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

Abstract We consider a directed network in which every edge possesses a latency function specifying the time needed to traverse the edge given its congestion. Selfish, noncooperative agents constitute the network traffic and wish to travel from a source s to a sink t as quickly as possible. Since the route chosen by one network user affects the congestion (and hence the latency) experienced by others, we model the problem as a noncooperative game. Assuming each agent controls only a negligible portion of the overall traffic, Nash equilibria in this noncooperative game correspond to s-t flows in which all flow paths have equal latency. A natural measure for the performance of a network used by selfish agents is the common latency experienced by each user in a Nash equilibrium. It is a counterintuitive but well-known fact that removing edges from a network may improve its performance; the most famous example of this phenomenon is the so-called Braess's Paradox. This fact motivates the following network design problem: given such a network, which edges should be removed to obtain the best possible flow at Nash equilibrium? Equivalently, given a large network of candidate edges to be built, which subnetwork will exhibit the best performance when used selfishly? We give optimal inapproximability results and approximation algorithms for several network design problems of this type. For example, we prove that for networks with n vertices and continuous, nondecreasing latency functions, there is no approximation algorithm for this problem with approximation ratio less than n/2 (unless P = N P). We also prove this hardness result to be best possible by exhibiting an n/2-approximation algorithm. For networks in which the latency of each edge is a linear function of the congestion, we prove that there is no ( 43- ffl)-approximation algorithm for the problem (for any ffl> 0, unless P = N P); the existence of a 43-approximation algorithm follows easily from existing work, proving this hardness result sharp. Moreover, we prove that an optimal approximation algorithm for these problems is what we call the trivial algorithm: given a network of candidate edges, build the entire network. A consequence of this result is that Braess's Paradox (even in its worst-possible manifestation) is impossible to detect efficiently.

Abstract — In this paper, we study the interaction between

Abstract — In this paper, we study the interaction between

Abstract — It has been shown that as long as traffic sources adapt their rates to aggregate congestion measure in their paths, they implicitly maximize certain utility. In this paper we study some counter-intuitive throughput behaviors in such networks, pertaining to whether a fair allocation is always inefficient and whether increasing capacity always raises aggregate throughput. A bandwidth allocation policy can be defined in terms of a class of utility functions parameterized by a scalar α that can be interpreted as a quantitative measure of fairness. An allocation is fair if α is large and efficient if aggregate throughput is large. All examples in the literature suggest that a fair allocation is necessarily inefficient. We characterize exactly the tradeoff between fairness and throughput in general networks. The characterization allows us both to produce the first counterexample and trivially explain all the previous supporting examples. Surprisingly, our counter-example has the property that a fairer allocation is always more efficient. In particular it implies that maxmin fairness can achieve a higher throughput than proportional fairness. Intuitively, we might expect that increasing link capacities always raises aggregate throughput. We show that not only can throughput be reduced when some link increases its capacity, more strikingly, it can also be reduced when all links increase their capacities by the same amount. If all links increase their capacities proportionally, however, throughput will indeed increase. These examples demonstrate the intricate interactions among sources in a network setting that are missing in a singlelink topology.

Braess' paradox is said to occur in a network if the addition of an extra link leads to worse performance. It has been shown to occur in transportation networks (such as road networks) and also in queueing networks. Here, we show that it can occur in loss networks.

published Transportation Research Record #1466 p124-131 This paper presents a multimodal trip distribution function estimated and validated for the metropolitan Washington region. In addition, a methodology for measuring accessibility, which is used as a measure of effectiveness for networks, using the impedance curves in the distribution model is described. This methodology is applied at the strategic planning level to alternative HOV alignments to select alignments for further study and Right-of-Way preservation.

The problem of vehicle guidance in a network with failures is considered. The network may be in one of finitely many states characterized by different travel times along the arcs, and transitions between the states occur according to a continuos-time Markov chain. The objective is to guide the vehicles in a manner minimizing the total expected travel time. Dynamic programming models and flow-oriented models are developed and analyzed in the uncapacitated and the capacitated case. It is shown that the robust plan can be found from a special two-stage stochastic programming problem in which the second stage problem describes the re-routing of vehicles that experienced state transition during their travel. The models are illustrated on an example of the Sioux Falls transportation network. The computational results reveal striking properties of different guidance policies and show that substantial improvements in both duration and size of traffic jams can be achieved by employing robust gu...

Abstract. In computer networks (and, say, transportation networks), we can consider the situation where each user has its own routing decision so as to minimize noncooperatively the expected passage time of its packet/job given the routing decisions of other users. Intuitively, it is anticipated that adding connections to such a noncooperative network may bring benefits at least to some users. The Braess paradox is, however, the first example of paradoxical cases where it is not always the case. This paper studies the bounds on the degrees of coincident cost improvement (benefits) and degradation (harms) for all users by adding connections to noncooperative networks. For Wardrop networks (noncooperative networks with infinitesimal users), the degree of benefits for all users can increase without bound by adding connections whereas no Wardrop network has been found for which the degree of harms can increase without bound for all users. In contrast, for Nash networks (noncooperative networks with a finite number of users), the degrees of both benefits and harms can increase without bound for all users. On the other

We provide a new simpler approach to the on-line load balancing problem in the case of restricted assignment of temporary weighted tasks. The approach is very general and allows to derive on-line distributed algorithms whose competitive ratio is characterized by some combinatorial properties of the underlying graph representing the problem.