A Multi-Agent Approach for Reactionary Delay Prediction of Flights

Flight schedules are highly sensitive to delays and witness these events on a very frequent basis. In an interconnected and interdependent air transportation system, these delays can magnify and cascade as the ﬂight itineraries progress, causing reactionary delays. The airlines, passengers and airports bear the negative economic implications of such phenomenon. The current research draws motivation from this behavior and develops a multi-agent based method to predict the reactionary delays of ﬂights, given the magnitude of primary delay that the ﬂights witness at the beginning of the itinerary. Every ﬂight is modeled as an agent which functions in a dynamic airport environment, receives information about other agents and updates its own arrival and departure schedule. To evaluate the performance of the method, this paper carries out a case study on the ﬂights in Southeast Asia, which covers eleven countries. The model is tested on a six-month ADS-B dataset that is collected for the calendar year 2016. Through the reactionary delay values predicted by the multi-agent based method, the ﬂights are ﬁrst classiﬁed as delayed or un-delayed in terms of departure. The classiﬁcation results show an average accuracy of 80.7%, with a delay classiﬁcation threshold of 15 minutes. Further, a delay multiplier index is evaluated, which is a ratio of the total delays (primary + reactionary delays) and the primary delays for each aircraft. The majority of delay multiplier values range between 1-1.5, which signiﬁes that for except a few outliers, the primary delays do not signiﬁcantly cascade into reactionary delays for the ﬂights in Southeast Asia. The outliers represent scenarios where primary delays magnify and propagate as reactionary delays over subsequent ﬂight legs. Therefore, the proposed method can assist in better ﬂight scheduling by identifying itineraries which experience higher reactionary delays.


I. INTRODUCTION A. BACKGROUND AND LITERATURE REVIEW
The commercial civil aviation sector is a complex, distributed network, with a vast number of elements interacting with each other to meet a common objective of safe and in-time transport of passengers [1].This sector has witnessed immense growth in terms of infrastructure, territorial coverage and customers, over the past few decades.The International Air Transport Association (IATA) forecast predicts 8.2 billion passengers by the year 2037, at an annual compounded growth rate of 3.5% [2].With the ever-increasing air traffic The associate editor coordinating the review of this manuscript and approving it for publication was Weiguo Xia .and limited CNS (communication, navigation and surveillance) and airspace capacities, the flight schedule planners try to reduce the buffers between flight arrivals and departures in order to maximize aircraft utilization and meet the increasing demand.Similarly, the airport management aims to service and prepare the aircraft for departure faster, to increase the airport's gate availability.Such plans and practices increase the likelihood of delay generation [3], [4].
The direct and indirect costs associated with delays [5], its effect on passengers and an increasingly competitive commercial aviation market have driven research to predict and minimize air traffic delays [6]- [8].Strategies such as the Ground Delay Programs (GDP) [9], [10], Collaborative Decision Making (CDM) [11] and Air Traffic Flow VOLUME 7, 2019 This work is licensed under a Creative Commons Attribution 4.0 License.For more information, see http://creativecommons.org/licenses/by/4.0/Management (ATFM) [12], [13] have been heavily researched and implemented in order to improve the information flow between the participating airports and contain the overall flight delays.It has been reported in the literature that the major portion of all the flight delays occurs on ground at the airports [14].These delays originating at one location propagate downstream to other airports, leading to the emergent behaviour which is called delay propagation.
Over the past few decades, research methodologies to characterize and predict delay propagation have evolved from pure statistical methods and heuristics [15], [16], to queuing models, network theory approaches, machine learning and agent based techniques [14], [17]- [19].
With regard to delay propagation, Pyrgiotis et al. [20] considered an analytical queuing and network decomposition model to characterize delay propagation.This study, however, was only able to give a macroscopic analysis of daily and hourly delay at 30 main airports of US.Rebello and Balakrishnan [21] developed a two-step approach to first classify the delay above or below a threshold and then, estimate the departure delay propagation along a link at some time in the future.Their delay classification results for a day's forecast with a threshold of 60 minutes yielded an accuracy of 72.8%.On similar lines, Belcastro et al. [22] attempted to classify and predict flight delays due to weather conditions.They reported an accuracy of 74.2% while classifying delays with a delay threshold of 15 minutes.Choi et al. [18] proposed a binary classification model to predict weather induced arrival delays of flights, which was tested on multiple algorithm like random forest, AdaBoost, kNearest-Neighbors and Decision Tree.Researchers have also explored Bayesian network models to understand the effects of delay propagation [23], [24].In one of the recent research efforts, Chen and Li [25] introduced an optimum feature selection process to improve the prediction performance of their machine learning based model and claimed to overcome the problem of feature selection, prevalent in most machine learning works in air traffic management.
Agent based modelling is a different paradigm, which has also been used in transportation studies.In the past, agent based methods have been implemented in research involving aircraft collision avoidance [26], air traffic flow management [27] and aircraft sequencing and scheduling [28].Bouarfa et al. [19] discussed the emergent phenomenon shown by air transportation systems and used an agent based model to assess the safety risk of an active runway crossing; due to the dependency of safety on the joint functions of many parameters like pilots, controllers, ground staff, technology, etc. Agent based models have also been implemented in delay propagation analysis.Fleurquin et al. [7] developed an agent based model to access the effect of three factors namely, airport congestion, aircraft rotation and flight connectivity on delay propagation by evaluating the size of the delayed airport clusters.The basis of selection of only these parameters is although not clear.In their subsequent paper [8], they extended their work to analyze the effect of meteorological disruptions (weather) in the US air traffic network.For both of the papers, aircraft were modeled as agents.

