Abstract

Unlimited access to a motorway network can, in overloaded conditions, cause a loss of capacity. Ramp metering (signals on slip roads to control access to the motorway) can help avoid this loss of capacity. The design of ramp metering strategies has several features in common with the design of access control mechanisms in communication networks.

Inspired by models and rate control mechanisms developed for Internet congestion control, we propose a Brownian network model as an approximate model for a controlled motorway and consider it operating under a proportionally fair ramp metering policy. We present an analysis of the performance of this model.

AMS subject classification (MSC2010) 90B15, 90B20, 60K30

Introduction

The study of heavy traffic in queueing systems began in the 1960s, with three pioneering papers by Kingman [26, 27, 28]. These papers, and the early work of Prohorov [35], Borovkov [5, 6] and Iglehart [20], concerned a single resource. Since then there has been significant interest in networks of resources, with major advances by Harrison and Reiman [19], Reiman [37], Williams [43] and Bramson [7]. For discussions, further references and overviews of the very extensive literature on heavy traffic for networks, Williams [42], Bramson and Dai [8], Harrison [17, 18] and Whitt [41] are recommended.

Research in this area is motivated in part by the need to understand and control the behaviour of communications, manufacturing and service networks, and thus to improve their design and performance.