A piecewise-deterministic Markov model of freeway accidents

TitleA piecewise-deterministic Markov model of freeway accidents
Publication TypeConference Papers
Year of Publication2014
AuthorsJin, L., and S. Amin
Conference Name53rd IEEE Conference on Decision and Control
Date PublishedDec
Keywordsaccident-prone freeway control, Accidents, CTM, freeway accidents, freeway traffic dynamics modeling, intra-modal representation, linear systems, macroscopic traffic state, Markov processes, nonlinear cell transmission model, nonlinear dynamical systems, nonlinear dynamics, PDMP, piecewise-deterministic Markov model, Piecewise-deterministic Markov process, piecewise-linear dynamics, qualitative property, road safety, road traffic control, state-dependent congestion level, stochastic switched system, stochastic transitions model, Switched dynamical systems, Switches, Traffic control, Traffic modeling and control, Trajectory, Vectors

This article develops a piecewise-deterministic Markov process (PDMP) for modeling freeway traffic dynamics due to random incidents. The random uncertainties in the occurrence and clearance of freeway accidents are modeled as stochastic transitions between a set of discrete modes. For a given accident location, the transition rates from an accident mode are determined by state-dependent congestion level. The impact of an accident is captured as reduced capacity at the location of the accident. The macroscopic traffic state within each accident mode evolves according to the nonlinear cell transmission model (CTM). The resulting stochastic switched system admits an intra-modal representation, where the nonlinear dynamics can be represented as piecewise-linear dynamics. This piecewise linear dynamics naturally leads to a PDMP representation. Some qualitative properties of a two-cell example are studied. Finally, a few design implications for control of accident-prone freeways are discussed.