B. RESEARCH MOTIVATION
According to the Central Office for Delay Analysis (CODA), Eurocontrol, reactionary delay remained the largest cause of departure delay of the flights for July 2019 (see Fig. 1).Similar trend has been documented for the months of April, May, June, etc for 2019 and 2018 as well.In order to contain the problem of delay propagation, identifying the individual influence of major sources of delay is believed to be critical, so that remedial actions to curb delay are focused on reducing these critical parameters.It can be seen from the documented literature that the problem of flight delay has been studied with a view to predict delays due to the aggregated effect of multiple factors.Research efforts which focus on the effect of individual factors on the overall delays are mainly concentrated to predicting weather related effects, with no significant literature on predicting reactionary delays over an aircraft's flight itinerary and its influence on the total delays.With an aim to bridge this research gap, the current research provides a unique yet simple approach to predict the reactionary delays and identify cases where primary delays show a magnified and cascading effect leading to higher reactionary delays, with a case study of the Southeast Asian (SEA) airport network.This research can assist in better flight schedule planning through prior knowledge of flights expecting higher delay.We develop a multi-agent based method to evaluate the reactionary delays on various flight legs of a daily aircraft itinerary, wherein each flight is regarded as an agent.In order to maximize flight services, an aircraft normally has to undertake multiple flight legs.Given that each aircraft has a primary departure delay in the first flight leg, we let the agents (flight) travel among the airports based on their daily itineraries and predict the reactionary delays on each of the subsequent flight leg.The functionality of the proposed method is tested through a case study by analyzing the Automatic Dependent Surveillance Broadcast (ADS-B) data for SEA Airport network, for a period of six months.
A higher level abstract diagram of the central idea of research in this paper is shown in Fig. 2. The ADS-B data is filtered to extract information of departure delays, arrival delays and actual en-route time for every flight and flight itineraries are obtained.Every agent (flight) receives information regarding its initial departure delay and its schedule.The agents then, function in the airport environment according to this information and the rules discussed in Section 3. The output of this analysis is the reactionary delays for every aircraft's subsequent flight legs, predicted flight arrival and departures details for subsequent legs and the evaluation of delay multiplier index.
The document is further organized as follows -Section II documents the preliminaries of the paper.Section III describes the research problem and research methodology for reactionary delay prediction.In section IV we discuss the case study used to test the methodology, data reprocessing and discussions on the results obtained.Section V accumulates the concluding comments and the future work scopes of this research.

