Probability distribution of travel times in signalized flow networks: a horizontal queuing theory approach

This article was submitted in April 2012 to Operations Research, INFORMS.
Authors: A. Hofleitner, R. Herring and A. Bayen

Abstract:
Urban traffic flow dynamics are driven by the presence of traffic signals, which leads to important vehicle-to-vehicle travel time variability. We develop a comprehensive model of horizontal queuing theory to derive an analytical expression for the probability distribution of travel times, parameterized by physical parameters (signals, free flow speed distribution, queue lengths). The distributions are derived between any two locations on the network allowing to learn the model parameters from sparsely sampled probe vehicles, without need for site specific calibration. The main sources of measurements with the prospect of global coverage in the near future come from vehicles which report their location periodically in time (emph{e.g.} every minute), not necessarily at the beginning and at the end of the links of the network. Moreover, probe vehicles may traverse several links between successive location reports. We prove that the travel time distributions are mixture of log-concave distributions and introduce a convex formulation to decompose the travel time between successive location reports into individual link travel times (travel time allocation) and learn the parametric distribution of travel times on the network. Using data collected by emph{Sensys Networks} in Chula Vista, CA, we show that the distribution derived in this article more accurately represents the empirical distribution of travel times than other commonly used distributions. The estimation capabilities can be further improved by inputing prior information on the physical parameters characterizing the probability distributions.

The code used to produce the results presented in this paper is available for download