Network Topology and the Efficiency of Equilibrium

Milchtaich, Igal

doi:10.1007/978-3-662-05219-8_14

Cited by 29 publications

(74 citation statements)

References 18 publications

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“…Since Milchtaich, [15], has shown that Braess' paradox does not occur in graphs with the serial-parallel structure, this corollary implies that as long as the network under consideration has a serial-parallel structure (for example, a network of parallel links), partially optimal routing always improves the overall network performance.…”

Section: Xomentioning

confidence: 99%

Partially Optimal Routing

2006

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Most large-scale communication networks, such as the Internet, consist of interconnected administrative domains. While source (or selfish) routing, where transmission follows the least cost path for each source, is reasonable across domains, service providers typically engage in traffic engineering to improve operating performance within their own network. Motivated by this observation, we develop and analyze a model of partially optimal routing, where optimal routing within subnetworks is overlaid with selfish routing across domains. We demonstrate that optimal routing within a subnetwork does not necessarily improve the performance of the overall network. In particular, when Braess' paradox occurs in the network, partially optimal routing may lead to worse overall network performance. We provide bounds on the worst-case loss of efficiency that can occur due to partially optimal routing. For example, when all congestion costs can be represented by affine latency functions and all administrative domains have a single entry and exit point, the worst-case loss of efficiency is no worse than 25% relative to the optimal solution. In the presence of administrative domains incorporating multiple entry and/or exit points, however, the performance of partially optimal routing can be arbitrarily inefficient even with linear latencies. We also provide conditions for traffic engineering to be individually optimal for service providers. *This work was partially supported by research grants from the Okawa Foundation and the National Science Foundation. We thank Nicolas Stier-Moses for helpful discussions on the proof of Lemma 4.

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Section: Xomentioning

confidence: 99%

Partially Optimal Routing

2006

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“…A s − t network has linearly independent paths if every s − t path contains at least one edge not belonging to any other s − t path 4 . Milchtaich [24,Proposition 5] proved that an undirected s − t network has linearly independent paths if and only if it is extension-parallel. Therefore, every (directed) extension-parallel network has linearly independent paths (see also [20,Theorem 1]).…”

Section: φ(σmentioning

confidence: 99%

“…Milchtaich [24] was the first to consider networks with linearly independent paths (under this name). Milchtaich proved that an undirected network has linearly independent paths if and only if it is extension-parallel.…”

Section: Introductionmentioning

confidence: 99%

Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy

Fotakis

2009

Theory Comput Syst

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We investigate the effect of linear independence in the strategies of congestion games on the convergence time of best improvement sequences and on the pure Price of Anarchy. In particular, we consider symmetric congestion games on extension-parallel networks, an interesting class of networks with linearly independent paths, and establish two remarkable properties previously known only for parallel-link games. More precisely, we show that for arbitrary (non-negative and non-decreasing) latency functions, any best improvement sequence reaches a pure Nash equilibrium in at most as many steps as the number of players, and that for latency functions in class D, the pure Price of Anarchy is at most ρ(D). As a by-product of our analysis, we obtain that for symmetric congestion games on general networks with latency functions in class D, the Price of Stability is at most ρ(D).

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“…Shows that the BP can not occur in purely series-parallel networks CK Theorem 12. Shows that "A two terminal network is series-parallel if and only if there is no embedded network having the WB configuration" (see Calvert [2] p14 and also Milchtaich [6]).…”

Section: Ck Theoremmentioning

confidence: 99%

Braess's Paradox and Power-Law Nonlinearities in Five-Arc and Six-Arc Two-Terminal Networks

Penchina

2009

TOTJ

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We extend a general network theorem of Calvert and Keady (CK) relating to the minimum number of arcs needed to guarantee the occurrence of the Braess Paradox. We rephrase the CK theorems and express our proof in the terminology of traffic networks. CK described their theorem in relation to a two-terminal network of liquid in pipes. "Approximately stated, it is: if every relationship between flow and head difference is not a power law, with the same (power) s on each arc, given at least 6 pipes, one can arrange (lengths of) them so that Braess's paradox occurs, i.e. one can increase the conductivity of an individual pipe yet require more power to maintain the same consumptions." In relation to the original Braess situation of traffic network flows, the relationship is between flow and link-cost on a congested link. Our extended theorem shows that 5 pipes (roads, links, arcs) arranged in a Wheatstone Bridge (WB) network (as in the original Braess network) are necessary and sufficient to produce a Braess paradox (BP) in a two-terminal network (not limited to liquid in pipes) if at least one of the five has a different conductivity law (not power s).

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Network Topology and the Efficiency of Equilibrium

Cited by 29 publications

References 18 publications

Partially Optimal Routing

Partially Optimal Routing

Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy

Braess's Paradox and Power-Law Nonlinearities in Five-Arc and Six-Arc Two-Terminal Networks

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