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Internet Protocols Steven Low CS/EE netlab.CALTECH.edu October 2004 with J. Doyle, L. Li, A. Tang, J. Wang

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Internet Protocols Selects paths from sources to dests TCP/AQM IP x i (t) p l (t) Selects source transmission rates Link Selects topology, capacities, power,… Application Selects user criteria, web layout, utility

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Internet Protocols TCP/AQM IP x i (t) p l (t) Link Application Protocols determines network behavior Critical, yet difficult, to understand and optimize Local algorithms, distributed spatially and vertically global behavior Designed separately, deployed asynchronously, evolves independently

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Internet Protocols TCP/AQM IP x i (t) p l (t) Link Application Protocols determines network behavior Critical, yet difficult, to understand and optimize Local algorithms, distributed spatially and vertically global behavior Designed separately, deployed asynchronously, evolves independently Need to reverse engineer … to forward engineer new large networks

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Internet Protocols TCP/AQM IP x i (t) p l (t) Link Application Protocols determines network behavior Critical, yet difficult, to understand and optimize Local algorithms, distributed spatially and vertically global behavior Designed separately, deployed asynchronously, evolves independently Need to reverse engineer … much easier than biology with full specs

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Internet Protocols Minimize path costs (IP) TCP/AQM IP x i (t) p l (t) Maximize utility (TCP/AQM) Link Minimize SIR, max capacities, … Application Minimize response time (web layout)

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Internet Protocols Each layer is abstracted as an optimization problem Operation of a layer is a distributed solution Results of one problem (layer) are parameters of others Operate at different timescales TCP/AQM IP Link Application IPLink

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IP TCP/ AQM Applications Link Chiang: X-ities?? Utility maximization Chiang: Wireless issues ?? Outline General Approach: 1) Understand a single layer in isolation and assume other layers are designed nearly optimally. 2) Understand interactions across layers 3) Incorporate additional layers, with the ultimate goal of viewing entire protocol stack as solving one giant optimization problem (where individual layers are solving parts of it).

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IP TCP/ AQM Applications Link Outline Utility maximization Some implications

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Network model F1F1 FNFN G1G1 GLGL R R T TCP Network AQM x y q p Reno, Vegas DT, RED, … IP routing

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Network model - example Reno, Vegas DT, RED, … IP routing TCP Reno: currently deployed TCP AI MD TailDrop

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Network model - example Reno, Vegas DT, RED, … IP routing TCP FAST: high speed version of Vegas

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Duality model Flow control problem (Kelly, Malloo, Tan 98) TCP/AQM Maximize utility (& solve Dual) with different utility functions (L 03): (x*,p*) primal-dual optimal iff Primal-dual algorithm Reno, Vegas, FASTDT, RED, REM/PI, AVQ

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Duality model Historically Packet level implemented first Flow level understood as after-thought But flow level design determines performance, fairness, stability Vegas, FAST, STCP HSTCP (homogeneous sources) Reno (homogeneous sources) infinity XCP (single link only) (Mo & Walrand 00)

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Duality model Historically Packet level implemented first Flow level understood as after-thought But flow level design determines performance, fairness, stability Now: can forward engineer Given (application) utility functions, can generate provably scalable TCP algorithms

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Protocol decomposition TCP-AQM: TCP algorithms maximize utility with different utility functions Congestion prices coordinate across protocol layers TCP-AQM IP TCP/ AQM Applications Link

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Protocol decomposition TCP-AQM IP TCP-AQM IP TCP/ AQM Applications Link TCP/IP: TCP algorithms maximize utility with different utility functions Shortest-path routing is optimal using congestion prices as link costs Congestion prices coordinate across protocol layers

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Protocol decomposition TCP-AQM IP TCP/IP (with fixed c ): Equilibrium of TCP/IP exists iff zero duality gap NP-hard, but subclass with zero duality gap is LP Equilibrium, if exists, can be unstable Can stabilize, but with reduced utility Inevitable tradeoff bw utility max & routing stability TCP-AQM IP TCP/ AQM Applications Link

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Protocol decomposition IP Link TCP/IP with optimal c : With optimal provisioning, static routing is optimal using provisioning cost as link costs TCP/IP with static routing in well-designed network TCP-AQM IP TCP-AQM IP TCP/ AQM Applications Link

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IP TCP/ AQM Applications Link Outline Utility maximization Some implications

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Implications Is fair allocation always inefficient ? Does raising capacity always increase throughput ? Intricate and surprising interactions in large-scale networks … unlike at single link

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Implications Is fair allocation always inefficient Does raising capacity always increase throughput

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Fairness Identify allocation with An allocation is fairer if its is larger (Mo, Walrand 00)

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Fairness maximum throughput proportional fairness min delay fairness (Reno) infinity maxmin fairness (Mo, Walrand 00)

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Efficiency Unique optimal rate x () An allocation is efficient if T () is large

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Conjecture T () is nonincreasing i.e. a fair allocation is always inefficient

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Example 1 Conjecture T () is nonincreasing i.e. a fair allocation is always inefficient 0 max throughput 1 1/(L+1) proportional fairness L/L(L+1) 1/2 maxmin fairness 1/2

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Intuition “The fundamental conflict between achieving flow fairness and maximizing overall system throughput….. The basic issue is thus the trade-off between these two conflicting criteria.” Luo,etc.(2003), ACM MONET

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Results Theorem: Necessary & sufficient condition for general networks (R, c) provided every link has a 1-link flow Corollary 1: true if N(R)=1

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Counter-example There exists a network such that dT/d > 0 for almost all >0 Intuition Large favors expensive flows Long flows may not be expensive Max-min may be more efficient than proportional fairness expensive long

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Counter-example Theorem: Given any 0 >0, there exists network where Compact example

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Implications Is fair allocation always inefficient ? Does raising capacity always increase throughput ? Intricate and surprising interactions in large-scale networks … unlike at single link

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Throughput & capacity Intuition: Increasing link capacities always raises throughput T Theorem: Necessary & sufficient condition for general networks (R, c) Corollary: For all , increasing a link’s capacity can reduce T all links’ capacities equally can reduce T all links’ capacities proportionally raises T

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Protocol decomposition TCP-AQM IP Link TCP algorithms maximize utility with different utility functions IP shortest path routing is optimal using congestion prices as link costs, with given link capacities c With optimal provisioning, static routing is optimal using provisioning cost as link costs Congestion prices coordinate across protocol layers

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Some implications TCP-AQM TCP/AQM: TCP maximizes aggregate utility (not throughput) Fair bandwidth allocation is not always inefficient Increasing capacity does not always raise throughput Intricate network interactions paradoxical behavior

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