Data and queueing analysis of a Japanese air-traffic flow

Highlights

• Pre-scheduled traffic flows exhibit a serial correlation structure.

• We solved a special case and analyzed the transient properties of the corresponding queueing system.

• Based on this we derived a strategic rule for delay management.

Abstract

Congestion is a major cause of inefficiency in air transportation. A question is whether delays during the arrival phase of a flight can be absorbed more fuel-efficiently in the future. In this context, we analyze Japan’s flow strategy empirically and use queueing techniques in order to gain insight into the generation of the observed delays. Based on this, we derive a rule to balance congestion delays more efficiently between ground and en-route. Whether fuel efficiency can be further improved or not will depend on the willingness to review the concept of runway pressure.

Introduction

Many airports and airspaces are already congested today, but growing traffic demand will cause increasing delays in the future if no actions are taken (ICAO, 2005, JPDO, 2010, Sesar-Consortium, 2007). Congestion delays materialize either on the ground, where aircraft have to wait before accessing a runway or during the flight, where they are deviated from their intended trajectory. When the schedule buffers are tight, delays may also propagate through the whole transportation network. Congestion delays can be managed on a strategical level (by runway expansion or shorter separation standards), a pre-tactical level (by splitting flows and sectors) or a tactical level (by sequencing and re-sequencing aircraft).

Fig. 1 shows the typical situation. Prior to take-off, departure slots are allocated in order to balance demand with available capacity. Before landing, flows are merged and sequenced in order to efficiently use the runway. In this context, one speaks of radar vectoring, when traffic controllers ask the pilots to stretch their flight paths in the form of specific flight angles and of holding stacks, when pilots are asked to circulate in the vicinity of the airport. Departure slot allocation and en-route sequencing operations create delays, and we call them metering delays in this paper.

The Japanese flow managers currently allocate up to 10 min of metering delay to the en-route phase and the remaining delay to the ground. One can argue that en-route delays are unnecessary, once ground delays are correctly allocated. At least, speed control shall synchronize traffic flows so that radar vectoring can be reduced. But due to arrival-time uncertainties, en-route delays serve as buffers in order to keep a high pressure on the runways. On the other hand, future reduction of arrival time errors promises to reduce en-route delays, allocating more and more delay on the ground. The benefits are smoother traffic flows, less controller workload and reduced fuel consumption. In this paper we derive a decision rule to quantify this new balance.

The deterministic ground delay and aircraft sequencing problems are well known in the OR and the transportation communities, see for example Erzberger, 1995, Beasley et al., 2000, Bayen et al., 2004, Lulli and Odoni, 2007, Artiouchine et al., 2008, Balakrishnan and Chandran, 2010. The stochastic phenomenon of congestion was pioneered by Cox (1955), defining it as

• (i) a flow of customers needing service,

• (ii) some restrictions on the availability of service, and

• (iii) irregularity in the flow of customers, the servicing operation or both.

Moreover, when average demand is higher than available capacity (e.g. during peak hours or bad weather conditions), predictable congestion occurs. Phenomena with the above characteristics, such as telecommunication networks, passenger flows, and many more, are often modeled as stochastic or deterministic queueing systems (Newell, 1982, Wolff, 1989). The air transportation system also exhibits the classical queuing behavior: as demand approaches capacity, delays increase sharply (Ball et al., 2010).

Early contributions in this regard are by Bell, 1949, Dunlay and Horonjeff, 1976. Often, arguments for Poissonian arrival flows are elaborated on which steady-state control strategies are based. A homogeneous Poisson process assumes essentially that the numbers of arrivals in disjoint time intervals are independent random variables, and that no more than one arrival takes place per time instant (see Daley and Vere-Jones (2003) for an axiomatic derivation and historic derivations from Erlang and Bateman). Also since long time, the existence of steady-states in air transportation are questioned (e.g. Barnhart et al., 2003, Janic, 2000). One of the few transient analyzes is Peterson et al. (1995), based on an algorithmic approach. We will later show that the Poisson hypothesis is not unreasonable whenever congestion is moderate, and that steady-states can be reached for pre-scheduled flows in the order of a few hours.

The assumptions of homogeneous Poisson flows have been relaxed in at least three ways. Non-homogeneous queueing models allow for variations of arrival and service rates. This seems more realistic to capture high traffic peaks, particularly during bad weather. Typically, time-dependent Poisson arrivals are modeled with time-dependent service distributions (Bäuerle et al., 2007, Fan and Odoni, 2002, Hansen et al., 2009, Knessl and Yang, 2002, Pyrgiotis et al., 2013, Yang and Knessl, 1997). Models with deterministic service times serve as lower bounds and models with exponentially distributed service times as upper bounds to the real delays (Barnhart et al., 2003). Multiple arrivals per time instant (batch arrival models) are another relaxation of the Poisson assumption. Corresponding queueing models are proposed for aircraft landings (Falin, 2010, Krishnamoorthy et al., 2009). More recently, a third departure from Poisson arrivals was presented in Guadagni et al., 2011, Guadagni et al., 2013. They clarify that the numbers of arrivals in subsequent time intervals will be negatively correlated, whenever aircraft are pre-scheduled at a critical resource but arrive with random errors. Pre-scheduled queues are also studied in the field of ‘appointment scheduling’, where customers receive initial assignments, but may arrive with a positive or negative delay. From the queueing methodology point of view, there was some activity in the 1960’s and 1970’s, but it loses its traces then (Bloomfield and Cox, 1972, Mercer, 1960, Mercer, 1973, Winsten, 1959). Today, the field is widely occupied with algorithmic questions (e.g. Begen and Queyranne, 2011, Green, 2008 and the references therein) or numerical approaches (Nikoleris and Hansen, 2012).

The remainder of the article is organized as follows: in the next section we describe a radar-data analysis of arrival traffic for a Japanese airport. We then analyze two types of queueing models as generators for metering delays: pre-scheduled random arrivals (PSRA) and Poissonian arrivals. Based on this, we derive a rule how to balance metering delays between ground and air efficiently.