LegalFarePlan A Label-Setting Framework for Fare-Transparent Urban Rail Route Planning under Non-Additive Fare Rules

Jul 16, 2026

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Urban rail fare systems may be non-additive, where the fare for a continuous paid journey can differ from the sum of fares over multiple legally separated legs. LegalFarePlan provides a fare-aware route-planning framework that models legal exit-and-reentry operations as explicit, auditable constraints. Given a rail network, fare function, transfer rules, exit/reentry costs, and user limits, it computes explainable route plans over paid journey segments and supports multiple planning modes.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages6

Reading Time15 min

Abstract

Introduction

Related Work

Motivating Example

Method and Framework

Planning Modes and Algorithms

Evaluation Setup and Benchmarks

LegalFarePlan: A Label-Setting Framework for Fare-Transparent Urban Rail Route Planning under Non-Additive Fare Rules Tanghui Li Tongji University Shanghai, China [thli@tongji.edu.cn](thli@tongji.edu.cn) 5 Jul 2026 Abstract—Urban rail fare systems may be non-additive: the fare of a single paid journey from an origin to a destination can differ from the sum of fares over multiple legally separated journey legs. This paper presents LegalFarePlan, a faretransparent route-planning framework that models legal exitand-reentry operations as explicit, auditable constraints. Given a transit network, fare function, transfer rules, station-level exit/reentry costs, an extra-time budget, and a split limit, the planner computes explainable route plans over paid journey segments. The artifact implements Dijkstra shortest-time and direct routeplanner baselines, a greedy split heuristic, bounded exact labelsetting, and Pareto-frontier search. Evaluation uses controlled synthetic data and a 57-station semi-synthetic benchmark with 360 OD pairs. On the semi-synthetic benchmark, bounded exact search identifies positive modeled fare reductions for 71.11% of OD pairs, with mean reduction 3.78 and maximum reduction 9.0 synthetic fare units under a 45-minute extra-time budget. These results demonstrate method behavior and reproducibility; they are not empirical conclusions about MTR or any transit operator. arXiv :2607 .09755v1 through normal gates, re-enters through normal gates, and pays the published fare for every paid leg. The artifact does not model fare evasion, ticket misuse, system tampering, gate manipulation, or regulatory avoidance. The included datasets are synthetic or semi-synthetic and are used only for algorithm validation and reproducibility. I. INTRODUCTION Transit route planning is usually framed as a shortest-path or multicriteria routing problem in which the planner optimizes travel time, transfers, walking, reliability, or generalized cost. Fare is often treated as a static OD attribute. This simplification is insufficient for transit systems with non-additive fare rules. In such systems, the fare for one continuous paid journey from station o to station d may differ from the total fare obtained by splitting the journey into several legal paid legs. A passenger may legally exit at an intermediate station and re-enter, but this action has time, inconvenience, and sometimes monetary costs. This work studies the following route-planning problem: Given a rail network, a non-additive fare table, explicit transfer rules, legal exit/re-entry costs, and user constraints, compute a route plan that minimizes total paid fare while reporting time, transfers, number of exit/re-entry operations, and a human-readable explanation. The problem is not reducible to a physical shortest path. The planner must combine two layers: a physical routing layer that checks whether each leg can be traveled through the network, and a fare layer that prices each legal paid journey. This separation is important for reproducibility: physical network data, fare tables, transfer rules, and legal exit assumptions can each be audited independently. The contributions are: 1) A formal definition of fare-aware route planning with legal exit-and-reentry operations under non-additive transit fare rules. 2) A reproducible CSV schema covering stations, physical edges, fares, transfer rules, exit/re-entry penalties, and OD benchmarks. 3) A standard-library Python artifact with Dijkstra shortesttime, direct route-planner, greedy, bounded exact labelsetting, and Pareto-frontier modes. 4) A controlled 8-station synthetic benchmark and a larger 57-station semi-synthetic benchmark for reproducible evaluation when licensed real data are unavailable. 5) Experiment scripts, tests, tables, and figures that make all reported modeled fare-reduction results traceable to program output. II. RELATED WORK The physical routing component builds

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What evaluation setup and results does the paper report?

It evaluates on controlled synthetic data and a 57-station semi-synthetic benchmark with 360 OD pairs; bounded exact label-setting finds modeled fare reductions for 71.11% of OD pairs with mean reduction 3.78 and maximum reduction 9.0 under a 45-minute extra-time budget.

Jul 16, 2026

Upload by Hazel