Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays.
How many minutes does the average customer wait in line?
A) 7
B) 8
C) 9
D) 10
E) 11

Question

Quizplus · Accepted Answer

The average arrival rate (λ) is 14 customers per hour, and the service rate (μ) is 20 customers per hour (since 60/3 = 20). Using the formula for the average waiting time in line for an M/M/1 queue, Wq = λ / (μ(μ - λ)), we get Wq = 14 / (20(20 - 14)) = 7 minutes.

Customers Arrive at a Suburban Ticket Outlet at the Rate