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.
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 [
Since the global air transportation network is a scale-free small-world network [
Based on these models, simulation tools can be constructed, for example, in the final approach phase to reduce airport arrival delays [
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 [
Our previous papers have described daily congestion propagation and modeled the evolution of congestion clusters in airports [
The rest of the paper is structured as follows. In Section
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.
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
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
Correlation between delay clusters and departure schedule flights.
Correlation | schedule Flights | Delay clusters | |||
---|---|---|---|---|---|
Schedule Flights | Pearson Correlation | 1 | | ||
Sig. (2-tailed) | 0.000 | ||||
N | 744 | 744 | |||
Repeated | Deviation | 0 | 0.000 | ||
Error of Mean | 0 | 0.019 | |||
95% Confidence Interval | Lower Limit | 1 | 0.577 | ||
Upper Limit | 1 | 0.653 | |||
| |||||
Delay Clusters | Pearson Correlation | | 1 | ||
Sig. (2-tailed)) | 0.000 | ||||
N | 744 | 744 | |||
Repeated | Deviation | 0.000 | 0 | ||
Error of Mean | 0.019 | 0 | |||
95% Confidence Interval | Lower Limit | 0.577 | 1 | ||
Upper Limit | 0.653 | 1 |
b. Repeated sampling will be based on a sample of 1000
Scatter diagram of delay flights and schedule flights.
Data of delay clusters used in this paper can be found in the website https://www.faa.gov/. Figures
Evolution of delay flights with time.
The analysis of schedule flights
We model the propagation course as a complex undirected dynamic network. In the network, each node is a flight, and two nodes are linked if congestion exists between them. Each node is weighted equally, and each link is weighted according to the connection intensity, as shown in Figure
Congestion propagation in departure airport network.
Aircraft in airport activity areas share same resources, for example, taxiway, runway, apron, flight crew, and vehicles. Delay and/or congestion usually derive from the scarcity of these resources. At the same time, the congestion connection between departure flights is varied, and its intensity can be analyzed based on the weighted sum of the shared resources. Let
Congestion connection between departure flights in the airport activity area.
According to the congestion status and evolution, the departure flights are divided into three clusters, those are congestion clusters
To simplify the computation, we do not consider the canceled flights for
Prediction process of congestion clusters based on heterogeneous network model.
If we make an assumption, every flight on the airport network has same connection intensity; the congestion propagates on a homogeneous network.
In a homogeneous network, we suppose that every departure flight has a homogeneous distribution of congestion connection/degree, by simplifying the operational environment. The other parameter definitions are the same as those for the heterogeneous network model. The process of congestion propagation of departure flow in a homogeneous network is shown in Figure
Multievent and multistage model on homogeneous network.
Congestion propagation exhibits a cyclical fluctuation due to the daily schedules. Hence, its propagation and dissipation rates are variable at different stages. Similar to spread of disease, the process of propagation can be divided into four stages: latent, prodromal, maturation, and convalescent. These are shown in Figure
Congestion propagation in multistage schedule.
Based on the description of above stages, we can model congestion propagation in multistage schedule for short-term prediction.
Usually, congestion may be caused by just one “event”; for example, losing luggage may delay a flight and create local congestion. On the other hand, thunderstorm always results in a wider range of congestion. Ignoring the coupling of multievents, we can specify the simplified model in expression (
The scheduled flights vary with airports and time periods. Take the case of one of the most congested airports, ATL, as our example. ATL is the busiest and most efficient airport in the world and, by some accounts, the best in North America. It also holds the distinction of being the first airport in the world to serve more than 100 million passengers in a single year. From January 2016 to December 2017, the proportion of delayed gate departures is 15.56%, and the average minutes of delay per delayed gate departure is 46.25 minutes [
Comparisons between scheduled flights on different typical days demonstrate the similarity of schedule distribution. Figure
Schedule flights on typical congestion days.
Comparison between the visibilities on typical congestion days.
In Figure
Comparison between
The multistage models are applied to describe the congestion evolution and predict the congestion trend. Ignoring the complexity and probability of “event” coupling, prediction focuses on the congestion propagation resulting from a single “event”. We still take the data on the Dec 22-24 2014 in ATL airport as our case analysis and predict the congestion clusters with the simplified models.
Descriptions of historical data and prediction result on stage II.
Comparison | Maximum | Minimum | Standard | Variance | Standard error |
---|---|---|---|---|---|
Historical data | 0.3600 | 0.7692 | 0.9980 | 0.1000 | 0.4075 |
Prediction result | 0.3568 | 0.9615 | 0.9985 | 0.1000 | 0.4076 |
Comparison between the prediction result and historic data for stage II.
Comparison between the prediction result and historic data for stage III.
Prediction result on stage IV in different days.
Comparing two models, complex model (expression (
Comparison between complex model and simplified model.
Comparison | Complex model | Simplified model |
---|---|---|
| 0.0091 | 0.0208 |
| 0.0077 | 0.0159 |
time | 300s | 20s |
This paper builds on our previous work [
The prediction results compared with historical data find that the models make a good prediction performance in the different stages of congestion propagation. Note that “event” coupling is not considered in this paper due to its complexity and difficulty of quantization. Research is underway to address it.
See Table
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
Our paper gets generous help from Prof. Washington Yotto Ochieng, an academician from the Royal Academy of Engineering, in the aspects of article structure and description. This work is partially supported by National Natural Science Foundation of China (no. 71301074/no. 71701202) and Research Innovation Program for College Graduates of Jiangsu Province (no. KYLX16_0385) and supported by the Fundamental Research Funds for the Central Universities (no. NS2017044).