II. RESEARCH PRELIMINARIES A. AIRCRAFT, FLIGHT AND ITINERARY
An aircraft can be identified by its registration number, which is unique.An aircraft is tagged as a flight when it travels between different airports.As shown in Fig. 3, the aircraft with registration number 9MAQC is a different flight for each origin-destination pair.These two terminologies have been cautiously used in the paper.
An aircraft itinerary is a sequence of flights that an aircraft takes from origin to final destination.An itinerary may consist of a single or multiple flight legs, where one flight leg is an origin destination pair (see Fig. 3).

B. MULTI-AGENT BASED METHOD
Air traffic management (ATM) operations show an emergent behavior due to the combined dynamic interactions between various individual components such as human resources, technical facilities, passengers, airlines, airports, different ATM centres and other stakeholders.With the continuously increasing complexity of such ATM systems, agent based methods (ABMs) provide a suitable tool to model such systems with the desired level of abstraction [19].ABMs are suitable and can enhance the analysis of problem domains which are geographically distributed, contain subsystems in a dynamic environment and where subsystems are required to interact with the environment [30]- [32] and hence, are very suitable for applications in a complex airport network.Individual components of an dynamic, distributed system communicate with each other through simple rules.It is the interaction guided by the cumulation of these simple rules, that gives rise to complex behavior at the global level.On a similar note, agents in this method are guided by simplistic rules to interact with the environment and update their current state.The key components of the multi-agent based method used in the current research are described as below- modeled as an agent whose objective is to depart from the origin and arrive at the destination at the stipulated time and receive information from the environment regarding simultaneous arrivals or departures of multiple agents.The information of the primary departure delays of the first agent and a daily schedule are provided from the ADS-B data.
• Agent environment -For every agent, the environment corresponds to its previous departure airport and its current destination airport.All the agents in unison, function in an environment incorporating all the airports.
• Agent decisions (action and interaction) -an agent's actions involve utilizing information of scheduled departure time, scheduled en-route time, the agent's origin and destination, from the data, to complete its assigned task (travel from its origin to destination).Agents interact with the environment when there is a commonality in their origin or destination, i.e if multiple agents depart from or arrive at the same airport at the same time.In this case the agent decide their sequence of arrival and departure based on pre-defined rules.For instance, in case of simultaneous arrivals at an airport, the sequence of arrival is decided on the basis of departure delays that these agents witnessed on the flight leg.Similar rules apply for the agents departing from a common airport.

III. PROBLEM DESCRIPTION AND METHODOLOGY
A. PROBLEM DESCRIPTION An aircraft's schedule for the entire day may consist of multiple flight legs and it is prone to witnessing delay on one or all of these flight legs.The current research problem focuses on the prediction of reactionary departure delays that the aircraft witnesses on subsequent flight legs based on its delay in the primary flight leg and also, the inputs from the environment regarding the schedules of other flights.The departure delays that are obtained from the ADS-B data are 'observed delays', which can be a cumulation of multiple factors other than just the propagated delay, such as delays due to gate unavailability, ground holding due to weather or even crew unavailability at some instances, to name a few.In this research, a multi-agent based method has been used to predict the reactionary departure delays, i.e. the delays that have been solely propagated from the primary flight leg due to the initial departure delays, to the subsequent flight legs, The research focus i.e the SEA airport network possesses a unique characteristic of fairly short haul flights, with flight time of most flights within 2 hours (also discussed in Section IV-C, Fig. 7).With such short flight times the flights that incur delay during departures are unable to recover the delay en-route and most of the times, have a delayed arrival at the destination.This claim is also supported in Fig. 7 by the plot between departure delays and the subsequent arrival delays, which is linear, signifying the inability of the flight to recover delays.

B. METHOD OVERVIEW
In the proposed methodology, every flight acts as an agent which carries out its own flight schedule in an environment of multiple airports, receives information regarding arrivals and departures of other agents from the environment and updates its schedule accordingly.In this process generation of reactionary delays takes place.An overview of the methodology is shown by a flowchart in Fig. 5.

C. RESEARCH ASSUMPTIONS AND REASONS
In order to solve the research problem given in the above section, the following assumptions together with their corresponding reasons are provided below.

