Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come,first-served basis.The arrival rate follows a Poisson distribution,while service times follow an exponential distribution.If the average number of arrivals is four per minute and the average service rate of a single server is seven per minute,what proportion of the time is the server busy?
A)0.43
B)0.57
C)0.75
D)0.25
E)0.33

Question

Quizplus · Accepted Answer

The utilization factor (proportion of time the server is busy) can be calculated using:
utilization = (arrival rate / service rate)
= (4 / 7)
= 0.57
Therefore, the answer is B) 0.57.

Customers Enter the Waiting Line to Pay for Food as They