During the early morning hours, customers arrive at a branch post office at the average rate of 45 per hour (exponential interarrival times), while clerks can handle transactions on an average of 4 minutes each (exponential).
What is the average number of customers waiting for service if 6 clerks are used?
A) 0
B) 0.01
C) 0.1
D) 1
E) 10

Question

Quizplus · Accepted Answer

The average number of customers waiting for service is given by the formula Lq = (lambda^2)/(mu(mu-lambda)), where lambda is the average arrival rate, mu is the average service rate, and Lq is the average number of customers waiting for service. In this case, lambda = 45 per hour and mu = 60/4 = 15 per hour. Plugging these values into the formula, we get Lq = (45^2)/(15(15-45)) = 0.1.

During the Early Morning Hours, Customers Arrive at a Branch