The Role of Airline Frequency Competition in Airport Congestion Pricing

Airport congestion pricing has often been advocated as a means of controlling demand for airport operations and for achieving efficient resource allocation. Competition between airlines affects the extent to which an airline would be willing to pay for airport slots. Accurate modeling of competition is critical in order to determine the effectiveness of a congestion pricing mechanism. We develop an equilibrium model of airline frequency competition in the presence of delay costs and congestion prices. Using a small hypothetical network, we evaluate the impacts of congestion prices on the various stakeholders and investigate the dependence of effectiveness of congestion pricing on the characteristics of frequency competition in individual markets. We find that the effectiveness of congestion pricing critically depends on three essential parameters of frequency competition. Our results show that variation in the number of passengers per flight plays a vital role in determining the degree of attractiveness of congestion pricing to the airlines. A significant part of the impact of congestion pricing cannot be accounted for using the models in prior literature, which are based on the assumptions of constant load factors and constant aircraft sizes. Further, we find that, in comparison to flat pricing, marginal cost pricing is more effective in reducing congestion without penalizing the airlines with exceedingly high congestion prices. Draft completed August 29, 2011. 1. BACKGROUND With airport capacity being a scarce resource, market-based mechanisms such as congestion pricing and slot auctions are expected to bring demand and supply in balance by placing monetary prices on the airport capacity. These market-based mechanisms rely on the ability of the airlines to assess the economical value of airport slots, while bidding for slots in the case of auctions and for determining the demand for slots at a given level of prices in the case of congestion pricing. Airlines are typically assumed to be rational decision makers, each driven by its own profit-maximization objective. However, an airline needs to account for competition from other airlines operating in the same markets as it does, while ascertaining its own valuation of an airport slot. In this paper, we model the airline frequency decisions under congestion pricing through explicit modeling of competition and assess the dependence of the effectiveness, or lack thereof, of congestion pricing on the characteristics of airline markets. Many prior studies have accounted for airline competition using conventional micro-economic models of firm competition. However, these generalized models fail to capture the essential characteristics of competition which are peculiar to the airline industry and consequently, as we show in this paper, tend to underestimate congestion pricing benefits to the airlines. We capture these characteristics through an industry-specific competition model and generate insights that were not possible with the previous models. Section 2 summarizes the existing literature on airport congestion pricing. Section 3 provides details of our equilibrium model of frequency competition. Section 4 describes our delay model that captures the dependence of flight delays on airline frequency decisions. Section 5 outlines the data sources and experimental setup for the computational experiments. Section 6 provides results of delay function fitting. Section 7 presents computational results for a small hypothetical network. Section 8 concludes with a summary of the practical implications of this research and a description of directions for future research. 2. LITERATURE REVIEW A user (such as an airline) of a public resource (such as an airport) generates value for itself through the utilization of the resource. Such utilization might sometimes result in detrimental effects to the other users of the public resource. In particular, an airline operating at a congested airport imposes additional delay costs on the other airlines operating at the same airport. Economists have long been advocating the use of pricing of public resources in the presence of negative externalities such as congestion, wherein each user of the public resource is required to pay a price equal to the marginal cost imposed by that user on all the other users of the resource (1). Such prices based on marginal costs have been claimed to achieve efficient allocation of resources. Not surprisingly, early studies on airport congestion pricing have advocated marginal cost pricing of airport resources (2, 3). Levine (2) proposed to implement a system in which each airport user is charged fully for the marginal cost of an additional operation, while Carlin and Park (3) recommended a hybrid system involving pricing and administrative controls due to various practicality issues associated with a full marginal cost pricing scheme. Airport congestion pricing, however, is fundamentally different from pricing of resources such as highway infrastructure which involve a large number of users, each using a very small portion of the capacity of the resource, otherwise known as atomistic users. Airlines, on the other hand, are considered to be non-atomistic users of airport resources because each airline typically operates more than one flight at an airport, and the number of users of an airport resource is comparatively