Numerical analysis of a time-headway bus route model

TL;DR

This paper analyzes a time-headway bus route model, incorporating a no-passing rule, to understand stability conditions and realistic parameter ranges for efficient bus scheduling.

Contribution

It introduces a detailed stability analysis of a classical bus route model with no-passing, highlighting conditions for stability and practical implications.

Findings

Unstable modes can be enumerated and studied.

Stable operation requires careful monitoring of bus headways.

Parameter ranges for realistic scenarios are more limited than expected.

Abstract

In this paper, we consider a time-headway model, introduced in Physica A 296:320 (2001), for buses on a bus route. By including a simple no-passing rule, we are able to enumerate and study the unstable modes of a homogeneous system. We then discuss the application of the model to realistic scenarios, showing that the range of reasonable parameter values is more restricted than one might imagine. We end by showing that strict stability in a homogeneous bus route requires careful monitoring by each bus of the bus in front of it, but in many cases this is unnecessary because the time it takes for the instability to appear is longer than a bus would normally spend on a route.