Algebraic Approach for Performance Bound Calculus on Transportation Networks

Abstract

An application of the basic results of deterministic network calculus theory to road traffic flow theory is presented. Network calculus is a theory based on min-plus algebra. This calculus uses algebraic techniques to compute performance bounds in communication networks, such as maximum end-to-end delays and backlogs. The objective of this paper is to investigate the application of those techniques for determining performance bounds on road networks, such as upper bounds for travel times. A traffic model is proposed for cars moving in a single-lane ring road without passing. The model is compatible with network calculus theory and permits derivation of an upper bound of the travel time of cars on the road. An approach for extending the model to calculate upper bounds for the travel times of cars on paths passing through intersections in a whole network is also proposed.