A service counter employs two servers.On average,a server requires 8 minutes to process a customer and service times follow an exponential distribution.Customers arrive at the counter at the rate of 12 per hour according to a Poisson distribution.The probability that an arriving customer must wait for service is
A)0.7111
B)0.8000
C)0.8576
D)0.9327

Question

Quizplus · Accepted Answer

The arrival rate (λ) is 12 customers per hour, and the service rate (μ) is 7.5 customers per hour per server (since 60/8 = 7.5). With two servers, the total service rate is 15 customers per hour. The traffic intensity (ρ) is λ/(2μ) = 12/15 = 0.8. The probability that an arriving customer must wait is given by the Erlang B formula for M/M/2 queue, which results in approximately 0.7111.

A Service Counter Employs Two Servers