# No-boarding buses: Synchronisation for efficiency

## TL;DR

This paper analyzes a no-boarding policy for synchronized bus systems, demonstrating through theory and simulations that it can significantly reduce passenger waiting times, and proposes an adaptive algorithm for real-world implementation.

## Contribution

It provides an analytically tractable model for no-boarding policies, verifies results with simulations including real data, and introduces a dynamic algorithm for practical deployment.

## Key findings

- No-boarding policy reduces average waiting time significantly.
- Synchronization improves bus system efficiency.
- Adaptive algorithm enables real-time policy decisions.

## Abstract

We investigate a no-boarding policy in a system of $N$ buses serving $M$ bus stops in a loop, which is an entrainment mechanism to keep buses synchronised in a reasonably staggered configuration. Buses always allow alighting, but would disallow boarding if certain criteria are met. For an analytically tractable theory, buses move with the same natural speed (applicable to programmable self-driving buses), where the average waiting time experienced by passengers waiting at the bus stop for a bus to arrive can be calculated. The analytical results show that a no-boarding policy can dramatically reduce the average waiting time, as compared to the usual situation without the no-boarding policy. Subsequently, we carry out simulations to verify these theoretical analyses, also extending the simulations to typical human-driven buses with different natural speeds based on real data. Finally, a simple general adaptive algorithm is implemented to dynamically determine when to implement no-boarding in a simulation for a real university shuttle bus service.