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.
-What is the average number of customers waiting in line?
A)1 633
B)2 333
C)2 5
D)3 966
E)4

Question

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.
-What is the average number of customers waiting in line?
A)1 633 
B)2 333 
C)2 5 
D)3 966 
E)4

Quizplus · Accepted Answer

The average number of customers waiting in line is given by the formula L = λ^2 * S^2 / (2 * (1 - λ * S)), where λ is the arrival rate, S is the service rate, and L is the average number of customers waiting in line. In this case, λ = 14 customers per hour and S = 1 / 3 minutes per customer. Plugging these values into the formula, we get L = 14^2 * (1 / 3)^2 / (2 * (1 - 14 * 1 / 3)) = 2.5 customers.

Customers Arrive at a Suburban Ticket Outlet at the Rate