Probabilistic Graphical Models of Fundamental Diagram Parameters for Simulations of Freeway Traffic

Freeway traffic simulations must account for the probabilistic nature of model parameters to capture observed variations in traffic behavior. Fundamental diagrams specify freeway section parameters describing the flow–density relationship in macroscopic simulation models. A triangular fundamental diagram—specified with the free-flow speed, congestion wave speed, and capacity—is commonly adopted in first-order cell transmission models. Capacity (defined as the maximum flow observed in a given freeway section over a particular day) exhibits significant day-today variation, and capacity variations across different sections of the freeway are significantly correlated. Free-flow speeds do not exhibit significant variation, but congestion wave speeds exhibit variation uncorrelated with section capacities or parameters from other sections. A probabilistic graphical approach is presented to model the probabilistic distribution of fundamental diagram parameters of an entire freeway section chosen for simulation. More than 1 year of data from dozens of loop detectors along a 25-mi section of the I-210 freeway westbound in Los Angeles, California, are used for demonstration. The parameters of the distribution are estimated with the expectation–maximization algorithm to account for missing observations. Model selection from among plausible models indicates that a first-order spatial Markov model is appropriate to capture the capacity distribution, which is the joint probability distribution of freeway section capacities. Stochastic simulations with sampled parameters demonstrate that capacity variations can lead to significant variations in congestion patterns and freeway performance.