An Exact System Optimum Assignment Model for Transit Demand Management

TL;DR

The paper tackles the identification of true system-wide congestion relief in schedule-based transit assignment by formulating and solving an exact system-optimum (SO) model that incorporates hard capacity constraints and multi-line interactions. It introduces an analytic exact SO approach for the STAP, contrasted with conventional UE and approximate SO methods, and validates it on a Hong Kong MTR case study, showing substantial improvements over UE and clear gaps with Approx. SO. The results reveal that the exact SO can reduce system costs by $36.35\%$ relative to UE (versus $17.39\%$ for Approx. SO), and provides actionable insights into which origin-destination pairs to target for passenger shifting, how many can be shifted, and how potential gains evolve with demand and capacity. These findings have practical implications for congestion-relief policy design and planning, enabling more precise, incentive-based interventions and guiding network-scale optimization for future growth.

Abstract

Mass transit systems are experiencing increasing congestion in many cities. The schedule-based transit assignment problem (STAP) involves a joint choice model for departure times and routes, defining a space-time path in which passengers decide when to depart and which route to take. User equilibrium (UE) models for the STAP indicates the current congestion cost, while a system optimum (SO) models can provide insights for congestion relief directions. However, current STAP methods rely on approximate SO (Approx. SO) models, which underestimate the potential for congestion reduction in the system. The few studies in STAP that compute exact SO solutions ignore realistic constraints such as hard capacity, multi-line networks, or spatial-temporal competing demand flows. The paper proposes an exact SO method for the STAP that overcomes these limitations. We apply our approach to a case study involving part of the Hong Kong Mass Transit Railway network, which includes 5 lines, 12 interacting origin-destination pairs and 52,717 passengers. Computing an Approx. SO solution for this system indicates a modest potential for congestion reduction measures, with a cost reduction of 17.39% from the UE solution. Our exact SO solution is 36.35% lower than the UE solution, which is more than double the potential for congestion reduction. We then show how the exact SO solution can be used to identify opportunities for congestion reduction: (i) which origin-destination pairs have the most potential to reduce congestion; (ii) how many passengers can be reasonably shifted; (iii) future system potential with increasing demand and expanding network capacity.

Figures (13)

• Figure 1: Frameworks for evaluating promotion policies in the transit system (adapted from ref56)
• Figure 2: Comparison between Approx. SO and exact SO: (a) Measured system potential for promotions (current: UE, target: SO); (b) Potential cost reduction contribution per passenger: targeting the top 4 groups for potential shifts (a higher cost reduction indicates greater potential for congestion relief)
• Figure 3: Extracted Hong Kong MTR network (adapted from web image: https://www.mtr.com.hk/en/customer/services/system_map.html)
• Figure 4: Comparison of total system costs among user equilibrium, Approx. SO, and exact SO
• Figure 5: System performance comparison: departure time choice only versus simultaneous departure time and route choice