Book•
Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods
01 Jan 1985-
About: The article was published on 1985-01-01 and is currently open access. It has received 2277 citations till now. The article focuses on the topics: Mode choice & Traffic congestion.
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TL;DR: In this paper, a simple representation of traffic on a highway with a single entrance and exit is presented, which can be used to predict traffic's evolution over time and space, including transient phenomena such as the building, propagation, and dissipation of queues.
Abstract: This paper presents a simple representation of traffic on a highway with a single entrance and exit. The representation can be used to predict traffic's evolution over time and space, including transient phenomena such as the building, propagation, and dissipation of queues. The easy-to-solve difference equations used to predict traffic's evolution are shown to be the discrete analog of the differential equations arising from a special case of the hydrodynamic model of traffic flow. The proposed method automatically generates appropriate changes in density at locations where the hydrodynamic theory would call for a shockwave; i.e., a jump in density such as those typically seen at the end of every queue. The complex side calculations required by classical methods to keep track of shockwaves are thus eliminated. The paper also shows how the equations can mimic the real-life development of stop-and-go traffic within moving queues.
2,781 citations
2,140 citations
TL;DR: The degradation in network performance due to unregulated traffic is quantified and it is proved 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.
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.
1,703 citations
Cites background from "Urban Transportation Networks: Equi..."
...Dafermos and Sparrow [7] were perhaps the first authors interested in computing the equilibrium efficiently, and many subsequent papers gave increasingly efficient methods for computing equilibria (see [10] for a survey); others have extended these results to more sophisticated models (see for example [1, 6, 10, 13, 21, 22, 27, 29, 30])....
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Book•
01 Jan 2005TL;DR: A survey of recent work that analyzes the price of anarchy of selfish routing, a classical mathematical model of how self-interested users might route traffic through a congested network.
Abstract: Selfish routing is a classical mathematical model of how self-interested users might route traffic through a congested network. The outcome of selfish routing is generally inefficient, in that it fails to optimize natural objective functions. The price of anarchy is a quantitative measure of this inefficiency. We survey recent work that analyzes the price of anarchy of selfish routing. We also describe related results on bounding the worst-possible severity of a phenomenon called Braess's Paradox, and on three techniques for reducing the price of anarchy of selfish routing. This survey concentrates on the contributions of the author's PhD thesis, but also discusses several more recent results in the area.
952 citations
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...Sheffi [77])....
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2,140 citations
2,036 citations
TL;DR: In this paper, the authors integrate economic concepts of supply and demand equilibrium for urban activities using the concept of traffic equilibrium within transportation networks and describe the cutting edge in travel demand analysis using the latest methods.
Abstract: Describes the cutting edge in travel demand analysis using the latest methods. Emphasizing mathematical modeling techniques, this is the first book to integrate economic concepts of supply and demand equilibrium for urban activities using the concept of traffic equilibrium within transportation networks. Models for optimal transportation are integrated with demand models. Transit travel and goods movement are specifically addressed.
1,601 citations