Week 2 Discussion

For an M/M/1 queue with mean interarrival time 1.25 minutes and mean service time 1 minute, find a five of \(W_q\), W, \(L_q\), L, and p. For each, interpret with words. Be sure to state all your units aand the relevant time frame of the operation.

\(W_q\) = the steady-state average time in queue (excluding service times) of entities.

\(W\) = the steady-state average time in system (including service times) of entities.

\(L_q\) = the steady-state average number of entities in queue. This is a time average.

\(L\) = the steady-state average number of entities in the system. This is a time average.

\(\rho\) = the steady-state utilization of a server or group of parallel identical servers.

Using the mmc.exe utility; input the following parameters:

\(\lambda\) = 1/1.25 = 0.8
\(\mu\) = 1
\(c\) = 1 for the number of servers

Question #1 M/M/1

Question #1 M/M/1

Results

\(W_q\) = 4 steady-state average time in queue in minutes (TimeInQueue)
\(W\) = 5 steady-state average time in system in minutes (TimeInSystem)
\(L_q\) = 3.2 entities in the queue per minute (NumInQueue)
\(L\) = 4 entities in the system per minute (NumInSystem)
\(\rho\) = 0.8 (Utilization)
\(\rho(0)\) = 0.2 the probability of having 0 entities in the system in steady state

Simio Results

Question #1 M/M/1 Simio Results

Question #1 M/M/1 Simio Results