Answer to Question #201026 in Excel for Nana kofi

Question

Drivers using the Accra-Tema motorway have to stop at the tollbooth to pay their tolls. Motorists arrive at the tollbooth at a rate of 200 per 8-hour-day. The single tollbooth attendant can serve, on average, 220 motorists per 8-hour-day.

i) What is the average minutes’ time a motorist waits in the queue to receive service at the toll?

ii) What is the average number of motorists in the queuing system?

iii) Management of the motorway likes to have its operators working 90% of the time. What must the arrival rate be for the tollbooth attendant to be as busy as management would like?

Answer 1

1. For serving 1 car tollbooth needs in avarage 8x60/220=2.2 minutest. As it is 200/220=0.9 motorists in the queuing system. So the average minutes' time a motorists wait is 2.2x0.9=2 minutes.

2. 200/220=0.9

3. 220x 0.9=198 motorists per 8-hour-day