The information counter at a large shopping mall employs only one customer

service officer. The number of customers requiring assistance appears to follow a

Poisson distribution with mean arrival rate of 24 per hour. Customers are served

on a first-come, first-served basis. The time it takes to assist a customer appears

to be exponentially distributed, with a mean of 2 minutes.

(a) Determine the average number of customers queuing for assistance or being

served at the information counter.

(b) How much time should a customer expect to spend queuing for assistance or

being served?

Solution

Average time customer spend in system (i.e. queuing for assistance or being

served at the information counter):

=/ =4/24=1/6 hour or 10 minutes

(c) Determine the percentage of idle time for the customer service officer.

(d) Determine the average time a customer spent waiting for service.

(e) Find the probability that the service time will be more than 10 minutes.