4.12 Imposing fees at a congested facility It is often necessary to impose congestion tolls to assure that expensive transportation facilities (tunnels, bridges, terminal space at bus terminals, etc.) are used efficiently. Consider a city-owned airport and assume that this airport has a runway that is used only for landings during the peak traffic hours. Under peak conditions, the arrivals of airplanes at the vicinity of the airport are assumed to be Poisson with a rate = 55 aircraft/hour. Of these airplanes, 40 on the average are commercial jets and 15 are small private airplanes ("general aviation"). The pdf for the duration of the service time to a random aircraft landing on the runway is given by the uniform pdf of Figure P4.12(a).

a. Peak-hour conditions occur during 1,000 hours/year and the average cost of 1 minute's waiting (i.e., "going into a holding pattern" near the airport) is $12 for commercial jets (this accounts primarily for the extra fuel spent, the extra flight crew time and extra aircraft maintenance costs). Estimate the yearly costs to the airlines of peak-hour delays at this runway.

b. To alleviate peak-hour congestion, the airport's managers are considering an across-the-board increase in the fees that aircraft pay for using the runway ("landing fees"). While airline demand is insensitive to moderate increases in landing fees, general aviation demand is expected to drop drastically as these fees increase (since there are some good small airports near the city in question which can be used by small aircraft). In fact, a study of the general aviation runway users revealed that the relationship between demand per hour by general aviation and increase in landing fee is as shown in Figure P4.12(b). What is the most desirable amount of increase in landing fees from the point of view of the airlines? (Remember that the airlines will also be paying the higher fees.)