CHARACTERIZATION OF DELAY PROPAGATION IN THE AIRPORT NETWORK

Transcription

1 CHARACTERIZATION OF DELAY PROPAGATION IN THE AIRPORT NETWORK Pablo Fleurquin 1,2, *, José J. Ramasco 1, Victor M. Eguíluz 1 1 Instituto de Física Interdisciplinaria y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, E07122 Palma de Mallorca, Spain. 2 Innaxis Foundation & Research Institute, Jose Ortega y Gasset 20, E28006 Madrid, Spain * pfleurquin@ifisc.uib-csic.es ABSTRACT Complex networks provide a suitable framework to model air traffic. Previous works described the world air-traffic network as a graph with direct flights between airports as edges and passenger commercial airports as vertices. In this work we study the US airport network, in the time period We characterize the topological structure of the network and identify how the plane rotations adjust to it. The reactionary delays are supposed to propagate following the structure of this network. We analyze the properties of flight delays including the total distribution of delays, the delays per day of the week and the hour-by-hour evolution of the delays within each day. We pay special attention to the long-delayed flights, those accumulating delays longer than 12 hours, and study when and where this type of incidences is most common. The goal of this work is to gain a better understanding of the factors contributing to the reactionary delay propagation with the aim of developing models able to realistically simulate the delay propagation. This investigation is expected to help devise more efficient strategies for delay management, both from the point of view of ATM (e.g., flight prioritization criteria) and of airline planning (e.g., robust scheduling). KEYWORDS: delay propagation, complex networks, dynamic of communities, queuing model, ATM. CLASSIFICATION: Operations Research in Air Transport: Modeling and/or Applications, Airport and Airline Performance. Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 1

2 INTRODUCTION The use of network analysis to characterize complex systems has become widespread in the last decade. The potential of graphs for describing social systems was pointed out almost a century ago (see Freeman 2004 for a review). However, the generalization of these concepts and tools had to wait much longer, after the seminal works by Watts and Strogatz 1998 and by Barabasi and Albert Ever since complex networks have been applied in a growing range of disciplines such as technology (Huberman et al. 1999), biology (Jeong et al. 2001), sociology (Castellano et al. 2009), or economy (Mantegna et al. 2007). The application of network theory to air transportation has a much shorter history, for which the first results were published in 2004 and The world airport network is described as a graph formed with the passenger commercial airports as vertices and the direct flights between airports as edges (Barrat et al. 2004, Guimera et al. 2005). Each edge also bears a weight corresponding to the number of seats available in the connection. The main source of this database is IATA; while some other studies have presented data from the US Bureau of Transport Statistics (BTS) or from OAG. The initial works (Guimera et al. 2005) include a network description with an analysis of the degree (number of connections per node) and node strength (sum over the weights of the connections of a node) distributions, degree-degree correlations, density of triangles, etc. A second work (Barrat et al. 2004) focuses on the correlations between network topology and fluxes of passengers finding a non-linear relation between them:, where is the number of seats available in the connection w ij = k i k j ( ) q w ij k i between airports i and j, while is the number of connections with other airports of airport i, and q is a parameter whose value was estimated to be approximately 1/2. The world airport network has been analyzed later with graph clustering techniques (Sales-Pardo et al. 2007) to classify airports according to their connectivity patterns. US Airports network dynamics due to seasonal effects has also been investigated (Gautreau et al. 2009, Kuma Pan et al. 2011). Recently, information regarding human mobility through the airport network has also been used to model and forecast the propagation pathways of infectious diseases transmitted by contact such as influenza (Balcan et al. 2009, 2009b). Within the ATM community, even if reactionary delays have a great impact on air traffic performance, the research effort to understand delay propagation has been scarce so far, and mostly limited to a descriptive work. A good reviews of previous work on delay propagation can be found in (Belobaba et al. 2009, Jetzki 2009). Very recently, some research efforts have begun to apply network theory, in combination with stochastic modeling, to the modeling of delay propagation (Bonnefoy et al or EPISODE 3). Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 2

