Markov Chain Monte Carlo based inverse modeling of traffic flows using GPS data

Olli-Pekka Tossavainen; Daniel B. Work; Olli-Pekka Tossavainen; Daniel B. Work

doi:10.3934/nhm.2013.8.803

Networks and Heterogeneous Media

2013, Volume 8, Issue 3: 803-824. doi: 10.3934/nhm.2013.8.803

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Markov Chain Monte Carlo based inverse modeling of traffic flows using GPS data

Olli-Pekka Tossavainen ^{1
,},
Daniel B. Work ^{2
,}

1.
Microsoft, 1065 La Avenida St, Mountain View, CA 94043
2.
University of Illinois at Urbana-Champaign, 1203 Newmark Civil Engineering Laboratory, 205 N. Mathews Ave, Urbana, IL 61801

Received: 01 October 2012 Revised: 01 June 2013
90B20, 65C05, 65C40, 35L65, 65N21.

In large scale deployments of traffic flow models, estimation of the model parameters is a critical but cumbersome task. A poorly calibrated model leads to erroneous estimates in data--poor environments, and limited forecasting ability. In this article we present a method for calibrating flow model parameters for a discretized scalar conservation law using only velocity measurements. The method is based on a Markov Chain Monte Carlo technique, which is used to approximate statistics of the posterior distribution of the model parameters. Numerical experiments highlight the difficulty in estimating jam densities and provide a new approach to improve performance of the sampling through re-parameterization of the model. Supporting source code for the numerical experiments is available for download at https://github.com/dbwork/MCMC-based-inverse-modeling-of-traffic.
- Parameter estimation,
- fundamental diagram,
- Markov Chain,
- Monte Carlo,
- traffic flow,
- cell transmission model
Citation: Olli-Pekka Tossavainen, Daniel B. Work. Markov Chain Monte Carlo based inverse modeling of traffic flows using GPS data[J]. Networks and Heterogeneous Media, 2013, 8(3): 803-824. doi: 10.3934/nhm.2013.8.803

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Abstract

In large scale deployments of traffic flow models, estimation of the model parameters is a critical but cumbersome task. A poorly calibrated model leads to erroneous estimates in data--poor environments, and limited forecasting ability. In this article we present a method for calibrating flow model parameters for a discretized scalar conservation law using only velocity measurements. The method is based on a Markov Chain Monte Carlo technique, which is used to approximate statistics of the posterior distribution of the model parameters. Numerical experiments highlight the difficulty in estimating jam densities and provide a new approach to improve performance of the sampling through re-parameterization of the model. Supporting source code for the numerical experiments is available for download at https://github.com/dbwork/MCMC-based-inverse-modeling-of-traffic.

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