A stochastic model of traffic flow: Theoretical foundations

Jabari, Saif Eddin; Liu, Henry

doi:10.1016/j.trb.2011.09.006

Cited by 112 publications

(79 citation statements)

References 22 publications

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“…Most studies have considered stochastic cell-transmission models (CTMs; Boel and Mihaylova;Sumalee et al;Jabari and Liu;. Boel and Mihaylova (2006) consider the sending and receiving functions of the CTM as random variables.…”

Section: Introductionmentioning

confidence: 99%

“…The evaluation of the model involves computationally intensive sampling in order to estimate the main link performance measures. Jabari and Liu (2012) consider headways to be random variables. The fluid limit of their stochastic model is consistent with the CTM.…”

Section: Introductionmentioning

confidence: 99%

“…The stochasticity results from adding noise in the form of a second-order wide-sense stationary process to otherwise deterministic model variables. Jabari and Liu (2012) detail the limitations of using such types of noise terms.…”

Section: Introductionmentioning

confidence: 99%

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Capturing Dependency Among Link Boundaries in a Stochastic Dynamic Network Loading Model

Osorio

Flötteröd

2015

Transportation Science

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This work adds realistic dependency structure to a previously developed analytical stochastic network loading model. The model is a stochastic formulation of the link-transmission model, which is an operational instance of Newell's simplified theory of kinematic waves. Stochasticity is captured in the source terms, the flows, and, consequently, in the cumulative flows. The previous approach captured dependency between the upstream and downstream boundary conditions within a link (i.e. the respective cumulative flows) only in terms of time-dependent expectations without capturing higher-order dependency. The model proposed in this paper adds an approximation of full distributional stochastic dependency to the link model. The model is validated versus stochastic microsimulation in both stationary and transient regimes. The experiments reveal that the proposed model provides a very accurate approximation of the stochastic dependency between the link's upstream and downstream boundary conditions. The model also yields detailed and accurate link state probability distributions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Capturing Dependency Among Link Boundaries in a Stochastic Dynamic Network Loading Model

Osorio

Flötteröd

2015

Transportation Science

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“…But it lacks an additive noise term to approximate the traffic flow. A stochastic traffic flow model is offered in Jabari and Liu [10]. This renders accounts stochastic for the uncertainty in driver gap choices.…”

Section: Introductionmentioning

confidence: 99%

An Analysis of Vehicular Traffic Flow Using Langevin Equation

Koşun

Çelik

Ozdemir

2015

PROMET

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“…Helpful guidelines for traffic engineers about the study and application of counting distributions are also contained in Gerlough and Huber (1975) and in May (1990). After a few decades theoretical research has restarted and some works in the field have been produced by Jabari and Liu (2012), Clementi, Monti and Silvestri (2011) and Cao, Tai and Chan (2012) who have analysed some statistical models for counting distributions.…”

Section: Introductionmentioning

confidence: 99%

Update on the Statistical Analysis of Traffic Countings on Two-Lane Rural Highways

Mauro¹,

Branco²

2013

MAS

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This paper deals with the problem of model identification, calibration and validation for traffic countings on two-lane rural highways. A criterion for preliminary selection of arrival laws as a function of appropriate sample statistics and a technique for deciding whether sample data sets of traffic counting are congruent with stationary time series behavior are suggested; besides arrival laws currently used in research and engineering practice, the Neyman distribution has been also applied although it is not frequently implemented in the field of traffic engineering. Moreover, this work aims at applying these methods to a set of empirical data derived from a recent survey on two two-lane rural highways; the arrival laws that best agree with the observations are found and the relations between the parameters identifying the arrival laws and the flow rates are worked out. Finally, the results have been compared to those achieved in similar observations, carried out by one of the authors in the past.

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A stochastic model of traffic flow: Theoretical foundations

Cited by 112 publications

References 22 publications

Capturing Dependency Among Link Boundaries in a Stochastic Dynamic Network Loading Model

Capturing Dependency Among Link Boundaries in a Stochastic Dynamic Network Loading Model

An Analysis of Vehicular Traffic Flow Using Langevin Equation

Update on the Statistical Analysis of Traffic Countings on Two-Lane Rural Highways

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