debug){
print("[DEBUG] SERVICE TIME IS BEYOND THE END [DEBUG]")
}
totalDepartures = totalDepartures - 1
}
if (busyTime > endTime){
busyTime = endTime
}
busyRate = round(busyTime/endTime, 4)*100
if (showResults){
cat('Nombre de requêtes reçues: ', totalArrivals, "\n\t", totalFA," prioritaires\n\t", totalNA," normales\n\t", totalSA," lentes\n")
cat('Nombre de requêtes traitées: ', totalDepartures, "\n")
cat('Nombre de requêtes perdues: ', totalArrivals - totalDepartures, "\n")
# Remaining queries are considered lost queries since simulation ended too early
cat('Nombre de requêtes restantes à la fin de la simulation: ', queue, "\n")
cat('Taux d\'utilisation: ', busyRate, "%\n")
}
if (simType == "busy"){
return(busyRate)
} else if (simType == "lostQueries") {
return(totalArrivals - totalDepartures)
} else if (simType == "queue"){
plotSeq = seq(1, timeStep-1)
plot(timeState, mQState, xlab="temps", ylab="Nombre de requetes",type="s", main="Nombre de requetes dans la file d'attente") # On plote
points(timeState, fQState, col="red", pch=NA_integer_)
lines(timeState, fQState, col="red")
points(timeState, nQState, col="blue", pch=NA_integer_)
lines(timeState, nQState, col="blue")
points(timeState, sQState, col="green", pch=NA_integer_)
lines(timeState, sQState, col="green")
legend("topleft",legend=c("total","prioritaires","normales","lentes"), col=c("black", "red","blue","green"),lty=c(1,1,1,1), ncol=1)
}
}
cat("- STARTING SIMULATION -\n")
# Arguments to edit to customize the server simulation
duration = 10^4 # Duration of the simulation
lambda = 1 # Queries arrival rate
mu = 1 # Queries service/departure rate
fP = 0.1 # Fast queries queue proportion
nP = 0.3 # Normal queries queue proportion
nS = 1 # Number of servers
nSim = 1:100 #
# Lost queries simulation
cat("1 Serveur ; mu = 1\n")
lostQueries = 0
lambda = 0.1
mu = 1
nS = 1
plotSeq = seq(0.1, 10, 0.1)
for (n in nSim){
lostQueries[n] = serverSim(duration, ns, lambda, mu, fP, nP, "lostQueries")
lambda = lambda + 0.1
}
plot(plotSeq, lostQueries, main=expression(paste("Perte des requêtes en fonction du taux d'arrivée pour 100 simulations ( ", mu, "=1 )")), xlab=expression(lambda) , ylab = "Nombre de pertes", las=1)
# Busy time/rate simulation
cat("n Serveurs ; lambda = 2 ; mu = 1\n")
nSim = 1:50
busyRate = 0
lambda = 2
mu = 1
nS = 1
plotSeq = seq(1, 50)
for (n in nSim){
busyRate[n] = serverSim(duration, ns, lambda, mu, fP, nP, "busy")
nS = nS + 1
}
plot(plotSeq, busyRate, main=expression(paste("Taux d'utilisation en fonction du nombre de serveurs pour 50 simulations ( ",lambda,"=2, ", mu, "=1 )")), xlab="Nombre de serveurs" , ylab = "Taux d'utilisation", las=1)
# Queue proportions simulation
duration = 10^2
lambda = 1
mu = 1
nS = 2
serverSim(duration, ns, lambda, mu, fP, nP, "queue")
# Normal simulation
duration = 10^4
lambda = 1
mu = 1
nS = 2
serverSim(duration, nS, lambda, mu, fP, nP, simType = "", showResults = TRUE)
cat("- SIMULATION ENDED -")