Despite measures to reduce congestion, occurrences of both recurrent and non-recurrent congestion cause large delays in road networks with important economic implications. Educated use of Intelligent Transportation Systems (ITS) can significantly reduce travel times. We focus on a dynamic stochastic shortest path problem: our objective is to minimize the expected travel time of a vehicle, assuming the vehicle may adapt the chosen route while driving. We introduce a new stochastic process that incorporates ITS information to model the uncertainties affecting congestion in road networks. A Markov-modulated background process tracks traffic events that affect the speed of travelers. The resulting continuous-time routing model allows for correlation between velocities on the arcs and incorporates both recurrent and non-recurrent congestion. Obtaining the optimal routing policy in the resulting semi-Markov decision process using dynamic programming is computationally intractable for realistic network sizes. To overcome this, we present the edsger⋆ algorithm, a Dijkstra-like shortest path algorithm that can be used dynamically with real-time response. We develop additional speed-up techniques that reduce the size of the network model. We quantify the performance of the algorithms by providing numerical examples that use road network detector data for The Netherlands.

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Transportation Research Part B: Methodological
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Levering, N., Boon, M., Mandjes, M., & Núñez Queija, R. (2022). A framework for efficient dynamic routing under stochastically varying conditions. Transportation Research Part B: Methodological, 160, 97–124. doi:10.1016/j.trb.2022.04.001