Complex World 2015 Workshop Analysis of air transportation using complex networks Pablo Fleurquin José J. Ramasco Victor M Eguíluz @ifisc_mallorca www.facebook.com/ifisc

Does the ABM model have predictive power? What are the internal key drivers behind delay propagation/reactionary delay? What are the internal key drivers behind delay propagation/reactionary delay? Does the ABM model have predictive power? Does the ABM model have predictive power? What can we say about the system robustness to external perturbations? What can we say about the system robustness to external perturbations?

Model Generalities Why ABM? What type of ABM? Which are the processes to simulate? Which are the model agents? Programming Language & computational features? Processes known. Type of understanding. Data availability. Scale model: reduction in the level of detail or complexity of the system. K.I.S.S modeling principle. Among several processes we select the ones that we thought most significant to our problem. Fundamental modeling agent: aircraft/flight Other model objects: air-carrier, airports. C++: object oriented, low-level memory manipulation & computational efficient. 1 day simulation takes on average 20 mins. Run in parallel mode.

Data specifics Database: Airline On-Time Performance Data (www.bts.gov) Schedule & actual departure (arrival) times Origin & destination airports Airline id Tail number In numbers: 6,450,129 flights (74 %) 18 carriers 305 airports Network: Nodes: airports Edges: direct flights between airports Node attributes: average delay per flight

Modeling details Flight rotation (same tail number) Airport Congestion Ts Schedule (arrival/departure) Flight connectivity (different tail number) ΔT α Modeling details Airport Congestion Schedule Airport Arrival Rate (SAAR) First Arrived First served β Initial Conditions From the data… Known  when, where and the departure delay for the first flight of the sequence. Random initial conditions… Fixed initial delay (min) % of initially delayed planes In order to analyze how this dynamic is generated and evolves, we developed an agent-based model (in which agents are the 4 thousand aircrafts that are part of the system every day) and also the model is data-driven because it takes into account the actual schedule and the aircraft itinerary for each day. The model has three internal mechanisms to propagate the delays: the rotation (or path) of the aircraft itself, the connectivity between flights and airport congestion. The first mechanism is the rotation of the aircraft. It is clear that if a plane that goes from Palma to Madrid through Barcelona and is delayed in Palma, probably the next flight leg from Barcelona-Madrid is going to be delayed. Provided that the ground time in Barcelona is not sufficient to absorb the delay. This mechanism includes the schedule and a minimum service time accounting for the operations at the airport. The second mechanism considers the connection between flights of the same airline. Through this subprocess a flight may be delayed because it has to wait for passengers or crew from another flight. As we have no information of which flight is connection of which other we randomly select the connections. Allowing for a 3-hour time window prior to the schedule departure of a particular flight we consider as possible connections the schedule arrivals of the same company within that time window. To modulate the effect of the flight connectivity we consider the connectivity parameter. As we will see afterwards only by adjusting this parameter the model is able to reproduce what we observed in reality. Finally by the internal mechanism of airport congestion we take into account nodes with finite capacity. The capacity is measured according to the Scheduled airport arrival rate. As you can see in the figure this rate varies over time and is different for each airport so this introduces more heterogeneity in the system. According to this mechanism if the Real Rate of arrivals exceeds the Schedule rate the next plane will become part of the airport queue waiting to be served. The protocol is First Arrived - First served. The initial conditions can be of two types. Same initial conditions as found in the data, ie for the first flight of an itinerary we know when, where and with what intensity happened. Or taking random initial conditions according to a fixed value of delay and a percentage of initially delayed flights.

Results Predictive power: 70% accuracy Key drivers: Crew & Passenger connectivity, reinforcement flights Influence of schedule on system robustness & external perturbations Explore Trees of Reactionary Delays Let us now compare the model results with what has actually happened. This figure shows the results for the March 12 and April 19 (the best day in terms of delay). Importantly, we performed the comparison for every day of the year and we found that the model reproduces very well the data. For every day the connectivity parameter is fitted and we use the nominal capacity of each airport (ie beta equal to 1). Figures show the evolution of the size of the largest cluster throughout the day. As we can see the selected days have a very different behavior. Another question we want to answer with the model is which internal mechanism is more efficient for propagating the delays. To do so we can turn on or off the different mechanisms. In the right figure flight connectivity and airport congestion mechanisms are turned off. In this case by only taking into account the rotation of the plane is not possible to generate a wide congestion as observed in the real data. The same applies only with airport congestion and aircraft rotation.  So, only considering flight connectivity (ie assuming infinite capacity nodes) the answer is positive, concluding that this process is the most important one.