A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 8.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)4;33 percent D)6;25 percent E)4;25 percent

Question

Quizplus · Accepted Answer

Using Little's Law, L = λW, where L is the average number in the system, λ is the arrival rate, and W is the average time spent in the system.

W = 1/(μ-λ) = 1/(8-2) = 0.2

L = λW = 2(0.2) = 0.4

Therefore, the average number in the system is 0.4.

The utilization of the system can be calculated as ρ = λ/μ = 2/8 = 0.25 or 25 percent.

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