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84
How bad is selfish routing?
 JOURNAL OF THE ACM
, 2002
"... 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 t ..."
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Cited by 506 (27 self)
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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 minimumlatency 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
Bayesian Inference on Network Traffic Using Link Count Data
 J. Amer. Statist. Assoc
, 1996
"... We study Bayesian models and methods for analysing network traffic counts in problems of inference about the traffic intensity between directed pairs of origins and destinations in networks. This is a class of problems very recently discussed by Vardi in a 1996 JASA article, and of interest in both ..."
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Cited by 82 (1 self)
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We study Bayesian models and methods for analysing network traffic counts in problems of inference about the traffic intensity between directed pairs of origins and destinations in networks. This is a class of problems very recently discussed by Vardi in a 1996 JASA article, and of interest in both communication and transportation network studies. The current paper develops the theoretical framework of variants of the origindestination flow problem, and introduces Bayesian approaches to analysis and inference. In the first, the socalled fixed routing problem, traffic or messages pass between nodes in a network, with each message originating at a specific source node, and ultimately moving through the network to a predetermined destination node. All nodes are candidate origin and destination points. The framework assumes no travel time complications, considering only the number of messages passing between pairs of nodes in a specified time interval. The route count, or route flow, pro...
Uncertainty Propagation in an Integrated Land UseTransportation Modeling Framework: Output Variation via UrbanSim
 TRANSPORTATION RESEARCH RECORD
, 2002
"... This study examines the impact of uncertainty in the land use component of a partially integrated land usetransportation modeling system called UrbanSim. Outputs from the land use model (LUM) act as inputs for a traditional 4step travel demand model (TDM), and travel times from the trafficassignm ..."
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Cited by 19 (7 self)
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This study examines the impact of uncertainty in the land use component of a partially integrated land usetransportation modeling system called UrbanSim. Outputs from the land use model (LUM) act as inputs for a traditional 4step travel demand model (TDM), and travel times from the trafficassignment stage of the TDM are fed forward into the subsequent years LUM. This work examines the propagation of uncertainty across model stages as well as at each model stage over time. A factorized design approach is used to model uncertainty in demographic inputs (which include aggregate growth rates and mobility rates) to the land use model, as well as uncertainty in various model parameters. The results suggest that while several model inputs may affect model outputs in the short run, only those inputs that have a cumulative effect are likely to have a significant impact on outputs in the long run. The results also suggest that uncertainty in model outputs may increase for the first few years for which the model is run, as modified inputs send shocks through the urban system. However, the level of uncertainty appears to come down in later years, as households, jobs, and developers respond to changed input conditions.
A toll pricing framework for traffic assignment problems with elastic demand
 Transportation and Network Analysis: Current Trends. Miscellanea in honor of Michael Florian
, 2002
"... Abstract: This paper extends the notion of toll pricing and the toll pricing framework previously developed for fixed demand traffic assignment [4, 13] to the problem with elastic demand. The system problem maximizes net benefit to the network users [9, 20] and the user problem is the usual one of f ..."
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Cited by 17 (3 self)
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Abstract: This paper extends the notion of toll pricing and the toll pricing framework previously developed for fixed demand traffic assignment [4, 13] to the problem with elastic demand. The system problem maximizes net benefit to the network users [9, 20] and the user problem is the usual one of finding equilibrium with elastic demand. We define and characterize T, the set of all tolls for the user problem that achieve the system optimal solution. When solutions to the two problems are unique, T is a polyhedron defined by the optimal solution of the system problem, similar to the case in [4, 13]. The Toll Pricing Framework in [13] is also extended to allow optimization of secondary criteria over T. Examples include minimizing the number of toll booths and minimizing the maximum toll on any link. A numerical example illustrates the results. Keywords:
An Augmented Lagrangean Dual Algorithm for Link Capacity Side Constrained Traffic Assignment Problems
 Transportation Research
, 1995
"... As a means to obtain a more accurate description of traffic flows than that provided by the basic model of traffic assignment, there have been suggestions to impose upper bounds on the link flows. This can be done either by introducing explicit link capacities or by employing travel time functions w ..."
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Cited by 15 (8 self)
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As a means to obtain a more accurate description of traffic flows than that provided by the basic model of traffic assignment, there have been suggestions to impose upper bounds on the link flows. This can be done either by introducing explicit link capacities or by employing travel time functions with asymptotes at the upper bounds. Although the latter alternative has the disadvantage of inherent numerical illconditioning, the capacitated assignment model has been studied and applied to a limited extent, the main reason being that the solutions can not be characterized by the classical Wardrop equilibrium conditions; they may, however, be characterized as Wardrop equilibria in terms of a welldefined, natural generalized travel cost. The introduction of link capacity side constraints makes the problem computationally more demanding. The availability of efficient algorithms for the basic model of traffic assignment motivates the use of dualization approaches for handling the capacity c...
