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/M/1 will be twice that of the M/D/1.

Question

Quizplus · Accepted Answer

The average queue length of an M/M/1 model can be calculated using the formula Lq = (ρ^2)/(1-ρ), where ρ is the traffic intensity, which is equal to λ/μ in this case (arrival rate/ service rate). Thus, ρ = 1/3, and Lq = (1/9)/(2/3) = 1/6. 
For the M/D/1 model, the queue length will be zero if the service time is less than the inter-arrival time, and will be equal to the arrival rate minus the service rate otherwise. Since the service rate (3) is greater than the arrival rate (1), the queue length for the M/D/1 model will be 2, which is twice as small as the queue length for the M/M/1 model. Therefore, the statement is true.

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