Algebraic Approach for Performance Bound Calculus on Transportation Networks (Road Network Calculus)

TL;DR

This paper adapts deterministic network calculus, based on min-plus algebra, to model and compute performance bounds like maximum travel times in road traffic networks, including intersections and large-scale systems.

Contribution

It introduces a traffic model compatible with network calculus for single-lane roads and extends the approach to complex road networks and intersections.

Findings

Derived maximum travel time bounds for single-lane roads

Extended the model to intersections and large networks

Provided a framework for performance analysis in traffic networks

Abstract

We propose in this article an adaptation of the basic techniques of the deterministic network calculus theory to the road traffic flow theory. Network calculus is a theory based on min-plus algebra. It uses algebraic techniques to compute performance bounds in communication networks, such as maximum end-to-end delays and backlogs. The objective of this article is to investigate the application of such techniques for determining performance bounds on road networks, such as maximum bounds on travel times. The main difficulty to apply the network calculus theory on road networks is the modeling of interaction of cars inside one road, or more precisely the congestion phase. We propose a traffic model for a single-lane road without passing, which is compatible with the network calculus theory. The model permits to derive a maximum bound of the travel time of cars through the road. Then, basing on that model, we explain how to extend the approach to model intersections and large-scale networks.