Deriving Link Travel-Time Distributions via Stochastic Speed Processes

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2004
Accession Number
ADA575316

Entities

People

  • Jeffrey P. Kharoufeh
  • Natarajan Gautam

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Complex Variables
  • Differential Equations
  • Distribution Functions
  • Equations
  • Flow Network
  • Fourier Series
  • Markov Chains
  • Markov Processes
  • Partial Differential Equations
  • Probability
  • Probability Distributions
  • Random Variables
  • Stochastic Processes
  • Time Intervals
  • Travel Time
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Acoustical Oceanography.
  • Computational Modeling and Simulation
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)