1) One of the fundamental assumptions in the current
work is that the flights do not witness or absorb delays enroute their destination.Similar assumption has been made for the delay analysis in existing works [35].Further, for the SEA region, the majority of flight are short haul (see Fig. 7 for reference).It can be argued that due to smaller enroute times, recovering delays enroute is not feasible.2) Further, flight arrival and departure take place at separate runways at every airports considered in the analysis.This has been done to relatively simplify the model and keep it generic in nature.3) A flight is classified as delayed if the arrival or departure takes place 15 minutes after the scheduled time.This is in reference to the delay definition used by the Federal Aviation Administration (FAA) [36].4) It has also been hypothesized that no flight can departure more than 5 minutes prior to its actual departure.
If a flight has an early departure of more than 5 minutes, the actual departure time is set to be equal to the scheduled departure time.5) The minimum turn around time for every flight has been fixed at 70 minutes.This is based on the data analysis in section IV-C.The abbreviation used in the algorithms have been mentioned in Table 1.
Based on the above assumptions, we then predict T AD f i and T AA f i for all f i ∈ [1, N f ] in the following way.
1) If f i is the first flight leg of an aircraft's itinerary, then we estimate T AD f i as 2) If f i is an intermediate flight leg of an aircraft's itinerary, then we calculate T AD f i in the following ways. When The term T ED is the maximum early departure time which is set to be 5 minutes, and the term TAT is the minimum turnaround time which is set to be 70 minutes.
When T AA f i−1 + TAT f i < T SD f i − T ED , then we set 3) Based on T AD f i , we then update T AA f i as The algorithm starts with a daily itinerary generated from the ADS-B data.For an aircraft's flight itinerary, the first agent (flight) has its specified actual departure time and the primary departure delay and it departs from the origin at that specified time.In case of multiple departures at the same time from an airport, we propose a departure sequence management principle, which is explained in Algorithm 1.
A list of all origin and destination airports is obtained for all agents (flights) from the itinerary and is filtered to obtain the list of agents departing at time T .A list of unique origins is the obtained and the agents departing from common airports are identified.
Step 5 of the algorithm sequences the flights in case multiple agents depart from the same airport.The agents are sequenced in the increasing order of magnitude of delays, for the case when departure delays are different.If the departure delays are a combination of negative and positive delays, the agents with positive delays are sequenced first, followed by the agents with negative delays, all on the basis of the previous rules.For the rare case of same departure delays, random sequencing has been adopted.After an agent departs for the airport, the other agents are assigned a delay T δ .For every departing agent, its arrival time at the destination is updated.

E. ARRIVAL SEQUENCE MANAGEMENT PRINCIPLE
The algorithm for arriving agents (flights) follows the same logic as the departure sequence assignment mechanism.For the flights arriving at an airport at the same time, Algorithm 2 is followed to sequence them for arrival.Similar to the case of departure sequence management, Step 4 of the algorithm defines the rules for sequencing the arriving flights at an airport.When the arrival delays are different, the arriving flight are sequenced in the increasing order of their magnitude of delays.If the arrival delays are a combination of negative and positive delays, the flights with positive delays are sequenced first, followed by the flights with negative delays.For the case of same arrival delays for all flights arriving at an airport, random sequencing has been adopted.The sequencing of the arriving and the departing flights is fundamentally based on 'first come first served' principle but this is applicable if the arrivals and departures are at different times.Due to delays, if multiple departures are scheduled at the same time at a given airport, we assign a departure delay of 2 minute to the next sequenced flight, to compensate for the vortex effects.The Manual of Standards-Air Traffic Services, Civil Aviation Authority of Singapore (CAAS), [37] mentions a 2 minute separation while take-off and landing when a medium category aircraft follows a heavy category aircraft and a 3 minutes separation when a medium category aircraft follows a super heavy category aircraft.This value has been standardized to 2 minutes for the current research considering that the majority of aircraft used for short haul flight are medium and heavy aircraft.For flights arriving at a common airport, if the final approach fix is the same due to the delays associated with the flights (which we refer to as simultaneous arrival for the current research), we assign a 2-minute delay to the arriving aircraft which, on a higher abstraction level represents the ATC actions such as holding the aircraft in order to maintain the separation standards.

