Question

The post office uses a multiple channel queue, where customers wait in a single line for the first available window. If the average service time is 1.5 minutes and the arrival rate is 72 customers every hour, using the Queuing.xlsx calculator tool, find, when two service windows are open,

a.	the probability both windows are idle.
b.	the average number of customers waiting in line.
c.	the average time a customer is in the post office.

Answer 1

Arrival rate lambda = 72 per hour

Service rate mu= 60/1.5 = 40 per hour

utilisation rho = 72/40=1.8

Probability of no customer in the system = P(0)

= 1 / [ 1+ rho+(rho)²* mu / ( 2*mu-lambda) ]

= 1 / [ 1+1.8+3.24 *40/ (2*40-72) ]

= 1 / 19 = 0.0526

Avg number of customers in line Lq with 2 channels and rho =1.8

= 7.6737

Waiting time in line = Wq = Lq /lambda = 7.6737 /72 =0.1065 hour = 6.3947 minutes

Total time in system = Wq + time spent in service = 6.3947+1.5 = 7.8947 min.