Endogenous control of service rates in stochastic and dynamic queuing models of airport congestion

Highlights

• Integration of tactical operating procedures into a strategic model of congestion.

• Estimation of airport delays using a stochastic and dynamic queuing model.

• Formulation of an efficient control of arrival and departure service rates.

• The model estimates well the average and variability of delays at JFK, EWR and LGA.

• Large delay declines between 2007 and 2011 largely explained by small changes in demand.

Abstract

Airport congestion mitigation requires reliable delay estimates. This paper presents an integrated model of airport congestion that combines a tactical model of capacity utilization into a strategic queuing model. The model quantifies the relationships between flight schedules, airport capacity and flight delays, while accounting for the way arrival and departure service rates can be controlled over the day to maximize operating efficiency. We show that the model estimates the average and variability of the delays observed at New York’s airports relatively well. Results suggest that delays can be extremely sensitive to even small changes in flight schedules or airport capacity.

Introduction

Since the deregulation of the US airline industry in 1978, the air transportation sector has experienced tremendous growth worldwide while airport capacity has been lagging behind, resulting in imbalances between demand and capacity at many of the world’s busiest airports. These imbalances create significant air traffic delays, whose total cost in the United States was estimated at over $30 billion for the year 2007 (Ball et al., 2010). The mitigation of airport congestion has become a primary challenge in air traffic management and can take place through infrastructure expansion (e.g., construction of a new runway or a new airport), the development of new air traffic management technologies (e.g., NextGen in the United States, SESAR in Europe) and demand management measures (e.g., slot control, congestion pricing). The design and assessment of such measures require efficient and reliable models of congestion to quantify flight delays under different demand and capacity scenarios.

An important challenge in this class of models involves the representation and estimation of airport capacity. Airport capacity is defined as the expected number of movements that can be operated at the airport per unit of time under continuous demand (de Neufville and Odoni, 2013). Given the variability of airport operations, it is not a fixed quantity but depends on several operational factors, including weather conditions, the proportion of landings and takeoffs operated and the runway configuration in use (Gilbo, 1993, de Neufville and Odoni, 2013, Simaiakis, 2012). Some of these factors are not determined exogenously in advance. Instead, air traffic managers exercise a control over the runway configuration in use and the balance of arrivals and departures to make the best use of available capacity over the course of the day. However, existing models of congestion consider exogenous, often single-value capacity estimates and thus do not capture these controls exercised in practice.

This paper presents an original approach to airport congestion modeling that integrates recent, fine-grain characterizations of airport capacity and tactical capacity utilization procedures into a strategic queuing model of airport congestion. By “tactical”, we refer to optimizing the utilization of airport resources to process flights over the day, specifically through the control of runway configurations and the balancing of the arrival and departure loads allocated to different runways. By “strategic”, we refer to the planning of flight schedules well before the day of operations, taking into consideration long-term patterns of capacity availability. Our integrated approach is motivated by the fact that decisions concerning airport capacity utilization on any given day depend strongly on the schedule of flights, which is largely set months in advance, and on the capacity of the airport. Modeling the relationships between flight schedules, airport capacity and flight delays at the strategic level therefore requires the understanding of how flights will be operated at the tactical level.

We describe the formation and propagation of delays over the course of the day as a function of airport demand and arrival and departure service rates by means of a stochastic and dynamic queuing model. We formulate an efficient control of arrival and departure service rates as a function of flight schedules, operating conditions and observed queue lengths. This control simulates how service rates are selected over the day by air traffic managers to maximize airport efficiency in the short run, under capacity constraints. The model is then applied to the three primary airports in the New York Metroplex: John F. Kennedy International (JFK), Newark Liberty International (EWR) and LaGuardia (LGA). We show that it approximates well the dynamics and magnitude of airport queues over the day. Thus, the model provides a fast and flexible tool for forecasting the evolution of delays at different airports under different demand and capacity scenarios.

Models of airport congestion fall into three categories: microscopic, mesoscopic and macroscopic models. Microscopic models consider each aircraft individually and reproduce precisely the physical layout of the airport and the sequencing of movements (Bilimoria et al., 2000, Sood and Wieland, 2003, George et al., 2011). These models are not well-suited to performing strategic planning under a wide range of scenarios. Mesoscopic models predict runway delays and taxi-in and taxi-out times using operational data, such as the runway configuration in use, short-term arrival demand, pushback schedules, etc. (Shumsky, 1995, Pujet et al., 1999, Simaiakis and Balakrishnan, 2014). These models have been applied to the design of procedures for optimizing surface operations (Simaiakis et al., 2014, Khadilkar and Balakrishnan, 2014). However, their heavy reliance on detailed operational data limits their applicability to modeling delays for strategic planning purposes when such data are not available. Finally, macroscopic models aggregate operations at the airport level to provide computationally efficient estimates of the relationships between flight schedules, airport capacity and flight delays in support of strategic planning (e.g., to assess the benefits of capacity expansion or demand management). Our research falls within this third category.

