#M/D/1 vs M/M/1 Queue
#Deterministic distribution vs Markovian
MD1 = function(iar,serviceTime){
lambda = 1/iar
mu = 1/serviceTime
p = lambda / mu
L = p + (1/2)*(p^2/(1-p))
Lq = (1/2)*(p^2/(1-p))
W = 1/mu + p/(2*mu*(1-p))
Wq = p/(2*mu*(1-p))
return(c(L,Lq,W,Wq,p))
}
MM1 = function(iar,serviceTime){
lambda = 1/iar
mu = 1/serviceTime
p = lambda/mu
L = p/(1-p)
W = L/lambda
Wq = W-(1/mu)
Lq = lambda*Wq
return(c(L,Lq,W,Wq,p))
}
SteadyStateMetrics = c('L','Lq','W','Wq','p')
MD1ex = MD1(1,.9)
MM1ex = MM1(1,.9)
results = rbind(SteadyStateMetrics,MD1ex,MM1ex)
knitr::kable(results)| SteadyStateMetrics | L | Lq | W | Wq | p |
| MD1ex | 4.95 | 4.05 | 4.95 | 4.05 | 0.9 |
| MM1ex | 8.99999999999999 | 8.09999999999999 | 8.99999999999999 | 8.09999999999999 | 0.9 |
Question 15 : Create the M/D/1 Queue in Simio; show L/W metrics. Source set to random.exponential(1) Server set to .9 Connectors without travel time Experiment set for 10 hours at 25 replications with a 1 hour warm up period 