IV. CASE STUDY A. ADS-B DATA
The findings represented in the current paper have been obtained using the ADS-B data for the months of June, July, September, October, November and December 2016, Related variables and their definitions.
procured from Flight Aware.The ADS-B data, out of the many parameters, provides information regarding the flight ID, registration number, origin, destination, actual departure time, actual arrival time, en-route time, scheduled and actual block in time and block out time.
Through the ADS-B data, the following information for each flight leg can be derived- The terminologies used in these equations are defined in Table 2.

B. SOUTHEAST ASIAN AIRPORT NETWORK
An air transport network is usually described and visualized as a graph with nodes indicating the airports and the edges  indicating the flight movements between the airports [38], [39].The Southeast Asian Airport Network can be visualized as an undirected network where the nodes represent the airports and the edges highlight the flights between the airports, as shown in Fig. 6.Contrasting geographical and weather conditions, relatively smaller flight duration in the SEA as compared to the US, and the lack of research inclination to this region has been the driving factor to analyze the SEA airport network.
The concept of centrality is used to identify the most important or central nodes in this network [40].Out of a multiple centrality measures like the degree centrality, between centrality, eign-vector centrality and closeness centrality, we choose degree centrality as the most apt for our analysis.Degree centrality is a measure of the number of connection or the number of edges connected to a node.The airports with highest degree centrality are shown in Table 3.Through this analysis we can identify the 20 most important airports from a total of 136 airports (ICAO codes) in the Southeast Asian Airport network.

C. STATISTICS FOR FLIGHTS IN THE SEA
ADS-B data for six months in 2016 is analyzed to draw initial inferences regarding the active airports, number of flights and delay patterns of the Southeast Asian airport network.The basic statistics for the flight data are provided in Fig. 7.
The monthly active number of airports can be seen in the first subfigure of Fig. 7.There are on average, 130 airports in operation in each of the studied months.The number of active airports in December is the highest.Also, the number of flights are the highest in July and December.
The third subfigure demonstrates the average departure delays as well as overall delays for the flights operated in the studied six months.We can see from the figure that the departure delays and the overall average delays are around 22 minutes.Since in July and December the flight activities are the highest, the average delays in this two months are also the largest, above 25 minutes as can be seen from the figure.
The second row of Fig. 7 further visualizes the probability distributions of arrival and departure delays of the flights TABLE 3. Top twenty airports in the Southeast Asia.The un-weighted degree represents the number of airports to which the current airport is connected.Weighted degree represents total arrivals to and departures from the current airport.
operated in the SEA.The plots show that arrival and the departure delays show similar trends over the months.In the literature, it has been reported that flight delays normally follow Weibull distribution.To verify whether this phenomenon also applies to flights in the SEA, we use three probability distribution functions, i.e., Weibull (1), Lognormal (2), and Exponential (3) [41], [42] to fit the departure delay distributions.The PDF of those three distributions are given below. (2) In the above equation, k is the shape and λ is the scale parameter, µ is the expected value (mean) and σ is the standard deviation.Table 4 lists out the statistics for the curve fittings of the departure delays.For each curve fitting we record the R 2 and RMSE values.We also record the confidence intervals for the parameters in the corresponding probabilistic distribution function at the significance level of 95%.
The R 2 test and the RMSE show the maximum value of 0.8533 and minimum value of 0.0034, respectively, for the Weibull distribution.The curve fitting results shown in Table 4 indicate that the delays of the flights operated in the SEA also follow the Weibull distribution.Capturing the correlation between departure delays from the previous airport and the arrival delay to the destination airport reveals that except for a few outliers, most of the flights that depart late tend to arrival late at the destination i.e a flight that witnesses positive departure delay will have a positive arrival delay.This is also the reason that the subsequent analysis focuses on departure situations.Plotting the distribution of the turn around time (TAT) reveals that majority of flight have a turn around time of 60 to 70 minutes.Hence, a TAT of 70 minutes is chosen for the analysis.
The distribution of the flight en-route time have also been analyzed it it can be see from the last subfigure that majority of flight are short haul, with en-route time between 40 to 120 minutes.

