Excluding Braess’s Paradox in Nonatomic Selfish Routing

Chen, Xujin; Diao, Zhuo; Hu, Xiaodong

doi:10.1007/978-3-662-48433-3_17

Cited by 12 publications

(22 citation statements)

References 8 publications

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“…When BP occurs in a network, IBP with a single information type also occurs (since IBP with a single information type can be shown to be identical to BP). Various aspects of BP and congestion games in general is studied in Murchland [1970], Steinberg and Zangwill [1983], Dafermos and Nagurney [1984], Patriksson [1994], Bottom et al [1999], Jahn et al [2005], Ordóñez and Stier-Moses [2010], Meir and Parkes [2014], Nikolova and Stier-Moses [2014], Chen et al [2015], and Feldman and Friedler [2015]. Our characterization of ICWE and IBP clarifies that our notion is different and, at least mathematically, more general.…”

Section: Introductionmentioning

confidence: 68%

Informational Braess’ Paradox: The Effect of Information on Traffic Congestion

Acemoğlu

Makhdoumi

Malekian

et al. 2018

Operations Research

106

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To systematically study the implications of additional information about routes provided to certain users (e.g., via GPS-based route guidance systems), we introduce a new class of congestion games in which users have differing information sets about the available edges and can only use routes consisting of edges in their information set. After defining the notion of Information Constrained Wardrop Equilibrium (ICWE) for this class of congestion games and studying its basic properties, we turn to our main focus: whether additional information can be harmful (in the sense of generating greater equilibrium costs/delays). We formulate this question in the form of Informational Braess' Paradox (IBP), which extends the classic Braess' Paradox in traffic equilibria, and asks whether users receiving additional information can become worse off. We provide a comprehensive answer to this question showing that in any network in the series of linearly independent (SLI) class, which is a strict subset of series-parallel networks, IBP cannot occur, and in any network that is not in the SLI class, there exists a configuration of edge-specific cost functions for which IBP will occur. In the process, we establish several properties of the SLI class of networks, which include the characterization of the complement of the SLI class in terms of embedding a specific set of networks, and also an algorithm which determines whether a graph is SLI in linear time. We further prove that the worst-case inefficiency performance of ICWE is no worse than the standard Wardrop equilibrium. * We thank anonymous referees as well as participants at several seminars and conferences for useful suggestions and comments.

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Section: Introductionmentioning

confidence: 68%

Informational Braess’ Paradox: The Effect of Information on Traffic Congestion

Acemoğlu

Makhdoumi

Malekian

et al. 2018

Operations Research

106

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“…This characterisation only holds for graphs where every node and every edge lie on at least one simple st-path. Later, in [4], the same characterisation is proved for directed multigraphs that satisfy the very same condition, called irredundancy therein. However, while checking redundancy and calculating the maximal irredundant subgraph can be efficiently done in undirected graphs [5], the same does not hold for directed graphs.…”

Section: Introductionmentioning

confidence: 76%

A Polynomial-Time Algorithm for Detecting the Possibility of Braess Paradox in Directed Graphs

2018

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A directed multigraph is said vulnerable if it can generate Braess paradox in Traffic Networks. In this paper, we give a graph-theoretic characterisation of vulnerable directed multigraphs; analogous results appeared in the literature only for undirected multigraphs and for a specific family of directed multigraphs. The proof of our characterisation also provides an algorithm that checks if a multigraph is vulnerable in O(|V | · |E| 2 ); this is the first polynomial time algorithm that checks vulnerability for general directed multigraphs. The resulting algorithm also contributes to another well known problem, i.e. the directed subgraph homeomorphism problem without node mapping, by providing another pattern graph for which a polynomial time algorithm exists.Contribution In this paper, we disprove this conjecture. First of all, we prove NP-hardness of checking and removing redundancy in directed multigraphs, thus formalizing the informal claim in [5]. Then, we provide a graph-theoretic characterisation of vulnerable directed nets, by proving that a directed multigraph is vulnerable if and only if it contains the graph W underlying the Wheatstone

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“…This term accounts for rare scenarios with one or multiple abnormally fast-moving vehicles that manage to exceed the usual saturation rate. Feeding the derived throughput function back into equation (12), we obtain a one-cycle gain in numbers of vehicles to the queue due to excessive flow. It is important to note that the imposed queue delay varies among vehicles within the same flow, and drivers in the head of a heavy traffic would spend significantly less time in the queue, than the ones in the tail.…”

Section: Appendix B Queue Delay Function Derivationmentioning

confidence: 99%

“…In addition, the paper extends the result to account for any Pareto inefficiency in a two-terminal network. References [11] and [12] extend the characterization from undirected graphs to directed graphs and allow for multiple commodities. Another theoretical study, [13], explores the concept of matroids to identify networks that are immune to the Braess paradox.…”

Section: Introductionmentioning

confidence: 99%

Detecting Braess Routes: an Algorithm Accounting for Queuing Delays With an Extended Graph

Burov,

Kizilkale,

Kurzhanskiy

et al. 2021

Preprint

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The Braess paradox is a counter-intuitive phenomenon whereby adding roads to a network results in higher travel time at equilibrium. In this paper we present an algorithm to detect the occurrence of this paradox in real-world networks with the help of an improved graph representation accounting for queues. The addition of queues to the network representation enables a closer match with real data. Moreover, we search for routes causing this phenomenon ('Braess routes') rather than links, and advocate removing such routes virtually from navigation systems so that the associated links can continue to serve other routes. Our algorithm relies on a convex optimization problem utilizing Beckmann potentials for road links as well as queues, and results in a route reconfiguration with reduced delay. We assume the availability of historical data to build the optimization model. We also assume the existence of a centralized navigation system to manage the routing options and remove the Braess routes. The theoretical solution demonstrates up to 12% delay reduction in a network from Montgomery County, Maryland. We validate the improvement with simulations.

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Excluding Braess’s Paradox in Nonatomic Selfish Routing

Cited by 12 publications

References 8 publications

Informational Braess’ Paradox: The Effect of Information on Traffic Congestion

Informational Braess’ Paradox: The Effect of Information on Traffic Congestion

A Polynomial-Time Algorithm for Detecting the Possibility of Braess Paradox in Directed Graphs

Detecting Braess Routes: an Algorithm Accounting for Queuing Delays With an Extended Graph

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