Question

20. In a bank operating from 10 AM to 2 PM the cheques are cashed at a single
counter. Customers wishing to cash cheques arrive according to a Poisson
process at the rate of 20 customers a day. The cashier at the counter takes on
an average 16 minutes to cash the cheque. The service time has been shown to
be exponentially distributed.
() Compute the percentage of time the cashier is busy.
(ü) Compute the average time a customer is expected to wait.
(iii) Compute the average number of customers waiting in the queue.
(Ans. (i) 83.33%, (ü) 12.50 minutes,
tomers]​

Answer 1

process at the rate of 20 customers a day. The cashier at the counter takes on

an average 16 minutes to cash the cheque. The service time has been shown to

be exponentially distributed.

() Compute the percentage of time the cashier is busy.

(ü) Compute the average time a customer is expected to wait.

(iii) Compute the average number of customers waiting in the queue.