An Evolutionary Game Model and MCMC Estimation for Analyzing Stochastic Properties of Traffic State on a Road Network

Yuki Shittaka · Takeshi NAGAE

5 citations0/0 files storedIEEE International Conference on Agents (ICA)

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Transportation Planning and Optimization Traffic control and management Traffic Prediction and Management Techniques

Abstract

This paper proposes a novel methodology for evaluating the travel time reliability of an urban road network using latest advances in the evolutionary game theory and MCMC (Markov chain Monte Carlo). Because of the stochastic variation of congestion, the importance of travel time reliability on an urban road network is attractive for research. Moreover, analyzing the stochastic properties of travel time is essential for maintaining an urban road network reliable. Our proposed method has the following notable features: (i) it obtains a stationary distribution of traffic flow patterns which stems from a stochastic day-to-day dynamics of a population with rational users, (ii) this distribution is consistent with the traditional SUE (stochastic user equilibrium), and it is adaptable to an economical evaluation framework including cost-benefit analysis of road development projects that is standardized by government, and (iii) it can estimate the 95 percentile of minimum travel time of each OD pair for a practical size network. We first use an evolutionary game model proposed by Sandholm (2009) to describe the stochastic day-to-day dynamics of the traffic flow patterns generated by the perturbed best response of each user. This model is characterized by a stationary distribution of traffic flow patterns, and it is consistent with the SUE. We then develop a sampling method to generate sample traffic flow patterns from the stationary distribution by applying the MCMC re-sampling method proposed by Wei at el. (2012). Finally, we develop a numerical method for estimating the 95 percentile of minimum travel time efficiently applying the importance sampling and a randomized algorithm. Several numerical applications of the proposed method are demonstrated on a moderate size network.

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References

2005Population Games and Evolutionary Dynamics 2001Potential Games with Continuous Player Sets 1984An Efficient Method for Computing Traffic Equilibria in Networks with Asymmetric Transportation Costs 2005Evolution in games with randomly disturbed payoffs 2010A prospect-based user equilibrium model with endogenous reference points and its application in congestion pricing 1998Algorithms for logit-based stochastic user equilibrium assignment 2011Simulation and Estimation of Extreme Quantiles and Extreme Probabilities 2002A Second Order Stochastic Network Equilibrium Model, II: Solution Method and Numerical Experiments

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