A parallel splitting method for coupled monotone inclusions
"... A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces, and its convergence is established under the assumption that solutions exist. Unlike existing alternating algorithms, which are limited to two variables and linear coupling, our parallel met ..."
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Cited by 13 (5 self)
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A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces, and its convergence is established under the assumption that solutions exist. Unlike existing alternating algorithms, which are limited to two variables and linear coupling, our parallel method can handle an arbitrary number of variables as well as nonlinear coupling schemes. The breadth and flexibility of the proposed framework is illustrated through applications in the areas of evolution inclusions, variational problems, best approximation, and network flows.
Individual Adaptation In A PathBased Simulation Of The Freeway Network Of Northrhine Westfalia
, 1996
"... Traffic simulations are... This paper shows, in a realistic road network, how repeated simulations can be used so that drivers can explore different paths, and how macroscopic quantities such as locations of jams or network throughput change as a result of this. ..."
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Cited by 12 (5 self)
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Traffic simulations are... This paper shows, in a realistic road network, how repeated simulations can be used so that drivers can explore different paths, and how macroscopic quantities such as locations of jams or network throughput change as a result of this.
A Unified Description of Iterative Algorithms for Traffic Equilibria
 European Journal of Operational Research
, 1992
"... The purpose of this paper is to provide a unified description of iterative algorithms for the solution of traffic equilibrium problems. We demonstrate that a large number of well known solution techniques can be described in a unified manner through the concept of partial linearization, and establis ..."
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Cited by 11 (9 self)
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The purpose of this paper is to provide a unified description of iterative algorithms for the solution of traffic equilibrium problems. We demonstrate that a large number of well known solution techniques can be described in a unified manner through the concept of partial linearization, and establish close relationships with other algorithmic classes for nonlinear programming and variational inequalities. In the case of nonseparable travel costs, the class of partial linearization algorithms are shown to yield new results in the theory of finitedimensional variational inequalities. The possibility of applying truncated algorithms within the framework is also discussed.
Modeling and Simulation of Large Biological, Information and SocioTechnical Systems: An Interaction Based Approach
 Interactive Computation: The New
, 2005
"... Summary We describe an interaction based approach for computer modeling and simulation of large integrated biological, information, social and technical (BIST) systems 1 Examples of such systems are urban regional transportation systems, the national electrical power markets and grids, gene regulato ..."
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Cited by 11 (8 self)
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Summary We describe an interaction based approach for computer modeling and simulation of large integrated biological, information, social and technical (BIST) systems 1 Examples of such systems are urban regional transportation systems, the national electrical power markets and grids, gene regulatory networks, the worldwide Internet, infectious diseases, vaccine design and deployment, theater war, etc. These systems are composed of large numbers of interacting human, physical, informational and technological components. These components adapt and learn, exhibit perception, interpretation, reasoning, deception, cooperation and noncooperation, and have economic motives as well as the usual physical properties of interaction. The theoretical foundation of our approach consists of two parts: (i) mathematics of complex interdependent dynamic networks, and (ii) mathematical and computational theory of a class of finite discrete dynamical systems called Sequential Dynamical Systems (SDSs). We then consider engineering principles based on such a theory. As with the theoretical foundation, they consist of two basic parts: (i) Efficient data manipulation, including synthesis, integration, storage and regeneration and (ii) high performance computing oriented system design, development and implementation. The engineering methods allow us to specify, design, and analyze simulations of extremely large systems and implement them on massively parallel architectures. As an illustration of our approach, an interaction based computer modeling and simulation framework to study very large interdependent societal infrastructures is described. 1
2004), “Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous
 Commuters,” Transportation Science
"... This paper discusses uniqueness of user equilibrium in transportation networks with heterogeneous commuters. Daganzo (1983, Transportation Science) proved the uniqueness of (stochastic) user equilibrium when commuters have heterogeneous tastes over possible paths but identical disutility functions f ..."
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Cited by 8 (0 self)
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This paper discusses uniqueness of user equilibrium in transportation networks with heterogeneous commuters. Daganzo (1983, Transportation Science) proved the uniqueness of (stochastic) user equilibrium when commuters have heterogeneous tastes over possible paths but identical disutility functions from time costs. We Þrst show, by example, that his result may not apply in general networks if disutility functions are allowed to differ. However, for “simple ” transportation networks, we show that user equilibrium is always unique and weakly Pareto efficient (cf. the Braess example) for a general class of utility functions. We investigate if this result applies to more general networks. We also show that user equilibrium is unique in a dynamic bottleneck model with a simple network. We discuss an interesting relationship between the following two problems: the existence of user equilibrium in a Þnite model and the uniqueness of user equilibrium in a continuum model. In the appendix, we also provide a proof of a slightly generalized version of Daganzo’s theorem. Keywords: transportation network, user equilibrium, heterogeneous commuters, uniqueness, efficiency, bottleneck model, game theory 2