Supposing that, the government of Ghana has decided to bring back the tollbooth operations and drivers using the Kasoa-Cape cost highway 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. 

a) With your knowledge in queueing theory, how will you determine the average minutes time a motorist waits in the queue to receive service at the toll and also the average number of motorists in the queuing system? 

b) Based on the information in (a), if the 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? 

c) The motorway management perceives that the waiting time computed in (a) above is not acceptable and it wishes to reduce it, first, by adding an extra tollbooth assistant to help improve the Major Topic Queueing Theory Blooms Designation EV Score 7 Major Topic Queueing Theory Blooms Designation EV Score 6 5 service rate to 250 motorists every 8-hour-day. The tollbooth attendant will be paid a monthly salary of GH¢400. The second option is that management can add a toll-operated machine which will cost GH¢3,000 and this amount is a free gift from the Minister. This option will reduce the arrival rate to 35 motorists every 2 hours. 

However, management will have to pay the operator who will man the toll-operated machine a monthly salary of GH¢550. Which ever option management adopts, they avoid lost sales of GH¢1,200.00 per month for every minute that average waiting time is reduced. Advise management which option it must adopt?

Answer rating: 100% (QA)

a ANSWER The average time a motorist spends in the queue is equal to the average number of motorists ... View the full answer