An M/M/1 model and an M/D/1 model each have an arrival rate of 1 per minute and a service rate of 3 per minute; the average queue length of the M/D/1 will be twice that of the M/M/1.

Question

Quizplus · Accepted Answer

The M/M/1 model assumes exponential interarrival times and exponential service times, while the M/D/1 model assumes deterministic interarrival times and exponential service times.

For the M/M/1 model, the average queue length can be calculated as (lambda^2)/(mu*(mu-lambda)), where lambda is the arrival rate and mu is the service rate. Plugging in the values given, we get:

(1^2)/(3*(3-1)) = 0.33

For the M/D/1 model, the average queue length can be calculated as (rho^2)/(1-rho), where rho is the traffic intensity (lambda/mu). Since the service times in the M/D/1 model are deterministic, the traffic intensity is 1/3. Plugging in the value, we get:

((1/3)^2)/(1-(1/3)) = 0.22

Therefore, the average queue length of the M/D/1 model is not twice that of the M/M/1 model.

An M/M/1 Model and an M/D/1 Model Each Have an Arrival