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10/26/2005CCW05 1 Resolving Greedy Users via Stateless AQM Murat Alanyali Boston University Joint work with Ashraf Al Daoud

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10/26/2005CCW05 2 Queue Management Goal: fair and efficient bandwidth sharing among sessions. WFQ: Perfect isolation of traffic. Stateful. RED: Proactive packet discarding. Stateless. –Extensions well-protect less aggressive sessions (e.g. CHOKe -- Pan et al. 2000, Tang et al. 2003) –Well-studied under realistic settings (e.g. Hollot et al, Srikant et al, Low et al, with control-theoretic viewpoint). session i

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10/26/2005CCW05 3 Related work on Analysis of Conflict Single link Akella et al 2002: TCP game, under RED, CHOKe. Dutta et al. 2003: –Strategic sessions, action = pkt generation rate, utility = goodput. –Efficiency: tradeoff between goodput and packet loss. Altman et al. 2004: –Differentiated service to sessions –Utility: goodput – loss – price Packet discard prob Queue length 1

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10/26/2005CCW05 4 Overview Extend to richer topologies Consider packet discarding and pricing to stabilize good regimes Illustrate how known principles in circuit-switching may help Emphasis: on stateless AQM schemes

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10/26/2005CCW05 5 Model: Network Node operation: –RED-like: discard packet w/p D( packet arrival rate). D( ) arbitrary, subject to certain technical conditions. –Charge sessions for accepted packets – same price for all sessions. Topology: Feed-forward n1 session n2 n3 n4n5

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10/26/2005CCW05 6 Model: Packet Losses B n (v) : Packet discard probability at node n In general: Feed-forward topologies: B(v) is uniquely defined and it is smooth in v. n1 v2v2 n2 n3 n4n5 v1v1 v4v4 v3v3

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10/26/2005CCW05 7 Model: Sessions Greedy, non-strategic sessions. v s : Rate of packet generation by session s. Continuous time, deterministic model for v s. Assumption: –Delivered packets have monetary value –Change in v s is proportional to rate of profit generation:

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10/26/2005CCW05 8 Efficiency Social welfare: (not concave) Theorem: There exist parameters c n (v) such that Related work: Kelly (1988) on circuit-switched networks. Idea: Charge c n (v) per admitted packet at node n : in turn local maxima of SW(v) are locally stable.

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10/26/2005CCW05 9 Price Computation Theorem: Locally measurable:

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10/26/2005CCW05 10 Price Computation Theorem: Locally measurable: n1 v2v2 n2 n3 n4n5 v1v1 v4v4 v3v3 n6

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10/26/2005CCW05 11 Price Computation (2) Prices can be computed in a stateless manner: n1 v2v2 n2 n3 n4n5 v1v1 v4v4 v3v3 n6 ACK, sent per accepted pkt

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10/26/2005CCW05 12 Numerical Evaluation Packet-level simulation: –slotted time –time-slot = 1ms –Poisson arrivals per slot –rate-update step size = 0.1 v1 v2 v3 v4v5v6

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10/26/2005CCW05 13 Packet-level Simulation

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10/26/2005CCW05 14 Extensions Alternative measures of social welfare: –Fairness oriented: –Service differentiation: Alternate routes per session. Loopy topologies: –No conclusive result whether the fluid model is well-defined. –Special cases can be worked out: D(x) x 1

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