Journal of Advanced Transportation

Volume 2018, Article ID 6814348, 11 pages

https://doi.org/10.1155/2018/6814348

## Modeling Congestion Propagation in Multistage Schedule within an Airport Network

National Key Laboratory of Air Traffic Flow Management, Nanjing University of Aeronautics and Astronautics, China

Correspondence should be addressed to Xiaoxu Dai; moc.621@999xxiad

Received 26 April 2018; Revised 26 July 2018; Accepted 8 August 2018; Published 15 August 2018

Academic Editor: Luigi Dell’Olio

Copyright © 2018 Xiaoxu Dai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In order to alleviate flight delay it is important to understand how air traffic congestion evolves or propagates. In this context, this paper focusses on the aggravation of airport congestion by the accumulation of delayed departure flights. We start by applying a heterogeneous network model that takes congestion connection/degree into consideration to predict departure congestion clusters. This is on the basis of the fact that, from a micro perspective, the connection between congestion and discrete clusters can be embodied in models. However, the results show prediction to be of high accuracy and time consuming due to the complexities in capturing the connection in congested flights. The problem of being highly time consuming is resolved in this paper by improving the models by stages. Stage partitioning based on the variation of delay clusters is similar to the typical infectious cycle. For heterogeneous networks the model can describe the congestion propagation and its causes at the different stages of operation. If the connection between flights is homogeneous, the model can describe a more indicative process or trend of congestion propagation. In particular, for single source congestion, the simplified multistage models enable short-term prediction to be fast. Furthermore, for the controllers, the accuracy of prediction using simplified models can be acceptable and the speed on the prediction is significantly increased. The simplified models can help controllers to understand congestion propagation characteristics at different stages of operation, make a fast and short-term prediction of congestion clusters, and facilitate the formulation of traffic control strategies.

#### 1. Introduction

Airport congestion is an inherent problem in civil aviation, often resulting in substantial departure delays, reroutings, and even cancelations. Operating the aviation network is a complex task, where many factors need to be considered, especially disturbances. Congestion at airports is caused by an imbalance between the demand for flights and capacity of operation units. Flight schedule is in turn limited by both market demand and traffic capacity [1]. Therefore, airport flight delay per hour as a result of exceeding the hourly operational capacity can be seen as the congested flights, the temporal variation of which reveals their evolution. The other indices for congestion are queuing and queuing time [2–6].

Since the global air transportation network is a scale-free small-world network [7, 8], it provides a suitable framework to characterize air traffic. Therefore, a robust analysis can be undertaken of using flight performance data and the topological structure of the network to reveal the distribution of delays [9]. Metrics (delay time, centrality, degree distribution, and so on) have been defined to quantify the level of network congestion and various models introduced to describe or predict the delay/congestion propagation. Some of the models are derived from the observed data [10, 11]. The models combined with economic approaches have been proposed to estimate propagation delay [1, 12, 13], through repeated chain effects in aircraft rotations [13]. In computing the delays due to local congestion [14], the network delay models assume that every node corresponds to a given airport, two nodes are connected by means of flight routes, each node is weighted by its throughput capacity, and links are weighted by the Euclidean distance [14, 15]. At the same time, some of the research on delay/congestion propagation focus on the Bayesian network structure learning algorithm by combining genetic algorithms [16–21] with timed colored Petri nets [22].

Based on these models, simulation tools can be constructed, for example, in the final approach phase to reduce airport arrival delays [23] and for detailed policy formulation and assessment. Such tools have been used, for example, to reveal that local delays are dependent on the capacity to demand ratio of departures and arrivals [24].

In particular, some characteristics of delay/congestion have been found; for example, the objective delay statistics are sensitive measures of the effect of capacity improvements at airports [24], and the capacity and delay of different airports show different “spectral” characteristics, which can be used to examine airport performance [25]. At the same time, cyclic variations in air travel demand and weather at airports have been shown to have an impact on flight delay [26]. These characteristics are the foundation of this paper.