smaller. So each additional operation by an airline delays the flights of other airlines as well as the other flights of the same airline at that airport. More recent studies recognize the fact that airlines automatically internalize a part of the congestion costs they impose (4, 5, 6, 7, 8). A recent study by Morrison and Winston compared the atomistic (or flat) and non-atomistic pricing policies across 74 commercial US airports in 2005 (9). They found the difference between the net benefits generated by the two congestion pricing policies to be small because the bulk of airport delays are not internalized. In this paper, we analyze the impacts of various levels of flat pricing (also known as atomistic pricing) as well as the marginal cost pricing (also known as non-atomistic pricing) equilibrium for non-atomistic users. Daniel modeled the interaction between airport demand, slot prices and delays using detailed queuing theoretic models, but did not capture frequency-based competition for passenger share in a market, even though such competition between airlines is intricately related to the congestion problem at major airports (4, 5). Several other studies have tackled this problem from a microeconomic perspective and have mathematically derived Nash equilibrium outcomes under congestion pricing (6, 7, 8, 10). These studies model airline decisions using general micro-economic models of firm competition, which typically assume quantity-based (Cournot) competition. By assuming constant load factors and constant aircraft seating capacities, they fail to recognize the important distinguishing features of the airline industry for which the quantity produced can be captured by three different entities: number of flights, number of seats and number of passengers carried. The incremental profitability of having an extra flight in a particular market largely depends on the number of additional passengers that the airline will be able to carry because of the additional flight, which in turn depends on the schedule of flights offered by the competitor airlines in the same market. So, given a set of congestion prices, the total demand for slots should reflect these competitive interactions. However, Cournot models of firm competition do not incorporate the inverse dependence of one airline's market share on competitor airlines' frequencies, which is a critical component of such competitive interactions. Furthermore, the assumption of constant load factors and constant aircraft seating capacities means that studies such as Brueckner (6, 7), Pels and Verhoef (8), and Perakis and Sun (10), cannot account for the possibility of increases in average number of passengers per flights (through increased load factors, or increased number of seats per aircraft, or both) as the slots become expensive under congestion pricing. Consequently, delay cost reductions have often been considered as the only type of benefit from congestion pricing. Most of the prior studies evaluate congestion pricing benefits in terms of overall societal welfare gain, rather than in terms of the benefits to airlines and passengers. Perakis and Sun (10) conclude that, while congestion pricing leads to the welfare maximization solution, both airlines and passengers are worse off than without congestion pricing because the welfare gain from congestion pricing is in the form of the revenue generated from pricing. Many of the prior congestion pricing studies propose some form of direct or indirect mechanisms for re-distribution of this revenue gain if the congestion pricing scheme is to be attractive to the airlines. Our models are able to capture the phenomenon of varying number of passenger per flight explicitly. In fact, as we show in Section 7, a reduction in operating costs is an important driver of the benefits of congestion pricing to the airlines, which has not been considered in any of the prior studies. Schorr provided a model of airline frequency competition under flat pricing of airport slots and produced interesting results on the benefits of flat pricing, albeit focusing on symmetric equilibria for the somewhat restrictive case of identical airlines (11). We model airline frequency competition under congestion pricing using a popular market share model of frequency competition, which is similar to Schorr's model. We consider the general case of non-identical airlines and do not restrict our analysis to symmetric equilibria. The main objective of this research is to investigate the role of airline frequency competition under congestion pricing. The major contributions of this paper are threefold. First, we develop a model for airline frequency competition that explicitly accounts for the relationship between the number of flights operated, number of seats flown and the number of passengers carried by an airline under slot pricing. To the best of author's knowledge, this is the first computational study that accounts for this relationship. Second, using a small hypothetical network, we evaluate the impacts of congestion prices on the various stakeholders and investigate the dependence of effectiveness of congestion pricing mechanisms on the different characteristics of airline competition. Third, we provide computational results under flat as well as marginal cost pricing. Our results show that the variation in number of passengers per flight plays a vital role in determining the degree of attractiveness of congestion pricing to the airlines.