3 Fig. 1. US air-traffic network considering all flights from The main goal of this work is to broaden the understanding of delay propagation through complex networks theory, by analyzing the emergent networks behind air traffic, such as flights between airports, dependencies between flights, or passenger traffic. A further understanding of delay propagation is expected to lead to improved quality of service, more efficient strategies for airport congestion management, or new tools for airline planning, among others. In particular, we analyze the network formed by the airport as nodes and the flights as edges. The nature of such networks is highly dynamical since a different instance exists at every moment in time. As a practical procedure, the information is aggregated at yearly basis to generate a network per year. We analyze the topology and structure of the network corresponding to 2010 and characterize the delay appearing and propagating across it. RESULTS We used the Airline On-Time Performance Data available from the Bureau of Transportation Statistics ( This database provides information such as schedule and actual departure and arrival times, departure and arrival delays, origin and destination airports, taxi-in and taxi-out times, airline id, tail number and flight Fig. 2. Airport complementary cumulative distribution for the degree that is equivalent to the number of destinations per airport (on the left) and for the number of flights per airport (on the right). Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 3

4 date. Air carriers that exceed one percent of the total domestic scheduled-service passenger revenue, report on-time data and the causes of delay. We restricted our analysis to domestic flights conducted in the year Despite these data are 2 years old, no major changes concerning on-time performance has occurred since then. For the year 2010, 18 air carriers filed on-time performance data that combined represents 6,450,129 flights from 305 airports. From this database 1.75% were cancelled and 0.2% diverted. All scheduled domestic flights for the year 2010 (not only those from On-Time Performance Data) totalize 8,687,800 (BTS 2011), therefore the data used represent 74% of all scheduled flights in The resulting air-transportation network is composed of 305 nodes denoting airports and 2,318 edges accounting for direct connections between them. A graphical representation of the network can be seen in Figure 1. Nodes are sized according to their average delay per flight. Even though, the network is not completely bidirectional, i.e., if there is a flight from A to B there is always a flight from B to A, almost 98% of the edges are. If the network is constructed on a daily basis, 98% of the edges are bidirectional with a minimum of 92%. Small airports cause these minor anomalies. To simplify the analysis we symmetrized the network. Table 1. Major airports sorted according to their degree In Figure 2, we show the complementary cumulative distribution of degrees ( ) and the same distribution for the number of flights. Both distributions are wide and evince the heterogeneities present in the network. Some few airports are large hubs with many different connections and flights while most of the airports have low traffic. These topological characteristics are well known for this network but still are relevant for the dynamics of delay propagation. To be more precise on the central airports in the network in the sense of number of connections and flights, we are representing in Table 1 the ranking of the top 10 airports based on degree and displaying also the number of flights. In this case, the maximal degree corresponds to Atlanta International Airport (ATL) with 159 direct connections and the average degree of the whole network is Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 4

5 Fig. 3. Percentage of trajectories as a function of the number of leaps. A next issue to consider is the rotation of the planes because this is an important ingredient to characterize the propagation of reactionary delays. The database contains the tail number of the planes, which allows us to track their movements in the network. In Figure 3, we show the percentage of airplanes taking a certain number of leaps per day. It can be seen that 80% of trajectories are composed of a number of leaps between 2 and 7. Very few of the planes do longer rotations since there are time constraints for the duration of the flights and we are considering only one day. Most of these trajectories are not closed within a day but some of them follow a circular path, i.e., an airplane starts and finishes the day in the same airport. In Figure 4 we show the percentage of trajectories that are circular per day during We can see that these trajectories are a small percentage with respect to the total number of plane rotations. Fig. 4. Percentage of daily trajectories that start and end in the same airport. This finding does not mean that the trajectories cannot close taking into account longer periods of time weeks, months or years-. The airports can be classified according to the fraction of trajectories starting in them that are circular. Not Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 5

6 necessarily, these airports are the ones with highest degree (see Figure 5). This clearly indicates that the network hubs (nodes with highest degree) do not always coincide with the airlines hubs. We are assuming here that the airline hubs are those airports with a larger percentage of closed rotations. Fig. 5. Percentage of trajectories ending at an airport as a function of the airport degree. In the figure the IATA codes are: MIA (Miami), EWR (Newark), IAH (Houston) and ATL (Atlanta). We have described the topology of the network and the rotation of the flights. The next step is then to focus on the real data regarding flight delays. We plot in Figure 6 the complementary cumulative distribution of departure and arrival delays for all flights of 2010,. Firstly, we notice that just like the degree and flight distribution, the delay distribution is broad. It also shows a slight hump at large values of delays around and above 700 min. Secondly, we find that there is no significant difference for both types of delays: arrival and departure delays exhibit the same behavior. Fig. 6. Plot of the complementary cumulative distribution function of departure (black circles) and arrival (red stars) delay considering all flights of Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 6

