A Strategic Flow Model of Traffic Assignment in Static Capacitated Networks

Marcotte, Patrice; Nguyen, Sang; Schoeb, Alexandre

doi:10.1287/opre.1030.0091

Cited by 64 publications

(48 citation statements)

References 14 publications

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“…From a practical standpoint, capacity constraints are the simplest and perhaps most useful type of side constraints. In the context of traffic assignment, Hearn (1980), Larsson and Patriksson (1994, 1995, and Marcotte et al (2004), among others, have advocated the explicit inclusion of resource capacities as an obvious way of improving the quality of models. An equilibrium with side constraints is an equilibrium in the same game without side constraints, but where players experience infinite disutilities when their actions would result in infeasible solutions.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

A geometric approach to the price of anarchy in nonatomic congestion games

Correa

Schulz

Stier-Moses

2008

Games and Economic Behavior

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We present a short, geometric proof for the price-of-anarchy results that have recently been established in a series of papers on selfish routing in multicommodity flow networks and on nonatomic congestion games. This novel proof also facilitates two new types of theoretical results: On the one hand, we give pseudo-approximation results that depend on the class of allowable cost functions. On the other hand, we derive stronger bounds on the inefficiency of equilibria for situations in which the equilibrium costs are within reasonable limits of the fixed costs. These tighter bounds help to explain empirical observations in vehicular traffic networks. Our analysis holds in the more general context of nonatomic congestion games, which provide the framework in which we describe this work.

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Section: Discussion and Concluding Remarksmentioning

confidence: 99%

A geometric approach to the price of anarchy in nonatomic congestion games

Correa

Schulz

Stier-Moses

2008

Games and Economic Behavior

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“…In connection with this deficiency, Hearn (1980) noted that in the basic model described in Section 2, "the predicted flow on some links will be far lower or far greater than the traffic engineer knows they should be if all assumptions of the model are correct." Hearn and others, in particular Larsson and Patriksson (1994, 1999 and, most recently, Marcotte, Nguyen, and Schoeb (2003), have therefore advocated the inclusion of arc flow capacities as an obvious way of improving the quality of traffic assignment models.…”

Section: Network With Capacitiesmentioning

confidence: 99%

“…The flow that routes 1/2 on the only path consisting of three arcs and 1/2 on the arc with constant cost M is a capacitated user equilibrium. Its total travel time is It is worth mentioning that our definition of a capacitated user equilibrium includes solutions that Marcotte, Nguyen, and Schoeb (2003) consider "less natural" because drivers could contribute to the saturation of a shorter path by using a longer path that shares the same bottleneck arc with the shorter one. Actually, an alternative extension of the uncapacitated equilibrium concept is the following one:…”

Section: Network With Capacitiesmentioning

confidence: 99%

Selfish Routing in Capacitated Networks

Correa¹,

Schulz²,

Moses³

2003

SSRN Journal

149

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Abstract. According to Wardrop's first principle, agents in a congested network choose their routes selfishly, a behavior that is captured by the Nash equilibrium of the underlying noncooperative game. A Nash equilibrium does not optimize any global criterion per se, and so there is no apparent reason why it should be close to a solution of minimal total travel time, i.e. the system optimum. In this paper, we offer extensions of recent positive results on the efficiency of Nash equilibria in traffic networks. In contrast to prior work, we present results for networks with capacities and for latency functions that are nonconvex, nondifferentiable and even discontinuous.The inclusion of upper bounds on arc flows has early been recognized as an important means to provide a more accurate description of traffic flows. In this more general model, multiple Nash equilibria may exist and an arbitrary equilibrium does not need to be nearly efficient. Nonetheless, our main result shows that the best equilibrium is as efficient as in the model without capacities. Moreover, this holds true for broader classes of travel cost functions than considered hitherto.

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“…caused by the queue buildup in the oversaturated roads [49][50][51][52][55][56][57][58]. As shown, the beta which represents the value of toll or subsidy is a positive number, whereas the subsidy is supposed to be a negative value.…”

Section: Karush-kuhn-tucker Conditions and Lagrange Multipliermentioning

confidence: 99%

A modern congestion pricing policy for urban traffic: subsidy plus toll

Bagloee

Sarvi

2017

J. Mod. Transport.

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Congestion pricing is seen as an effective policy to address traffic congestion. In such policies where money, people and authorities are involved, the success generally hinges upon two factors: equity (being fair) and acceptability (to both people and authorities). The primary concern is the equity, for which ''tradable credit scheme (TCS)'' has been introduced and extensively studied in the literature. Nevertheless, due to the complexity of the trading schemes, the TCS has yet to find any foot in the real world. To this end, a novel idea of rewarding has substituted the trading component to be known as toll-and-subsidy scheme (TSS). The idea is to charge the drivers on some roads (toll) while rewarding them to use other alternative-and perhaps underutilizedroads (subsidy). The research of the TSS is in its infancy stage. The problem to be tackled in this study is as follows: Given a set of roads constituting a cordon line around the central business district (CBD) or across a screen line, how much toll or subsidy should be assigned to each road? The problem is first transformed into a capacitated traffic assignment problem. We employ a solution method based on augmenting the travel time of roads up to the level at which the traffic volumes do not exceed some target rates. A real dataset from the city of Winnipeg, Canada, is used as a pilot study. We then discuss policy-related applications of the TSS. It is proved in the literature that one can obtain optimal TSSs for various objectives and considerations. To this end, the non-negativity of the toll values is relaxed which results in a valid toll set. Nevertheless, the computational time is found to be of highest significance. Our method differs in the fact that the traffic volumes are bounded from the above and it is quite affordable. The main contribution is first to highlight the concept of subsidy along with traditional thought of merely toll. Second is to interpret the Lagrangian values of the capacity constraints as the values of the toll/subsidy.

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A Strategic Flow Model of Traffic Assignment in Static Capacitated Networks

Cited by 64 publications

References 14 publications

A geometric approach to the price of anarchy in nonatomic congestion games

A geometric approach to the price of anarchy in nonatomic congestion games

Selfish Routing in Capacitated Networks

A modern congestion pricing policy for urban traffic: subsidy plus toll

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