Dynamic stochastic travel time estimation: The stochastic cell transmission model based approach

Road networks are exposed to variability from both demand and supply sides. This causes the variability of travel time in both within-day and day-to-day contexts. Our previous work proposed and validated a stochastic cell transmission model (SCTM) for a freeway corridor (Sumalee et al., 2009). The SCTM provides an estimation of statistical distribution of the cell density over time given the stochastic fundamental diagram and inflow profile. This paper develops an algorithm for calculating the statistical distribution of the dynamic travel time from the outputs of the SCTM. The original approach for calculating the travel time from the deterministic cell transmission model (CTM) is based on the First-In-First-Out (FIFO) principle. In this paper, deterministic FIFO is extended to the case of SCTM to allow for the stochastic travel time estimation. The algorithm estimates the mean and variance of the travel time distribution for each entry time of the freeway segment, and was tested with a dataset of a freeway segment in California (PeMS database).The skewness of the travel time distribution is also calculated and compared with a previous empirical study of the skewness of travel time distribution. The proposed model and algorithm performs well under these comparisons.