7 Another factor that does not modify the shape of the delay distribution is the day of the week or season of the year. In Figure 7, we represent the cumulative distribution of delays for different weekdays and for the summer and winter. In both plots of the panel the baseline taken as the distribution of all flights in 2010 is also shown. As can be seen, there is no noticeable difference between the curve apart from that raising from a smaller statistics. A) B) Fig. 7. Plot of the complementary cumulative distribution function of departure delay considering all flights of In A), the continuous colour lines represent data differentiated by weekday and black circles for all flights of In B), green stars correspond to flights operated in winter, red triangles represent flights operated in summer and black circles for all flights of On the contrary, if we depict the cumulative distribution for different airports (Figure 8) a broad variety of behaviors are found. A peripheral airport like Honolulu International Airport (HNL) and two continental hubs are displayed in the Figure: Dallas/Fort Worth International Airport (DFW) and Denver International Airport (DEN). We can see that DFW and DEN still show a slight hump in the distribution but not HNL. On the other hand, Honolulu displays a broader distribution. This is probably due to the longer duration of the flights with destination or origin in HNL that allow for an easier absorption of short delays. The delays in the islands can be, therefore, much larger than those in the continent and as a consequence the distribution becomes more skewed. Fig. 8. Plot of the complementary cumulative distribution function of departure delay considering all flights of 2010 (black circles). Color symbols represents data for individual airports. In this case HNL (Honolulu International Airport) DFW (Dallas Fort Worth) and DEN (Denver International Airport). Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 7

8 In order to understand the nature of the hump in the delay distributions, we extract the flights with departure delay above 12 hours and compare them with all the flights of Plotting the departure delay as a function of the scheduled departure time we can distinguish how flights with delay > 12 hours are more abundant than the baseline at the beginning and at the end of the day (see Figure 9A). This is in contrast to flights with departure delay below 12 hours, whose distribution is almost flat. Regarding this point, we plotted the delay distribution for flights with different scheduled departure times in Figure 9B. The hump becomes more evident in the distribution of flights departing between 00am to 5am and 1pm to 11:59pm indicating a relatively higher A) B) Fig. 9. A) Probability of flight departure as a function of the scheduled departure hour. Blue bar represents the probability taking into account all flights of In red is the probability of flight departure only for those flights whose departure delay is 12 hours or more. B) Green triangles represents flights with scheduled departure from 00:00 am to 05:00 am or 01:00 pm to 11:59 pm. Black symbols represent flights with scheduled departure from 05:00 am to 00:59 pm. abundance of long delayed flights. Note that even so, these are still a small fraction of the total delayed flights. Another feature of the flights with departure delay longer than 12 hours is the relevance of the destination airport. In Table 3, we compare the data for long delayed flights with two sets of randomly selected flights: one among all the flights and the other with flights selected among those with any delay. From the data 51 airports (16.00%) are the destination of 414 delayed flights. If the 414 flights are randomly chosen, the number of destination airport increases up to 120 (more than double the results from the real data) regardless of the way we choose the flights. This means that a bias exists towards a smaller set of destination airports. Note that the same phenomenon is not observed for the departure airports that are in the same range both in the data and in the randomly selected flights. Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 8