D. FLIGHT ITINERARY EXTRACTION
The experimental design focuses on the airport network of 11 Southeast Asian countries namely Indonesia, Vietnam, Cambodia, Malaysia, Singapore, Laos, Myanmar, Thailand, Philippines, Brunie and Timor-Leste.The time horizon for itinerary generation has been kept as one day for the analysis.In order to choose a starting time to obtain primary delays and generate flight itineraries, the number of hourly departures of the flights are plotted.It is visible from Fig. 8 that the time period between 16:00 hours (UTC) and 20:00 hours (UTC) has the minimum departure activities.Hence, the starting time point of the itinerary is chosen from 19:00 hours (UTC) since this time is a relatively low activity period [7].

E. ANALYSIS OF REACTIONARY DELAYS
The method is tested on 2 days with the highest average delay and 2 days with lowest average delay from each of the six months, for the analysis of reactionary delays.summarizes the delay information of the studied 24 days.The values of average delays are in minutes.
For each studied day, we extract a one-day flight itinerary from the ADS-B data with the starting time point being chosen in the way described in subsection IV-D.We then apply the proposed agent-based method to the one-day flight itinerary to evaluate the reactionary delays for the flights contained in the itinerary.Fig. 9 demonstrates the two-day comparisons between the predicted departure delay values (blue dots) yielded by the proposed agent-based method and the original flight departure delays (red dots) as recorded in the ADS-B data.The first set of images (row 1) are for 8 th July 2016 and the second set is for 9 th June, 2016.It can be seen from the figure that the predicted results for departure delay (blue markers) overlap the departure delay obtained from the ADS-B data (red markers).The RMSE for these two days are 16.21 minutes and 29.18 minutes, respectively.From the residual plots, few instances of outliers can be detected where the residuals are abnormally positive and negative, which may be a reason  of higher RMSE values.Similar plots can be generated for all the critical days.An interesting conclusion can be drawn from these plots.The agent based method predicts reactionary delay only on the basis of primary delays and the information of other agents during arrivals and departures.The close proximity of these results to the actual delays suggests that most of the flights suffer form delays which originate from the first flight leg.For the 24 tested days, we further calculate the delay classification accuracy based on the reactionary delays.During the calculation, a flight is classified as delayed if the delay is 15 minutes or more than the scheduled time of departure.
Table 6 records the delay classification accuracy for the 24 studied days.In addition to this, average classification accuracy for all the days of the dataset, for a delay threshold of 15 minutes is obtained, which is 80.7%.Here, accuracy implies the flights which were delayed according to the data and were correctly classified as delayed by the model.The average value of recall (true positive rate) is 78.1%.By comparing these values with the existing literature, [21], [22] it is visible that the current multi-agent based method is able to match the accuracy with significantly less input data.Their delay classification results by Rebello and Balakrishnan [21] for a day's forecast with a threshold of 60 minutes yielded an accuracy of 72.8%.On similar lines, the machine learning algorithm proposed by Belcastro et al. [22] classifies flight delays due to weather conditions with an accuracy of 74.2%, with a delay threshold of 15 minutes.
The predicted departure delays on each aircraft's itinerary can be visualized as in Fig. 10.The departure delays on the subsequent flight legs constitute the reactionary component of departure delays.The figure on the left shows the predicted departure delays in the itinerary of a aircraft with 4 flight legs.The itinerary starts with an initial departure delays of 9 minutes from RPVM to RPLL.The Subsequent departure delays from RPLL to RPVD, RPVD to RPLL and RPLL to RPVK are 5, 30 and 31 minutes respectively.The lines are weighted according to the departure delay witnessed at the airport of the flight leg.Hence, here the relative weights are 1.8, 1, 6 and 6.2.The lines do not represent the actual trajectory of flight.Some lines have been curved to provide better visibility.
The figure on the right side has an itinerary of 5 flight legs, starting at WADD.From the predicted departures delays, it is visible that the initial departure delay of 28 minutes escalates to 46, 52 and 86 minutes for the departure in 2nd, 3rd and 4th flight leg.Thus, the weights on the lines are 1, 1.6, 1.8, 3.07, which are proportional to the predicted departure delays.From the ADS-B data, it is observable that for the first three flight legs of this itinerary, the scheduled turn around time are relatively shorter, which leads to the cumulation of delays over subsequent flight leg.The turn around time before the start of the 5th flight leg is 2hours and 28 minutes, which helps in absorbing the majority of the previously propagating departure delay.These two cases highlight the instances where primary departure delays visible magnify over the subsequent flight legs.The results on delays witnessed by each agent can contribute to develop a global picture as to which aircraft itineraries in a daily schedule witness significant magnification of the primary delays into higher reactionary delays Thus, the concept of delay multiplier [4]   departure delay over the subsequent flight legs of the aircraft and its primary departure delay at the start of the itinerary.The delay multiplier (D.M) can be described as - Here, D P is the primary departure delay and D R denotes the reactionary departure delay.The D.M, here, measures the ratio of the total departure delay in a flight's itinerary to the primary departure delay that it witnessed.Fig. 11 shows the distribution of delay multipliers for 3 out of the 24 critical days.It is evident from the probability distribution of the delay multipliers that for these days, the majority of values lie between 1 and 1.5.This implies that for most of the aircraft, the primary departure delays do not significantly propagate and magnify into reactionary delays.Some minority cases are visible where D.M values are significantly higher, signifying higher delay propagation over the subsequent flight legs as reactionary delays.

