Calculation of traffic flow breakdown probability to optimize link throughput

Haizhong Wang, Kimberly Rudy, Jia Li, Daiheng Ni

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


Traffic breakdown phenomenon is prevalent in empirical traffic system observations. Traffic flow breakdown is usually defined as an amount of sudden drop in traffic flow speed when traffic demand exceeds capacity. Modeling and calculating traffic flow breakdown probability remains an important issue when analyzing the stability and reliability of transportation system. The breakdown mechanism is still mysterious to practitioners and researchers in varying manner. Treating breakdown as a random event, this paper use discrete time Markov chain (DTMC) to model traffic state transition path, as a result, a transition probability matrix can be generated from empirical observations. From empirical analysis of breakdown, we found this formulation of breakdown probability follows the Zipf distribution. Therefore, a connection from traffic flow breakdown probability to how many vehicles are occupying a certain freeway segment (e.g. a link) will be established. Following from the results, a quantitative measure of breakdown probability can be obtained to optimize ramp metering rates to achieve optimum system performance measures.

Original languageEnglish
Pages (from-to)3376-3389
Number of pages14
JournalApplied Mathematical Modelling
Issue number11
StatePublished - Nov 2010


  • Breakdown probability
  • Discrete time Markov chain
  • Throughput optimization


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