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Deriving Link Travel–Time Distributions via Stochastic Speed Processes

Department of Operational Sciences, Air Force Institute of Technology, AFIT/ENS, 2950 Hobson Way, Wright–Patterson AFB, Ohio 45433–7765
Harold and Inge Marcus Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, 310 Leonhard Building, University Park, Pennsylvania 16802
jeffrey.kharoufeh{at}afit.edu
ngautam{at}psu.edu

We derive an analytical expression for the cumulative distribution function of travel time for a vehicle traversing a freeway link of arbitrary length. The vehicle's speed is assumed to be modulated by a random environment that can be modeled as a stochastic process. We first present a partial differential equation (PDE) describing the travel time distribution and obtain a solution in terms of Laplace transforms. Next, we present a numerical inversion algorithm to invert the transforms. The technique is demonstrated on two example problems. Numerical results indicate great promise for this approach to the link travel–time problem.

Key Words: highway link; travel time; stochastic processes; Markov chain
History: Received: February 2001; revised: March 2002; accepted: August 2002.