Existing macroscopic models of congestion are based on econometric models (Kwan and Hansen, 2010, Morrison and Winston, 2008, Xu, 2007), deterministic queuing models (Hansen, 2002), stochastic queuing models (Kivestu, 1974, Gupta, 2010, Pyrgiotis et al., 2013), or a combination thereof. In this paper, we consider a stochastic queuing model, which aims to capture the dynamics of formation and propagation of delays over the day as well as the uncertainty and variability associated with airport operations. Previous research has shown that this model approximates queue dynamics at major US airports well (Lovell et al., 2007, Pyrgiotis and Simaiakis, 2010).

The delay estimates obtained with any queuing model depend critically on the estimates of the rates at which arrivals and departures are serviced, which are constrained by the capacity of the airport. In existing models, service rates are generally kept constant over the day (Pyrgiotis, 2011, Jacquillat, 2012) or varied using ex post operational data, such as meteorological conditions, reported capacity estimates, etc. (Hansen et al., 2009). Clustering techniques were developed recently to generate capacity profiles using probabilistic weather forecasts (Liu et al., 2008, Buxi and Hansen, 2011) and used ex ante in queuing models (Nikoleris and Hansen, 2012). These variations in service rates are exogenous and depend neither on flight schedules nor on observed congestion.

However, other important variations in arrival and departure service rates are endogenous, i.e., they depend on the schedules of flights and on observed queue lengths. For instance, if a large number of landings are scheduled, then air traffic managers might decide to enhance the arrival throughput, at the expense of the departure throughput. As well, the arrival throughput might be enhanced if the observed arrival queue is longer than expected—or if the departure queue is shorter than expected. These controls are not taken into account in existing macroscopic models of airport congestion, although they might affect significantly the dynamics and the magnitude of delays. One recent application of a queuing model included variations in arrival and departure service rates that occur in response to changes in daily flight schedules caused by aircraft delays. However, these variations are introduced into the model manually and not systematically (Pyrgiotis and Odoni, 2014).

The contributions of this paper fall into four categories:

• We develop an original approach to airport congestion modeling that integrates a tactical model of capacity utilization into a strategic model of airport congestion. We combine a control of arrival and departure service rates into a stochastic and dynamic queuing model. This approach can be applied to quantify airport congestion under different capacity or flight scheduling scenarios, while accounting for the way airport capacity utilization procedures can react to such changes to maximize operating efficiency at the airport in the short run.

• We formulate an efficient control of arrival and departure service rates under stochastic queue dynamics and stochastic operating conditions. This control is based on a tactical decision-making support tool developed in previous research that optimizes the selection of runway configurations and the balance of arrival and departure service rates to minimize congestion costs (Jacquillat et al., 2013). In this paper, we formulate an approximate version of this control to incorporate it efficiently into our queuing model of airport congestion.

• We perform extensive comparisons with operational data at JFK, EWR and LGA to validate our model as a means of quantifying airport on-time performance. To the best of our knowledge, this represents the first attempt to compare the results of a macroscopic model of airport congestion to historical records of operations over a large sample of days. We develop estimates of on-time performance from historical records of operations. We show that our model approximates expected departure queue lengths and expected delays at the three airports relatively well, even though it underestimates delays slightly at off-peak hours. We also show that it provides good approximations of the range, hence of the variability, of departure queue lengths.

• We apply the model to study recent trends in scheduling and on-time performance at the New York airports. The analysis suggests that the large delay reductions observed between 2007 and 2011 can be largely attributed to the comparatively small reduction in demand over the period and, perhaps, to improvements in air traffic handling procedures.

The remainder of the paper is organized as follows. Section 2 presents the queuing model of airport congestion and the control of arrival and departure service rates. Section 3 compares the results of the model to historical records of operations at JFK, EWR and LGA. Section 4 discusses the opportunities and challenges associated with the application of the model in support of strategic planning and presents an example of such application. Section 5 concludes.