V. CONCLUSION
Delays are inherent in an air transportation network and and are detrimental to this transportation system as a whole.Flight delays occur and propagate due to a multitude of factors and identifying the major sources of delay can help in containing delays, if not completely mitigating them.This paper presents a multi-agent based method to predict the reactionary delays in an airport network and adopts the SEA region a case study.Each flight is modeled as an agent which operates in airport environment.Through this analysis, the reactionary departure delays in an aircraft's itinerary, emanating solely due to the primary departure delay witnessed by flights at the beginning of their first flight legs, are predicted.Each agent (flight), after experiencing an initial primary departure delay, operates in a dynamic airport environment consisting of other agents arriving and departing at stipulated times.Through the complex interaction of a multitude of agents with the airport environment, the primary delay of agent cascades further into reactionary delay.Such predictions can aid in better flight schedule planning through prior knowledge of potential delays on different flight legs, when the prediction of other events which may cause delays, such as en-route weather, airport services and equipment being unserviceable, are significantly uncertain.
The results on classification of flights as delayed or un-delayed show an average accuracy of 80.7% for a period of 6 months with a delay threshold of 15 minutes.This value is at par with the existing literature on delay propagation prediction.This method utilizes the information of the primary value of departure delay and the scheduled arrival and departure times of the agents (flights), unlike the other machine learning algorithms requiring multiple features, training and test sets.The evaluation of the delay multiplier for the SEA region highlights that the majority of values are in the range of 1-1.5.As the values of D.M increase, it suggests an increased contribution of the reactionary delays to the overall delay associated with an aircraft's itinerary.In other words, magnification and cascading of primary delays into reactionary components.The obtained range of D.M (1-1.5)indicates that for the SEA region, the primary delays do not significantly cascade and magnify to reactionary delays for most aircraft itineraries.There are some cases of itineraries where the magnified cascading effect of primary delays are witnessed.This method also enables evaluation of individual flight legs where the departure delay propagation is significantly high and at what stage the delay is absorbed.For instance, in Fig. 10, for the itinerary WADD-WMKK-WSSS-WADD-WIII, the departure delays of 86 minutes in the 4 th flight leg is absorbed during the departure of 5 th flight leg due to the turn around time of 2 hours and 28 minutes.
The methodology developed in this research is simple and generic but is able to provide key insights on the case study of the SEA Airport network and the behavior of delays in this region.This research problem can further be fine tuned by modelling the flight crew, ground staff and passengers as agents affecting the delay and contributing to the delay propagation effect.An analysis of these factors on individual aircraft's primary and reactionary delays can be done.Also, with the information of passenger distribution to and from flights, this research can be extended to evaluate delay propagation trees originating from individual flights, i.e the effect of delay of one flight on the other flights who have connecting passengers from it.

ANNEX
The tables below show the classification accuracy for each day, based on a delay threshold of 15 minutes.

FIGURE 1 .
FIGURE 1. Major causes of departure delay for July 2019 for the flights in Europe.The picture is obtained from the Central Office for Delay Analysis (CODA), Eurocontrol [29].

