MM1 System

#### Generating the time between customer arrivals ####

it =c(rep(0,1000)) # create space to put the trials
lambda = 1/15 # fix the parameter of exponential
it =rexp(1000,lambda) # draw random numbers from exponential
head(it)
hist(it, freq=F, main="Exp(1/15) Inter arrival times" )

s= c(rep(0,1000))
s=runif(1000,5,15)
head(s) # View first numbers in s

hist(s, freq=F, main = "Histogram of service times")

at= c(rep(0,1000)) # create space to put the cumulative numbers.
at=cumsum(it) # Cumulative sum of the numbers in it
head(at) # View the first few numbers created

qt = c(rep(0,1000)) # open space to put the numbers
exit = c(rep(0,1000)) # open space to put the numbers

for(i in 1:999) {
if(at[i] +s[i] + qt[i] <= at[i+1]){
qt[i+1]=0
exit[i]= at[i]+s[i]+qt[i]
}
else if(at[i] + s[i]+qt[i] > at[i+1]){
exit[i]=at[i]+s[i]+qt[i]
qt[i+1] = at[i]+s[i]+qt[i] -at[i+1]
}
}
exit[1000]=at[1000]+qt[1000]+s[1000]

tts = c(rep(0,1000))
tts = exit - at # total time= exit time-arrival time.

hist(tts, freq=F, main = "Histogram of total time in the system")

mean(tts)
sd(tts)
summary(tts)

at=matrix(at) # convert at to matrix object
exit = matrix(exit) #convert exit to matrix object
atexit = cbind(at,exit) # combine the two in one matrix
tatexit = t(atexit) # transpose the matrix.
realtime=matrix(tatexit,2000,1,byrow=T) # create the real time.
head(realtime)

customer = matrix(rep(1,2000),2000,1)
realtime=cbind(realtime,customer)


for(i in 1:1000) {
realtime[2*i,2]=-1
}

oo = order(realtime[,1])
trace = realtime[oo,]
head(trace)

tracecum= cumsum(trace[,2])

mean(tracecum)
sd(tracecum)
summary(tracecum)

plot( tracecum,type="l")