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A Comprehensive Stochastic Programming Model for Transfer Synchronization in Transit Networks

Zahra Ansarilari, Merve Bodur, Amer Shalaby

Abstract

We investigate the stochastic transfer synchronization problem, which seeks to synchronize the timetables of different routes in a transit network to reduce transfer waiting times, delay times, and unnecessary in-vehicle times. We present a sophisticated two-stage stochastic mixed-integer programming model that takes into account variability in passenger walking times between bus stops, bus running times, dwell times, and demand uncertainty. Our model incorporates new features related to dwell time determination by considering passenger arrival patterns at bus stops which have been neglected in the literature on transfer synchronization and timetabling. We solve a sample average approximation of our model using a problem-based scenario reduction approach, and the progressive hedging algorithm. As a proof of concept, our computational experiments on two single transfer nodes in the City of Toronto, with a mixture of low- and high-frequency routes, demonstrate the potential advantages of the proposed model. Our findings highlight the necessity and value of incorporating stochasticity in transfer-based timetabling models.

A Comprehensive Stochastic Programming Model for Transfer Synchronization in Transit Networks

Abstract

We investigate the stochastic transfer synchronization problem, which seeks to synchronize the timetables of different routes in a transit network to reduce transfer waiting times, delay times, and unnecessary in-vehicle times. We present a sophisticated two-stage stochastic mixed-integer programming model that takes into account variability in passenger walking times between bus stops, bus running times, dwell times, and demand uncertainty. Our model incorporates new features related to dwell time determination by considering passenger arrival patterns at bus stops which have been neglected in the literature on transfer synchronization and timetabling. We solve a sample average approximation of our model using a problem-based scenario reduction approach, and the progressive hedging algorithm. As a proof of concept, our computational experiments on two single transfer nodes in the City of Toronto, with a mixture of low- and high-frequency routes, demonstrate the potential advantages of the proposed model. Our findings highlight the necessity and value of incorporating stochasticity in transfer-based timetabling models.
Paper Structure (27 sections, 32 equations, 9 figures, 19 tables, 1 algorithm)

This paper contains 27 sections, 32 equations, 9 figures, 19 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Analytical Models for Stochastic Transfer Synchronization
  4. Mathematical Programming Models for Stochastic Transfer Synchronization
  5. Problem Description
  6. Assumptions
  7. Our New Approach of Transfer Synchronization Formulation in Stochastic Setting
  8. Types of Successful Transfer
  9. Dwell Time Determination Based on Passengers' Arrival Pattern at Bus Stops
  10. High-frequency lines
  11. Low-frequency lines
  12. Mathematical Formulation: Stochastic MIP Model
  13. High-frequency Connecting Lines
  14. Low-frequency Connecting Lines
  15. Unnecessary In-vehicle Time and Delay Penalty for Both High- and Low-frequency Lines
  16. ...and 12 more sections

Figures (9)

  • Figure 1: Different types of waiting times.
  • Figure 1: Two transfer nodes in Toronto
  • Figure 2: The process of three types of a successful transfer.
  • Figure 3: Local passengers arrival pattern for high-frequency line, Zone 1.
  • Figure 4: Local passengers arrival pattern for high-frequency line, Zone 2.
  • ...and 4 more figures