Distributed optimization of traffic delay on a periodic switched grid network

Abstract

Given a switched network, e.g. a city grid with semaphores in its intersections or a packet network, each unit (car or packet) accumulates some delay while traversing the network. This delay is undesirable but unavoidable, which makes minimizing the total average delay of the network given certain constraints, a desirable objective. In this work, we consider the case of periodic networks, meaning that in every traffic cycle inputs to the system are the same and we try to arrive to an allocation of phases in every intersection that minimizes the total delay per cycle. We propose a model for such networks in which the delay is given as a function of external parameters (arrivals to the system) as well as internal parameters (switching decisions). Additionally, we present a distributed algorithm which makes use of messages passed between adjacent nodes to arrive at a solution with low delay, when compared with what is obtained when nodes take decisions independently. Furthermore, dealing with large networks proves difficult to arrive to theoretical results. This distributed algorithm gives an insight on how one can analyze big networks by taking a local approach and determining bounds in smaller networks that are part of the big picture.