A Methodological Framework of Travel Time Distribution Estimation for Urban Signalized Arterial Roads

Urban travel times are rather variable as a result of a lot of stochastic factors both in traffic flows, signals, and other conditions on the infrastructure. However, the most common way both in literature and practice is to estimate or predict only expected travel times, not travel time distributions. By doing so, it fails to provide full insight into the travel time dynamics and variability on urban roads. Another limitation of this common approach is that the effect of traffic measures on travel time reliability cannot be evaluated. In this paper, an analytical travel time distribution model is presented especially for urban roads with fixed-time controlled intersections by investigating the underlying mechanisms of urban travel times. Different from mean travel time models or deterministic travel time models, the proposed model takes stochastic properties of traffic flow, stochastic arrivals and departures at intersections, and traffic signal coordination between adjacent intersections into account, and therefore, is able to capture the delay dynamics and uncertainty at intersections. The queue spillback phenomenon is explicitly taken into account by applying shockwave theory in a probabilistic way. The proposed model was further validated with both VISSIM simulation data and field GPS data collected in a Chinese city. The results demonstrate that the travel time distributions derived from the analytical model can well represent those from VISSIM simulation. The comparison with field GPS data shows that the model estimated link and trip travel time distributions can also represent the field travel time distributions, though a small discrepancy can be observed in both middle range travel times and higher travel times.