9 Sheet1 FLIGHTS WITH DEPARTURE DELAY > = 12 HOURS FLIGHTS ORIGIN DEST DAYS TAIL AR_ID WITH PROBLEM TOTAL PERCENTAGE 0.01% 38.00% 16.00% 62.00% 7.00% 77.00% RANDOMLY CHOSEN 414 FLIGHTS FLIGHTS ORIGIN DEST DAYS TAIL AR_ID WITH PROBLEM TOTAL PERCENTAGE 0.01% 38.00% 39.00% 67.00% 8.00% % RANDOMLY CHOSEN 414 FLIGHTS DELAYED FLIGHTS ORIGIN DEST DAYS TAIL AR_ID RANDOMIZE TOTAL PERCENTAGE 0.01% 36.00% 39.00% 67.00% 7.00% % Table 2. Statistical analysis of flight with departure delay larger than 12 hours Other variables as days, tail-number or air carries remain the same. This significance of the destination airports could be related to GDP or Ground Delay Program from the FAA (FAA). This program is implemented to control air traffic volume to airports where the estimated demand is expected to surpass the Airport Arrival Rate. When a GDP is issued flights destined to the affected airport are not permitted to depart until their Controlled Departure Time. In Figure 10, we plotted the number of flights with long delays versus the ranking of destination airport with respect to the number of long delayed flights. The data correspond to the blue bars while the randomly selected set of flights are the red curve. In the data, the first 8 airports are destination of 75 % of the long delayed flights, while in the randomly selected set the first 8 airports totalize only 52 %. Page 1 Fig. 10. Ranking of the number of flights delayed 12 hours or more for the 51 destination airport from the data (blue bars) and the randomly selected airports (red line). For the sake of clarity, from the 120 destination airports from the random case we only plot the first 51 airports. Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 9

10 DISCUSSION In summary, we have analyzed the characteristics of the US airport network paying special attention to the aspects related to delay propagation of secondary delays. A network per year has been built by taking into account the direct flights connecting couples of airports and its topological properties such as the distribution of number of flights per airport or the number of destination per airport has been studied. These features were already known from previous publications in the literature so these basic results have a confirmatory value. In addition to the topology, we consider also the properties of the airplane rotation in the network and of the real delays observed. The airplane rotation shows a complicated and highly heterogeneous profile with some airplanes covering essentially back and for routes and others not closing the routes in a simple periodic way. The heterogeneity of the rotation procedures can play a role in the development and propagation of delays. Regarding the real delays, we initially focus on basic properties as, for instance, delay distributions, which show long decays both for arrival and departure delays. The long tails are usually indicative of the complex nature of the mechanisms contributing to the propagation of delays. Similar distributions have been, for example, observed in the size of human epidemics when the infectiveness is close to the propagation threshold. In this case, the system is not necessarily working under critical conditions but the combined action of several factors such as connecting passengers, a predetermined schedule and the geographical distance of the airports can contribute to reach a similar system state at a global level. We study also the properties of the flights with a delay higher than 12 hours, those in the tail of the delay distribution. The evolution of the number of these long-delayed flights along the hours of the day shows a relative concentration early in the morning or late in the afternoon. The destination airport seems to be important to understand which are the elements influencing the surge of the flights with long delay. These results are relevant in order to understand the mechanism behind the propagation of real delays. This also allows us to develop realistic models for the delay propagation at a network scale. We are now working in the implementation and testing of such models. The basic information required is the schedule of the flights, some information on the connecting passengers and crew rotations in the airports, the rotation of the airplanes and capacities of the airports to bare a certain number of operations. In some cases this information is available, in some others realistic assumptions can be needed. This type of models could provide better insights in the weak points of the system: which mechanisms, airports, practices, etc, contribute to a more efficient reactionary delay propagation and also how resilient the system is to changes in external conditions as for instance atmospheric or geologic perturbations or to regulation modifications. ACKNOWLEDGES PF is funded by the PhD program of the Complex World network of the WPE of SESAR. JJR is funded by the Ramón y Cajal program of the Spanish Ministry of Economy and Competitiveness (MINECO). Partial support was also received from MINECO through the project MODASS (FIS ). Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 10

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12 Mantegna R., Stanley E.H. (2007), Introduction to Econophysics: Correlations and complexity in finance, Cambridge Univ. Press. Sales-Pardo M., Guimera R., Moreira A.A., Amaral L.A.N. (2007), Extracting the hierarchical organization of complex systems, Proc. Nat. Acad. Sci. USA 104, Watts D.J. and Strogatz S.H. (1998), Collective dynamics of small-world networks, Nature 393, Webpages. The Air Transport Association (IATA), Bureau of Transportation Statistics (US Government), OAG, BTS 2011, FAA, Pablo Fleurquin, José J. Ramasco, Victor M. Eguíluz 12