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Robust Path Recommendations During Public Transit Disruptions Under Demand Uncertainty

Baichuan Mo, Haris N. Koutsopoulos, Max Zuo-Jun Shen, Jinhua Zhao

TL;DR

This work tackles the problem of guiding passengers through public transit disruptions in a system-wide, demand-uncertainty setting. It develops a simulation-based first-order linearization to transform the non-analytical system travel time into a tractable linear objective, and then embeds this within a robust optimization framework to protect path recommendations against demand uncertainty. In a CTA Blue Line disruption case study, the nominal model reduces system travel time by about 9.1% and incident-line travel time by about 20.6% relative to the status quo, with robust variants offering additional improvements under uncertainty (best around a 2.9% further reduction for incident-line travelers). The approach demonstrates a practical, scalable pathway for real-time, OD-based path recommendations that account for network interactions and uncertainty, while also outlining extensions to rolling-horizon operation and incident-duration uncertainty for future work.

Abstract

When there are significant service disruptions in public transit systems, passengers usually need guidance to find alternative paths. This paper proposes a path recommendation model to mitigate congestion during public transit disruptions. Passengers with different origins, destinations, and departure times are recommended with different paths such that the system travel time is minimized. We model the path recommendation problem as an optimal flow problem with uncertain demand information. To tackle the lack of analytical formulation of travel times due to capacity constraints, we propose a simulation-based first-order approximation to transform the original problem into a linear program. Uncertainties in demand are modeled using robust optimization to protect the path recommendation strategies against inaccurate estimates. A real-world rail disruption scenario in the Chicago Transit Authority (CTA) system is used as a case study. Results show that even without considering uncertainty, the nominal model can reduce the system travel time by 9.1% (compared to the status quo), and outperforms the benchmark capacity-based path recommendation. The average travel time of passengers in the incident line (i.e., passengers receiving recommendations) is reduced more (-20.6% compared to the status quo). After incorporating the demand uncertainty, the robust model can further reduce system travel times. The best robust model can decrease the average travel time of incident-line passengers by 2.91% compared to the nominal model. The improvement of robust models is more prominent when the actual demand pattern is close to the worst-case demand.

Robust Path Recommendations During Public Transit Disruptions Under Demand Uncertainty

TL;DR

This work tackles the problem of guiding passengers through public transit disruptions in a system-wide, demand-uncertainty setting. It develops a simulation-based first-order linearization to transform the non-analytical system travel time into a tractable linear objective, and then embeds this within a robust optimization framework to protect path recommendations against demand uncertainty. In a CTA Blue Line disruption case study, the nominal model reduces system travel time by about 9.1% and incident-line travel time by about 20.6% relative to the status quo, with robust variants offering additional improvements under uncertainty (best around a 2.9% further reduction for incident-line travelers). The approach demonstrates a practical, scalable pathway for real-time, OD-based path recommendations that account for network interactions and uncertainty, while also outlining extensions to rolling-horizon operation and incident-duration uncertainty for future work.

Abstract

When there are significant service disruptions in public transit systems, passengers usually need guidance to find alternative paths. This paper proposes a path recommendation model to mitigate congestion during public transit disruptions. Passengers with different origins, destinations, and departure times are recommended with different paths such that the system travel time is minimized. We model the path recommendation problem as an optimal flow problem with uncertain demand information. To tackle the lack of analytical formulation of travel times due to capacity constraints, we propose a simulation-based first-order approximation to transform the original problem into a linear program. Uncertainties in demand are modeled using robust optimization to protect the path recommendation strategies against inaccurate estimates. A real-world rail disruption scenario in the Chicago Transit Authority (CTA) system is used as a case study. Results show that even without considering uncertainty, the nominal model can reduce the system travel time by 9.1% (compared to the status quo), and outperforms the benchmark capacity-based path recommendation. The average travel time of passengers in the incident line (i.e., passengers receiving recommendations) is reduced more (-20.6% compared to the status quo). After incorporating the demand uncertainty, the robust model can further reduce system travel times. The best robust model can decrease the average travel time of incident-line passengers by 2.91% compared to the nominal model. The improvement of robust models is more prominent when the actual demand pattern is close to the worst-case demand.
Paper Structure (45 sections, 2 theorems, 44 equations, 16 figures, 4 tables, 1 algorithm)

This paper contains 45 sections, 2 theorems, 44 equations, 16 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Objectives and Challenges
  4. Literature review
  5. Supply-side incident management
  6. Path recommendations during incidents
  7. Passenger evacuation under emergencies
  8. Travel time calculation in public transit networks
  9. Passenger queuing in over-saturated scenarios
  10. Simulation-based optimization
  11. Robust optimization (RO)
  12. Methodology
  13. Event-based public transit simulator
  14. Simulator design
  15. Simulating service disruptions
  16. ...and 30 more sections

Key Result

Proposition 1

If $\boldsymbol{d}$ is normally distributed with $\boldsymbol{d} \sim \mathcal{N}(\bar{\boldsymbol{d}}, \boldsymbol{\Sigma})$, then in a RO problem where constraint cons_t3 is guaranteed to be satisfied with probability of at least $1 - \varepsilon$ (i.e., $\mathbb{P}[\boldsymbol{a}^T \boldsymbol{p} where $\boldsymbol{A} \in \mathbb{R}^{|\mathcal{F}|\times HK}$ with entry $A_{hkr,h'k'} = \beta_{hk

Figures (16)

  • Figure 1: Structure of the network loading model (adapted from mo2020capacity
  • Figure 2: Explanation for the impact of adding an additional one unit flow to the system
  • Figure 3: Example for arbitrarily large $\beta_{hkr}(\Tilde{\boldsymbol{f}})$
  • Figure 4: Illustration of the rolling horizon implementation
  • Figure 5: Case study diagram
  • ...and 11 more figures

Theorems & Definitions (5)

  • Proposition 1
  • proof
  • Remark 1
  • Lemma 1
  • Example 1