At a particular exit ramp of a turnpike, there is a single tollbooth. It was originally thought that there would be insufficient traffic at this point to justify more than one booth, but the traffic has increased recently. There are now (during rush hour, which is the period of concern) an average of 210 cars per hours, and the average service time is fifteen seconds. Two proposal have been made. The first is to add another toll booth identical to the first (assume the traffic would split evenly and at random between the two). The second is to add an automatic (that is, no human operator, booth that accepts change only. That booth would have an average service time of only five seconds, but only a third of the arrivals (selected at random) would have exact change. The performance measure of concern is the average delay incurred by the people who exit at this ramp.
a. Using an appropriate queuing model, estimate the delay under the present system, the first proposal, and the second proposal.
b. Recognizing that the service times are probably not negative exponential but are certainly not constant either, consider whether the results of part a should be modified.
c. Taking into account any other factors that may have been neglected, what do you recommend?