Approximating Wardrop Equilibria with Finitely Many Agents

Abstract

We study adaptive routing algorithms in a round-based model. Suppose we are given a network equipped with load-dependent latency functions on the edges and a set of commodities each of which is defined by a collection of paths (represented by a DAG) and a flow rate. Each commodity is controlled by an agent which aims at balancing its traffic among its paths such that all used paths have the same latency. Such an allocation is called a Wardrop equilibrium.

In recent work, it was shown that an infinite population of users each of which carries an infinitesimal amount of traffic can attain approximate equilibria in a distributed and concurrent fashion quickly. Interestingly, the convergence time is independent of the underlying graph and depends only mildly on the latency functions. Unfortunately, a direct simulation of this process requires to maintain an exponential number of variables, one for each path.

The focus of this work lies on the distributed and efficient computation of the adaptation rules by a finite number of agents. In order to guarantee a polynomial running time, every agent computes a randomised path decomposition in every communication round. Based on this decomposition, agents remove flow from paths with high latency and reassign it proportionally to all paths. This way, our algorithm can handle exponentially large path collections in polynomial time.