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Optimal Routing in Stochastic Networks with Reliability Guarantees.

Wanzheng Zheng1, Pranay Thangeda2, Yagiz Savas3

  • 1Department of Aerospace Engineering, University of Illinois Urbana-Champaign, Urbana, USA.

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Summary
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This study introduces a new routing policy for congested roads that minimizes expected travel time while ensuring a target on-time arrival probability. This approach addresses limitations of traditional methods, especially with high travel time variance.

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Area of Science:

  • Operations Research
  • Transportation Science
  • Computer Science

Background:

  • Optimal routing in congested networks with stochastic travel times is complex.
  • Minimizing only expected travel time is insufficient when travel time variance is high.

Purpose of the Study:

  • To develop a routing policy minimizing expected travel time under a strict on-time arrival probability constraint.
  • To address the practical need for reliable travel times in urban navigation.

Main Methods:

  • Modeling stochastic travel times as discrete random variables.
  • Formulating the routing problem as a Markov decision process.
  • Solving the problem as a linear program.

Main Results:

  • The proposed method generates routing policies that balance expected travel time with arrival time reliability.
  • A case study in Manhattan, New York, demonstrated the approach's efficacy using real-world data.

Conclusions:

  • The developed Markov decision process and linear programming framework effectively solves the constrained optimal routing problem.
  • This approach offers a more robust solution for navigation in stochastic urban environments.