Question

A single-server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service time is 12 minutes. The service times are distributed according to the negative exponential distribution. The average time a customer can expect to wait in line is:

Answer 1

18 minutes

Explanation:

Given that:

The arrival time = 3 customers / hour

The avg. service rate (s) = 12 minutes per customer

To hour, we have:

`s = (60)/(12)`

s = 5 customers/ hour

Thus, the required average time for a customer needs to wait in line is:

`= (3)/(5)* (5-3) hours \\ \\ = (3)/(5)* 2 \\ \\ = (3)/(10) \ hours`

To minutes;

`= 3 * (60)/(10) \ minutes`

= 18 minutes