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Analytical modelling of a stop-less modular bus service with an application to charging strategies comparison

Haoran Zhao, Neema Nassir, Andres Fielbaum

Abstract

Buses are a vital component of metropolitan public transport, yet conventional bus services often struggle with inefficiencies including extended dwelling time, which increases in-vehicle travel time for non-alighting passengers. A stop-less autonomous modular (SLAM) bus service has emerged as a solution, enabling dynamic capacity to reduce dwelling time. Meanwhile, the electrification of buses is advancing as a strategy to mitigate greenhouse gas emissions and reduces operators' costs, but introduces new operational constraints due to charging requirements. This study develops analytical optimization models for SLAM bus service that integrates vehicle-to-vehicle (V2V) charging technology. By comparing the optimal designs and their feasibility across non-charging case and charging strategies, we identify a sequence of operational stages as ridership grows: from idle capacity under low demand, to full small buses, full large buses, and a proposed frequency-capped regime where only bus capacity expands. Under the mobile charging strategy, this progression further includes an energy-limited regime, in which frequency declines, and ultimately infeasibility under high demand. These findings enable operators to deliver more efficient services.

Analytical modelling of a stop-less modular bus service with an application to charging strategies comparison

Abstract

Buses are a vital component of metropolitan public transport, yet conventional bus services often struggle with inefficiencies including extended dwelling time, which increases in-vehicle travel time for non-alighting passengers. A stop-less autonomous modular (SLAM) bus service has emerged as a solution, enabling dynamic capacity to reduce dwelling time. Meanwhile, the electrification of buses is advancing as a strategy to mitigate greenhouse gas emissions and reduces operators' costs, but introduces new operational constraints due to charging requirements. This study develops analytical optimization models for SLAM bus service that integrates vehicle-to-vehicle (V2V) charging technology. By comparing the optimal designs and their feasibility across non-charging case and charging strategies, we identify a sequence of operational stages as ridership grows: from idle capacity under low demand, to full small buses, full large buses, and a proposed frequency-capped regime where only bus capacity expands. Under the mobile charging strategy, this progression further includes an energy-limited regime, in which frequency declines, and ultimately infeasibility under high demand. These findings enable operators to deliver more efficient services.

Paper Structure

This paper contains 30 sections, 48 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Autonomous Modular Bus
  4. Charging strategy design for bus systems
  5. Model formulation
  6. A recap on the traditional single-line model
  7. Stop-less autonomous modular (SLAM) bus service
  8. An analytical model for SLAM
  9. Formulation of the Core model
  10. Theoretical analysis
  11. Summary
  12. Discussion
  13. Feasibility
  14. Behavior of the Optimal Solution
  15. Charge Strategy Analysis
  16. ...and 15 more sections

Figures (5)

  • Figure 1: The SLAM bus service moving from left to right performing a non-stopping operation
  • Figure 2: The behavior of the optimal design for SLAM bus service (a) frequency, (b) bus capacity; (c) average costs
  • Figure 3: The behavior of the optimal design for SLAM bus service (a) frequency, (b) bus capacity; (c) average costs
  • Figure 4: The behavior of the optimal design for SLAM bus service (a) frequency, (b) bus capacity; (c) average costs
  • Figure 5: Bus trajectories during the evaluation period: (a) depot charging, (b) mobile charging.