Our previous papers have described daily congestion propagation and modeled the evolution of congestion clusters in airports [27] and at the intersection of sectors [28] using some classic epidemic models [29–31], based on the similarity between congestion propagation and disease transmission. And the prediction of congestion propagation is a complex work, due to the polytrope of operational environment. So the model of congestion propagation in different stage should take varied factors into account. In this paper, we focus on the congestion propagation of departure aircraft from airport using multistage and multievent models [32, 33]. The assumption is that propagation characteristics resulting from a particular “event” and at a particular “stage” manifest a distinct “spectrum” (defined as the evolution of congestion clusters with time in a given airport). An “event” can be equipment failure, extreme weather, luggage off-loading, and so on. Here, we focus on extreme weather, which is the main event that caused the disturbance and relatively easy for data acquisition, and compare the congestion propagation in different meteorological conditions to reveal the “spectrum”. The case study is the ATL airport, which is one of the busiest airports in the world. Analyzing the spectrum in hour should reveal the cyclic nature and enable the determination of the relationship between the spectrum and departure schedule. Predicting congestion clusters in cycle should improve the accuracy of prediction. Compared with the models in our previous research, modeling congestion propagation in multistage schedule can enable air traffic controllers to better understand the characteristics of congestion and its propagation and provides an accurate and fast way to predict congestion size. And accurate and timely prediction which controllers need for strategic and tactical choices is benefit of both congestion management and improvement of efficiency.

The rest of the paper is structured as follows. In Section 2 we describe congestion propagation and analyze its cyclic nature and schedule variation and the relationship between delay and congestion. Section 3 establishes multievent and multistage congestion propagation models, with a particular focus on simplicity for short-term and fast prediction. Section 4 summarizes the conclusions and future direction of our work.

#### 2. Congestion and Congestion Propagation

Traffic congestion results from demand exceeding capacity, with the most visible manifestation in terms of delays at airports. This is partly due to congestion in the terminal or airspace. Relative to the requirements, the main cause of delay is reduced capacity of air traffic units as a result of disturbance by incident(s). Although suboptimal distribution of flight scheduling also causes departure airport congestion, delay clusters give rise to additional unexpected congestion. Hence, congestion from departure flights can be divided into two parts due to schedule and delay clusters. This paper focuses on the unexpected part, congestion and its propagation resulting from delayed flights.

##### 2.1. Congestion and Delay Cluster

Focusing on the congestion caused by departure delay clusters, both the variation of capacity for departure and delay clusters with time are used to define the degree of congestion caused by delay at time as denotes the capacity for departure at an airport at time, and denotes the delayed flights at time. The degree of congestion is directly proportional to delay size and inversely proportional to departure capacity. If either there is no incident or the effect is negligible, is constant. Evolution of congestion mainly depends on the variation of delay clusters with time as in the following expression:It is well known that delay can be propagated on air traffic networks. Hence, congestion has the same characteristic.

##### 2.2. Delay Cluster and Schedule

Based on the relationship between congestion degree and delay clusters, research on the evolution of delay cluster is the key to revealing the mechanism of congestion transmission. Analysis of 744 pairs of data (delay flights and schedule flights) reveals the direct relationship between them, as shown in Figure 1. The probability of delay deterioration is proportional to the schedule flights. That is, when the number of schedule flights is large, the probability of widespread flight delays tends to be high, when the system is disturbed by an “event”. The red lines enveloping almost all the dots show the diffusion trend. Based on the linear regression line,where is the schedule flight; is the delay flight. The correlation between the delay clusters and schedule flights can be seen in Table 1 (in the Appendix) and is significant at the 1% level; i.e., flight schedule is the main factor that influences flight delay. Therefore, research on congestion propagation must take into account the variation in flight schedule and congestion degree can be described asBecause of the heterogeneous distribution of departure schedule, firstly, we need to find the temporal distribution of departure schedule. Then according to the characteristics of the stage the propagation period can be divided into different steps. Finally, multistage congestion propagation models are introduced to describe the evolution of congestion as influenced by departure scheduling. The relationship between congestion and delay is introduced in detail in next section.