DATA 604 Discussion 4
Ahsanul Choudhury
September 20, 2017
4.14.b
Theoretical
c <- 4 # Number of server($M/M/1$ queue)
lambda <- 2.4 # Mean rate of arrival (lambda)
mu <- 0.7 # 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 customers in the system
L_q <- (p0 * (lambda / mu)^c * rho) / ((factorial(c) * (1 - rho)^2)) # Mean number of customers in the queue
L <- L_q + lambda / mu # Mean number of customers in the system
W_q <- L_q / lambda # Mean wait in the queue
W <- W_q + 1 / mu # Mean wait in the system\(W_q\) = 1.7576158
\(W\) = 3.1861873
\(L_q\) = 4.218278
\(L\) = 7.6468494
\(\rho\) = 0.8571429
Simio ModelRun
I was stuck with the Simio model for hours, my results were way off. After looking at Brian and Walt’s thread, used servers as output list for transfernode and got the following results:
Run it for 200 hours.
Run
Used 200 minutes as warm-up-period and replicated 10 times.
Experiments
Results:
Results