Slot constraints are restrictions on the number of landings or takeoffs that airports permit during specified time periods known as slot windows. For a typical example, an airport that can perform sixty landings per hour, issues sixty slot permits for landings during each hour of the day and requires aircraft to operate during their assigned hour. Most major commercial airports throughout the world impose slot constraints to control access to their run-ways, ostensibly to reduce congestion delays. In the US, however, most major airports that receive federal funding are available on a first-come, first-served basis without requiring slot permits. When airports become severely congested, airport authorities, airline officials, and policy makers generally seem to favor slot constraints over congestion tolls as a means of managing demand. They argue that slot constraints are simpler to implement because the airports need only limit the number of slot permits to the airport's capacity, then sell, auction, or give the permits away. Slot markets can price and allocate the slot permits efficiently Congestion tolls, they argue, are too difficult (or politically incon-venient) for airports to assess correctly. Moreover, slot permits are supposed to avoid the problem of imposing different toll schedules on dominant airlines that already internalize their self-imposed delays than on fringe airlines that ignore the additional delays
they impose on other aircraft.
This case for slot constraints implicitly assumes that airports experience steady-state traffic during slot windows. Actual traffic patterns at major airports, however, exhibit rapid fluctuations that follow regular patterns due to airline scheduling practices. Airlines that operate hub-and-spoke networks schedule flights around passenger interchange periods. Consequently, many airports experience as many as ten substantial peaks during a day (see, Daniel and Harback, 2009). Actual traffic patterns call into ques-tion the effectiveness and practicality of slot-constraint systems that are based on steady-state traffic models that underlie most existing policy analysis. If traffic rates and queuing systems are in steady states, then restricting the number of hourly slot permits to the hourly airport capacity might reduce congestion. If congestion is actually caused by traffic rates fluctuating from slack to peak demand within hourly periods, then it is desirable to use a model that captures these features of the problem.
In this paper, I develop a (dynamic) bottleneck model with multi- ple slot windows in which the airport authority chooses the timing of slot windows and the quantity of landings or takeoffs (operations) to permit during each window. Airlines choose when to operate their aircraft within the slot windows to minimize the costs of their queuing delays and of arriving before or after their most preferred time.
A structural model of congestion has state-contingent queues that evolve endogenously in response to traffic adjustments. Congestion externalities cause traffic rates (i.e., the rates of arrivals at the landing
or take off queue) to exceed service rates (i.e., the rates at which airports can perform landings or takeoffs) during a portion of each slot window, even when the number of slot permits per slot window is within the airport's capacity. While airports chose the number of slot permits per slot window, airlines chose aircraft operating times within the slot windows, resulting in equilibrium traffic patterns that exceed capacity during the portions of slot windows that are closest to the preferred operating times. In the bottleneck model, slot constraints cause the queue to empty periodically by preventing airlines from scheduling aircraft too early. This results in smaller peaks during each slot window rather than a single large queue that persists throughout the busy period. As the airport authority adds more slot windows, it constrains aircraft to narrower operating windows and the queue empties more frequently, thus limiting the accumulation of aircraft in the queue and reducing total queuing delay.
The model also addresses the optimal timing of dominant and fringe airline operations, the efficient allocation of slots among dominant and fringe airlines, and the effect of slot constraints on
the distribution of surpluses between dominant airlines and atomistic fringe aircraft. A policy section discusses the problems with current and proposed implementations of slot constraints,
and the practical issues involved in designing and implementing efficient slot systems. The paper focuses on the more basic issues of timing and quantity of slot permits rather than how to design auctions or markets to distribute slot permits. The literature has largely overlooked these basic issues, but unless policymakers address them, the resulting slot-constraint system may have little effect on congestion at most airports, no matter how elaborately they design slot auctions or markets.
A brief preview of the conclusions I derive from the model is as follows: (1) Effective slot-constraint systems require numerous narrow slot windows that force traffic to spread out over the peak
period. Slot- constraint systems that force traffic to spread out over the peak period. Slot-constraint systems that hold the quantity of slot permits to the airport capacity over a single slot widow covering
the entire peak period are completely ineffective. (2) In uncon-strained equilibria, dominant airlines schedule some of their aircraft to operate at the service rate during the periods just before and after the atomistic traffic. These aircraft fully inter-nalize their delays, while the remaining dominant aircraft join
atomistic traffic and ignore the delays that they impose on other dominant aircraft. The fraction of internalizing aircraft varies from one to zero as fringe demand elasticity varies from zero to negative infinity. (3) If the airport authority has complete control over the allocation of slots, it will separate the dominant and fringe operations to enable the dominant airline to fully inter-nalize all self-imposed delays. If the airport is unable to enforce this separation, then the dominant airline will schedule some aircraft atomistically, depending on the elasticity of fringe demand. The first-best optimum requires one slot permit and window for every service interval.