A piecewise-deterministic Markov model of freeway accidents

Li Jin, Saurabh Amin

Research output: Contribution to journalConference article

Abstract

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.

Original languageEnglish (US)
Article number7039649
Pages (from-to)1733-1740
Number of pages8
JournalProceedings of the IEEE Conference on Decision and Control
Volume2015-February
Issue numberFebruary
DOIs
StatePublished - Jan 1 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

Fingerprint

Highway systems
Deterministic Model
Accidents
Markov Model
Piecewise Deterministic Markov Process
Piecewise Linear
Markov processes
Traffic Dynamics
Switched Systems
Qualitative Properties
Cell
Clearance
Stochastic Systems
Congestion
Nonlinear Dynamics
Traffic
Uncertainty
Dependent
Modeling

Keywords

  • Piecewise-deterministic Markov process
  • Switched dynamical systems
  • Traffic modeling and control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

A piecewise-deterministic Markov model of freeway accidents. / Jin, Li; Amin, Saurabh.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2015-February, No. February, 7039649, 01.01.2014, p. 1733-1740.

Research output: Contribution to journalConference article

Jin, Li ; Amin, Saurabh. / A piecewise-deterministic Markov model of freeway accidents. In: Proceedings of the IEEE Conference on Decision and Control. 2014 ; Vol. 2015-February, No. February. pp. 1733-1740.
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