Modeling Disruption Propagation in Networks: An Application to Airline Delays

Abstract

Propagation of disruptions across networks is a feature of the modern economy. An example of disruption propagation is in airline networks where disruptions, like hurricanes, cause delays which propagate through the network. Modeling the propagation of delays in airlines is difficult due to the complexity of schedules, the size of the network, and the inter-temporal nature of propagation. We propose a new parsimonious framework called time-lagged subordinated Markov chains to model propagation in networks directly from the delay data. We also develop an algorithm to calibrate the model and estimate the lag and the intensity of delay propagation across the nodes of the network. Through simulation, we quantify the total impact of propagation on delay times in the network and the contribution of each airport to delays for four airlines in USA. Our research helps managers separate the quantum of propagated delays from total delays, and identify the nodes in the network with the highest impact on propagation of delays.

Keywords: Network Propagation, Continuous-time Markov chains, Subordinated stochastic processes, Airline Delays