Chapter 4 of Kelton

Problem # 2

mm1 <- function (lam, mu) {
  
  # If p is less than 1,  we have a stable queue
  p <- lam/mu
  # Lq is the steady state average number of entities in the queue
  Lq <- p^2 / (1-p)
  #L is the steady state average number of entities in the system (rather than the number in queue)
  L <- p / (1-p)
  #Wq is the steady state average time in the queue
  Wq <- Lq/lam
  #W is the steady state average time in the system 
  W <- Wq + (1/mu)
  
  df <- data.frame(p=p, Lq=Lq, L=L, W=W, Wq=Wq)
  return(df)
  
}


df <- mm1((120/60), (190/60))
df
##           p       Lq        L         W        Wq
## 1 0.6315789 1.082707 1.714286 0.8571429 0.5413534
df$W
## [1] 0.8571429
#Steady State entities expected to be in the system in 100 hours
60/df$W*100
## [1] 7000

Problem # 3

Problem #9

As we would expect, the numbers using Simio Processes are very similar to those of the model using the standard library.

Problem #12