Delay Propagation and Delay Management in Transportation Networks

Should connecting trains wait for delayed feeder trains? Or is it better for the passengers if trains depart on time? Questions of this type are the subject of delay management, which will be treated in this chapter from the point of view of the passengers. We start by discussing how delays are propagated through a public transportation network, and how such propagations can be modeled using event-activity networks. We then focus on the question of finding an optimal solution to the delay management problem in case some (known) source delays have occurred. We discuss which decisions can be made and how these can be reflected by variables and constraints in integer programming models. In particular, we show how station capacities and the limited capacity of the tracks can be taken into account. Special emphasis will be given to the discussion of passenger-oriented objective functions. We introduce several ways on how to measure the effects that delays have on passengers and explain how to include the resulting objective functions in the models. Next, we discuss solution approaches for delay management. In particular, we discuss heuristics that decompose the delay management problem and solve it within short computation times. Finally, we give some insights into delay management in practice. We review some simple delay management strategies used today and discuss recent developments that make it possible to implement more advanced methods in practice as well.