Probability distributions of travel times on arterial networks: a　trac ow and horizontal queuing theory approach

摘要

In arterial networks, trac ow dynamics are driven by the presence of trac signals, forwhich precise signal timing is dicult to obtain in arbitrary networks or might change over time.A comprehensive model of arterial trac ow dynamics is necessary to capture its specic fea-tures in order to provide accurate trac estimation approaches. From hydrodynamic theory,we model arterial trac dynamics under specic assumptions standard in transportation engi-neering. We use this ow model to develop a statistical model of arterial trac. The statisticalapproach is essential to capture the variability of travel times among vehicles: (1) the delayexperienced by a vehicle depends on the time when it enters the link (in relation to the signalgreen/red phases) and this entrance time can occur at any random time during the cycle and (2)the free ow speed of a vehicle depends both on the driver and on external factors (jaywalking,double parking, etc.) and is another source of uncertainty. These two sources of uncertaintyare captured by deriving the probability distribution of delays (from hydrodynamic theory) andmodeling the nominal free ow travel time as a random variable (which encodes variability indriving behavior). We derive an analytical expression for the probability distribution of traveltimes between any two locations on an arterial link, parameterized by trac parameters (cycletime, red time, free ow speed distribution, queue length and queue length at saturation).We validate the model using probe vehicle data collected during a eld test in San Francisco,as part of the Mobile Millennium system. The numerical results show that the new distributionderived in this article more accurately represents the actual distribution of travel times thanother distributions that are commonly used to represent travel times (normal, log-normal andGamma distributions). We also show that the model performs particularly well when the amountof data available is small. This is very promising as the volume of probe vehicle data availablein real time to most trac information systems today remains sparse.