Question

Peri Thompson is the sole dispatcher for Thompson Termite Control. Peri’s job is to take customer calls, schedule appointments, and assist with billing issues over the phone. Peri can handle on average 15 calls per hour.

a) Typically, Peri gets about 10 calls an hour. Under these conditions, what is the average number of customers waiting, and what is the average waiting time?

b) Monday morning are unusually busy and Peri receives an average of 13 calls per hour during those peak times. Recalculate the average number of customers waiting and the average waiting time. What would you suggest if business takes off and Peri’s average increases to 13 calls per hour all of the time?

Answer 1

a)

Average number of customers waiting = arrival rate^2/(service rate*(service rate-arrival rate))

=10^2/(15*(15-10)) = 1.333333333

Average waiting time = arrival rate/(service rate*(service rate-arrival rate)) =10/(15*(15-10)) = 0.133333333 hour = 0.133333333*60 = 8 minutes

b)

On monday morning,
Average number of customers waiting = arrival rate^2/(service rate*(service rate-arrival rate))

=13^2/(15*(15-13)) = 5.633333333

Average waiting time = arrival rate/(service rate*(service rate-arrival rate)) =13/(15*(15-13)) = 0.433333333 hour = 0.433333333*60 = 26 minutes

If business takes off then it can be seen the waiting time for customers is very high (26 minutes) if Peri’s average increases to 13 calls per hour all of the time. So, Another worker needs to be recruited who can share the workload with Perry