FIGURE 2 .
FIGURE 2. Proposed multi-agent based method for reactionary delay prediction of flights.

FIGURE 3 .
FIGURE 3. A sample itinerary of a given aircraft with two flight legs.

FIGURE 5 .
FIGURE 5. Flowchart of the proposed method for reactionary delay prediction.

VOLUME 7, 2019 Algorithm 1
Departure Sequence Management Mechanism 1) Define the origin and destination sequences Orgs := (O 1 , O 2 , . . ., O N f ) and Dsts := (D 1 , D 2 , . . ., D N f ) with O i and D i being the origin and destination of flight f i ; 2) Given a time point T , ∀i ∈ [1, N f ], get the flight sequenceF := (f i , f j , . . ., f k ) with t AD f i = T ; 3) Get the subset Org = (O F i , O F j , . . ., O F k ) with O F ibeing the origin of flight f i ∈ F; 4) UniqOrg = unique(Org); //identify the unique origins 5)For i = 1 to length(UniqOrg), do a) F = find(Org == UniqOrg(i)); // F ⊂ F b) T DD F = T − T SD F ; //delays for all f i ∈ F c) If size(unique(T DD F )) == 1, i.e., all f i ∈ F have the same departure delay, then randomly select a f i from F ; d) If max(T DD F ) ≤ 0, then select the f i from F with the largest departure delay; e) If min(T DD F ) ≥ 0, then select the f i from F with the smallest departure delay; f) If min(T DD F ) < 0 ∧ max(T DD F ) > 0, then from the flights with nonnegative delays select the f i with the smallest departure delay; g) Set T AD f i = T and set

Algorithm 2
Arrival Sequence Management Mechanism 1) Given a time point T , ∀i ∈ [1, N f ], get the flight sequence F := (f i , f j , . . ., f k ) with T AAf i = T ; 2) Get the subset Dst = (D F i , D F j , . . ., D F k ) with D F i being the destination of flight f i ∈ F; 3) UniqDst = unique(Dst); //the unique destination 4) For i = 1 to length(UniqDst), do a) F = find(Dst == UniqDst(i)); // F ⊂ F b) T AD F = T − T SA F ; //delays for all f i ∈ F c) If size(unique(T AD F )) == 1, i.e., all f i ∈ F have the same arrival delay, then randomly select a f i from F ; d) If max(T AD F ) ≤ 0, then select the f i from F with the largest arrival delay; e) If min(T AD F ) ≥ 0, then select the f i from F with the smallest arrival delay; f) If min(T AD F ) < 0 ∧ max(T AD F ) > 0, then from the flights with nonnegative delays select the f i with the smallest arrival delay; g) Set T AA f i = t and set

FIGURE 6 .
FIGURE 6. Southeast Asian Airport Network.The airports are weighted according to the degree centrality, where bigger dots imply higher connectivity.

FIGURE 7 .TABLE 4 .
FIGURE 7. Statistics of flight over a period of 6 months (June, July, September, October, November and December) obtained from the ADS-B data.

FIGURE 8 .
FIGURE 8. Hourly flight departures plotted for a period of 6 month to select starting time point and primary delay on the basis of minimum flight activity period.It shows a total of 202 flights departing between the time period of 19:00 -19:30 hours (UTC).

FIGURE 9 .
FIGURE 9. Comparisons of departure delay values for each flight obtained from the ADS-B data (red) and the predicted departure delays by the multi-agent based method (blue).Figures in the second column show the residuals of the two values for every flight.

FIGURE 10 .TABLE 5 .
FIGURE 10.Departure delay visualization on subsequent flight legs of two flight itineraries for 8 th July 2016, highlighting the propagation of primary delays.

TABLE 6 .FIGURE 11 .
FIGURE 11.Delay multiplier calculated from the predicted reactionary delays for three of the chosen problematic days.Figures on the left show the delay multipliers for each aircraft.Probability of the delay multiplier values are plotted on the right.

TABLE 1 .
Definitions of parameters used in the proposed method.

Table 5
is invoked to evaluate a ratio, based on the downline reactionary