A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 6. The average number in the system, L_s, is ________ and the utilization of the system is ________. A) 3; 100 percent B) 0.33; 25 percent C) 0.5; 33 percent D) 3; 25 percent E) 4; 33 percent

Question

Quizplus · Accepted Answer

The average number in the system (L) for an M/M/1 queue is given by L = λ / (μ - λ), where λ is the arrival rate and μ is the service rate. Here, λ = 2 and μ = 6, so L = 2 / (6 - 2) = 0.5. The utilization (ρ) is given by ρ = λ / μ, so ρ = 2 / 6 = 0.33 or 33 percent.

A Queuing Model That Follows the M/M/1 Assumptions Has λ