Statistical Inverse Analysis for a Network Microsimulator

Abstract

CORSIM, a microsimulator for vehicular traffic, is being studied with respect to its ability to successfully model and predict behavior of traffic in a 36-block section of Chicago. Inputs to the simulator include information about street configuration, driver behavior, traffic light timing, turning probabilities at each intersection, and distributions of traffic ingress into the system. Data are available concerning the turning proportions in the actual neighborhood, as well as counts of vehicular ingress into the neighborhood and internal system counts, during a day in May 2000. Some of the data are accurate (video recordings), but some are quite inaccurate (observer counts of vehicles). Previous use of the full dataset involved “tuning” the parameters of CORSIM—in an ad hoc fashion—until CORSIM output was reasonably close to the actual data. This common approach, of simply tuning a complex computer model to real data, can result in poor parameter choices and completely ignores the often considerable uncertainty remaining in the parameters. To overcome these problems, we adopt a Bayesian approach, together with a measurement error model for the inaccurate data, to derive the posterior distribution of turning probabilities and of the parameters of the CORSIM input distribution. This posterior distribution can then be used to initialize runs of CORSIM, yielding outputs reflecting the actual uncertainty in the analysis. Determining the posterior via Markov chain Monte Carlo (MCMC) methodology is not directly feasible because of the running time of CORSIM. Fortunately, the turning probabilities and parameters of the input distribution enter CORSIM through a probability structure that can be almost exactly described by a stochastic network that does allow an MCMC analysis. The resulting MCMC has some novel features that should also be useful in dealing with general discrete network structures. The major conclusion of this study is that it is possible to incorporate uncertainty in model inputs into analyses of traffic microsimulators such as CORSIM, and that incorporating this uncertainty can significantly change the variability of engineering simulations performed with CORSIM. The second engineering conclusion, that traffic counts obtained by human observers can have very significant bias in a positive direction (corresponding to overcounting of vehicles), was unexpected.

KEY WORDS :

• Bayesian analysis
• CORSIM
• Discrete network
• Markov chain Monte Carlo
• Restricted parameter space
• Tuning