rm(list=ls())
# Five patients comes every hour on average to the clinic,
# and the single physicaina treats six patients every hour on average.
# n=40 ; lambda=5/60 ; mu=6/60
MM1sim <- function(n=40,lambda=5/60,mu=6/60,seed=FALSE,Print=TRUE,Round=FALSE){
# service starc clock time(ssct) since 9:00
ssct=numeric(n)
# waiting time(w8)
w8=numeric(n)
# service end clock time(sect)
sect=numeric(n)
# arrival clock time(act)
if(seed) set.seed(1234)
act=cumsum(rexp(n,lambda)) ; if(Round) act=round(act)
# duration of service(ds)
if(seed) set.seed(5678)
ds=round(rexp(n,mu)) ; if(Round) ds=round(ds)
# simulation assuming service starts at 9:00
head(act) # act : arrival clock time
head(ds) # ds : duration of service
# initial values
ssct[1]=act[1] # 9:15 service start clock time for 1st guest
sect[1]=act[1]+ds[1] # 9:25 sevice end clock time for 1st guest
w8[1]=0
# simulation step by step
#
# act[2] # 9:16 arrival clock time of 2nd
# max(sect[1]-act[2],0) # 9:25-9:16 vs 0 = ?sevice for 1st ends b4 2nd arrival
# w8[2]=max(sect[1]-act[2],0) # 9 min : w8ing time of 2nd
# ssct[2]=max(sect[1],act[2]) # 9:25 vs 9:16 = service start clock time for 2nd
# sect[2]=ssct[2]+ds[2] # 9:25 + 8 = 9:33 service end clock time for 2nd
#
# act[3] # 9:17 arrival clock time of 3rd
# max(sect[2]-act[3],0) # 9:33 - 9:17 vs 0 = ?serivce for 2nd ends b4 3rd arrival?
# w8[3]=max(sect[2]-act[3],0) # 16 min : w8ting time of 3rd
# ssct[3]=max(sect[2],act[3]) # 9:33 vs 9:17 = service start clock time for 3rd
# sect[3]=ssct[3]+ds[3] # 9:33 + 11 = 9:44 service end clock time for 3rd
#
for(i in 2:n){
w8[i]=max(sect[i-1]-act[i],0)
ssct[i]=max(sect[i-1],act[i])
sect[i]=ssct[i]+ds[i]
}
if(Print){
print(summary(w8))
hist(w8,freq=FALSE,col="lightblue",main="")
}
invisible(w8)
}
MM1sim(n=1e5)
MM1sim(n=100)
w8m=replicate(1e4,mean(MM1sim(n=40,P=F)))
summary(w8m)
hist(w8m,main='40 visits per day',freq=F,col='pink')
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