Kelton Chapter 4.

4.10.2

c <- 1                        # Machine capacity

lambda <- 120                 # Mean rate of arrival (lambda)
mu <- 190                     # Mean service rate (mu)

rho <- lambda / (c * mu)

m <- c(0:(c-1))

p0 <- 1 / (sum((c * rho)^m / factorial(m)) + (c * rho)^c / (factorial(c) * (1- rho)))  # Probability that there are 0 entities in the system

L_q <- (p0 * (lambda / mu)^c * rho) / ((factorial(c) * (1 - rho)^2))           # Mean number of entities in the queue

L <- L_q + lambda / mu       # Mean number of entities in the system

W_q <- L_q / lambda          # Mean wait in the queue

W <- W_q + 1 / mu            # Mean wait in the system

\(W_q\) = 0.0090226

\(W\) = 0.0142857

\(L_q\) = 1.0827068

\(L\) = 1.7142857

\(\rho\) = 0.6315789

Expected number of entities processed in 100 hours = 7000.

4.10.3

** SMORE plot for the time entities spend in the system: **

SMORE Plot

SMORE Plot

4.10.9

** Standard library object vs Simio process: **

Simio process run time is much more faster at running 50 replications then the satandard library object run.

Standard library object run time:

Standard Time

Standard Time

Results:

Standard library object results

Standard library object results

Process Run Results

Process Run Results

4.10.12

** Animate: **

Animate using Simio Standard Symbols

Animate using Simio Standard Symbols