M/G/c/c state dependent travel time models and properties

One of the most important problems in today's modeling of transportation networks is an accurate estimate of travel time on arterial links, highway, and freeways. There are a number of deterministic formulas that have been developed over the years to achieve a simple and direct way to estimate travel times for this complex task. Realistically, however, travel time is a random variable. These deterministic formula are briefly reviewed and also a new way to compute travel time over arterial links, highway, and freeways, is presented based on an analytical state dependent queueing model. One of the features of the queueing model is that it is analyzed within the context of the theoretical three-phase traffic flow model. We show that the model provides a quantitative foundation alternative to qualitative three-phase traffic flow theory. An important property shown with the model is that the travel time function is not convex, but a sigmoid S-shaped (i.e. logistic curve). Extensive analytical and simulation experiments are shown to verify the S-shaped nature of the travel time function and the use of the model's method of estimation of travel time over vehicular traffic links as compared with traditional approaches. Finally, it is shown that the point-of-inflection of the S-shaped curve represents the threshold point where the traffic flow volume switches from Free Flow to Congested Flow.