How bad is selfish routing?

Abstract

Abstract. We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times-the total latency-is minimized.In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimum-latency path available to it, given the network congestion caused by the other users. In general such a "selfishly motivated" assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance.In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total latency of the routes chosen by unregulated selfish network users may be arbitrarily larger than the minimum possible total latency; however, we prove that it is no more than the total latency incurred by optimally routing twice as much traffic.

On the Price of Stability for Designing Undirected Networks with Fair Cost Allocations

“…The main focus was latency minimization for linear and polynomial latency functions [3,5,9]. The price of stability for linear latency functions has been studied by Christodoulou and Koutsoupias [4].…”

Social coordination in unknown price-sensitive populations

“…Note that when β L / = 0, meaning that it is not possible to influence behavior with tolls, we obtain the well-known price of anarchy of 4/3 derived in [21]. On the other hand, if β L = β U , meaning that the price-sensitivity of all users is known precisely, we obtain a price of anarchy of 1, implying that complete information allows complete control.…”

“…Then we show that due to the properties induced by Definition 3.1, the coefficients defined in Lemma 4.1 satisfy (18)- (21).…”

“…In general, these marginal-cost tolls induce optimal routing. Homogeneity is a common assumption when analyzing worst-case behavior [21]; it is a simple approach that can often be used to bound the behavior of heterogeneous populations. The clear benefit of tolling functions of the Pigovian form is that they can be assigned in a distributed manner; each edge toll is a function only of the congestion properties of that edge.…”

“…More concisely, we investigate uncertain user price-sensitivity for a routing problem in a class of congestion games: the set of network routing games such that each edge in a network possesses a congestion function that is affine in the number of edge users. Congestion games of this type have been extensively studied in the existing literature [20], [21], [14].…”