Reconstruction of delay distribution at signalized intersections based on traffic measurements

In an urban road network, travel times are not uniquely determined by the traffic states due to stochastic properties of traffic flow, stochastic arrivals and departures at intersections and traffic signal control. As a result, for a given traffic state, a range of travel times (delays) is found. This can be represented by a distribution of travel times (delays). Calibrating a model for the travel time only for the expectation value gives a large `noise´ such that the model will have little value for the prediction purpose. In this paper, the delay distribution function as derived from the analytical model under different circumstances is introduced. The overflow queue distribution which is the parameter in the delay distribution function is estimated based on traffic measurements, e.g., the measured delays, flows and cycle time. The Least Squares (LS) and Maximum Likelihood (ML) Estimation are used to perform the parameter estimation in the delay distribution. The Genetic Algorithm (GA) is applied to find the optimal solution for the objective functions in terms of minimizing square error and maximizing the likelihood function. Based on the estimated model parameters, the delay distribution is reconstructed. The estimated delay distribution is compared with that obtained from VISSIM simulation. Results show that both ML and LS estimation methods perform well in the undersaturated condition. While in the oversaturated condition, the ML method performs considerably better than the LS method.