School of Aviation

Delay Propagation Modelling & The Implications in Robust Airline Scheduling
Delay Propagation Modelling & The Implications in Robust Airline Scheduling

Schedule delays are commonly seen in airline operations, given the complex flight operation procedures, aircraft turnaround operations, passenger connections and unexpected disruptions in scheduled operations. Delays affect not only passenger satisfaction but also result in costly consequences to airline operations, e.g. delay propagation and operation disruption in airline networks. Surely, airlines can apply tactical measures such as aircraft swaps, flight cancellations, or using standby crews in day-to-day operations to control delays. However, these operations control measures also incur extra operating costs on top of existing delay costs and travel inconvenience for passengers.

Airline operations are subject to stochastic disruptions coming from many sources such as weather, passengers, and aircraft turnaround operations. Among these delay causes, some are treated as business risks, e.g. weather influence and airport congestion, while some are caused by stochastic disrupting events such as passenger boarding delays and aircraft engineering delays. The departure delay of a flight may cause inbound delays to other flights at the destination airport, if these flights are to receive connecting traffic from the delayed inbound flight such as passengers, crews and goods. Accordingly, delays may propagate through the system via connecting traffic/resources, unless controlled by built-in schedule buffer time or operational interventions by airlines. This delay propagation phenomenon can be significant in a highly connected network, e.g. a hub-and-spoke network, due to complex resources and passenger connections at hub airports.

Post-operations flight delay analysis is essential for managing and reducing delays in future schedule planning and operations. The aim of this paper is to address the problem of delay propagation in airline networks by explicitly considering the stochastic characteristics of airline ground operations at airports and the delay propagation mechanism among flights in airline networks. The causal relationship between flight delays and stochastic disruptions in airline ground operations is studied based on the delay codes. A multiple regression model is developed to describe the departure/arrival delays of individual flights based on historical delay records. A route-based recursive delay propagation model is built to address the delay propagation effect among flights connected by resources and passenger itineraries. A set of airline data is used to develop the flight-based delay model and the subsequent route-based delay propagation model. Insights from developing the delay propagation model are further discussed to address the implications of delay propagation in robust airline scheduling and operations.

Statistical analyses of delay causes from various papers show that airports and flights may reveal certain types of delay patterns, meaning that some flights are prone to incur certain types of delays and the delay patterns often persist for a long period of time (Tu et al, 2005; Wang, et. al, 2003; Wu and Caves, 2003). To account for this observation and to model the contribution of potential delay causes in aircraft ground operations, multiple regression technique is used to develop the flight-based Departure Delay Model that describes the causal relationship between departure delays (the dependent variable), inbound delays, and ground operational delays.

The delay propagation mechanism between flights is modelled by the recursive relationship between the Departure Delay Model and the Arrival Delay Model. For flight f, the Leg-based Delay Propagation Model can be derived by the recursive relationship between the Departure and Arrival Delay model. For route j, the Route-based Delay Propagation Model (RDP) can be derived by combining all the Leg-based delay propagation models recursively.

Flight-based Departure and Arrival Delay Models for an example flight are derived from flight delay data. For this flight, both the Departure and Arrival Delay Models show a good fit to the recorded flight data with the adjusted R2 values higher than 0.8. T tests and F tests also validate the statistical significance of regression coefficients and the model itself. From this sample model we can find that some variables are selected, while others are not by stepwise regression. From the overall variable selection frequency, we can see that some ground operation variables reveal strong causal relationships with departure delays in the Departure Delay Model such as passenger and baggage handling (91%), aircraft ramp handling (92%) and inbound delays (88%). Though some variables enter the stepwise regression model frequently, the impact of these variables on the dependant variable, i.e. the departure delay, is not much higher than others.

By recursively combining the Flight-based Departure and Arrival Delay Models of flights on a route, we are able to establish the Route-based Delay Propagation Model (RDP) to describe the delay propagation mechanism among flights on a route basis. We can see from Figure 1 that most Departure Delay Models fit well to the recorded sample data with high R2 values in the range between 0.9 and 0.7. The standard deviations of R2 values of the Departure Models are below 0.2, showing the general consistency of model fitness on a flight basis. On the other hand, the mean values of the R2 of Arrival Delay Models range between 0.9 and 0.7 with some routes having lower mean R2 values. Standard deviation values shown in Figure 2 also reveal that the cause of lower mean R2 values for Arrival Models is due to the variance of regression models among flights on specific routes. This means that the overall fitness of the RDP model to the study data is good but further analysis is required for those routes that have lower R2 values.

This project is supported by the Australian Research Council (ARC) Discovery project (2005-2007), Faculty of Science, UNSW and an anonymous airline.
Any comments to this work are highly welcome. Please contact Dr. Richard Wu at
This paper has been accepted for presentation in the annual meeting of Transportation Research Bureau, Washington DC, 2008. This paper is also under peer review by TRB for publication in TRR. Copyright is reserved.

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