flow control kaist cs644 advanced topics in networking

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Flow Control KAIST CS644 Advanced Topics in Networking. Jeonghoon Mo School of Engineering Information and Communications University. Acknowledgements. Part of slides is from tutorial of R. Gibbens and P. Key at SIGCOMM 2000 S. Low’s OFC presentation. Overview. Problem - PowerPoint PPT Presentation

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  • Flow Control KAIST CS644Advanced Topics in NetworkingJeonghoon Mo

    School of EngineeringInformation and Communications University

    Jeonghoon MoOctober 2004

    AcknowledgementsPart of slides is fromtutorial of R. Gibbens and P. Key at SIGCOMM 2000S. Lows OFC presentation

    Jeonghoon MoOctober 2004

    OverviewProblemObjectivesKellys Framework - Wired Data NetworksExtensionsQuality of ServiceWireless NetworkHigh Speed Network: Aggregated Flow Control

    Jeonghoon MoOctober 2004

    ProblemHow to share the links bandwidth?Flows share links:

    Jeonghoon MoOctober 2004

    ProblemHow to control the network to share the bandwidth efficiently and fairly?

    Jeonghoon MoOctober 2004

    Link ModelSet of resources, J; set of routes, RA route r is a subset r J.Let

    Capacity of resource j is Cj.Ax c x 0

    Jeonghoon MoOctober 2004

    A Few System ObjectivesMax ThroughputMax-min Fairness (Most Common)Proportional Fairness (Kelly)-Fairness (Mo, Walrand)

    Jeonghoon MoOctober 2004

    Max System ThroughputMaximize: x(1) + x(2) + x(3)

    x*= (0,6,6) maximizes the total system throughput.

    However, user 1 does not get anything. => unfair

    Two links with capacity 6Three users: 1,2,3x(i) : bandwidth to user ix(1)+x(2)

  • AlgorithmsHow to achieve those system objectives?

    Jeonghoon MoOctober 2004

    Playerssourcecontrols its rate or window based on (implicit or explicit) network feedbackrouter (link)Generate (implicit) feedback or controls packets

    Jeonghoon MoOctober 2004

    Source AlgorithmTCP Vegas, RENO, ECNXCP

    Jeonghoon MoOctober 2004

    Active Queue Management (AQM)Priority QueueWFQREDREMXCP Router

  • Kellys Model and Algorithm

    Jeonghoon MoOctober 2004

    User: rate and utilityEach route has a user: if xr is the rate on route r, then the utility to user r is Ur(xr).Ur() --- increasing, strictly concave, continuously differentiable on xr [0 , ) --- elastic trafficLet C=(Cj, j J), x=(xr, r R) then Ax C.

    Jeonghoon MoOctober 2004

    System problemMaximize aggregate utility, subject to capacity constraints

    Jeonghoon MoOctober 2004

    User problemUser r chooses an amount to pay per unit time wr, and receives in return a flow xr = wr/r

    Jeonghoon MoOctober 2004

    Network problemAs if the network maximizes a logarithmic utility function, but with constants (wr, rR) chosen by the users

    Jeonghoon MoOctober 2004

    Three optimization problemsSYSTEM(U,A,C)

    USERr(Ur;r)

    NETWORK(A,C;w)

    Jeonghoon MoOctober 2004

    Decomposition theoremThere exist vectors , w and x such thatwr = rxr for r Rwr solves USERr(Ur; r)x solves NETWORK(A, C; w)

    The vector x then also solves SYSTEM(U, A, C).

    Jeonghoon MoOctober 2004

    Thus the system problem may be solved by solving simultaneously the network and user problems

    Jeonghoon MoOctober 2004

    ResultA vector x solves NETWORK(A, C; w) if and only if it is proportionally fair per unit charge

    Jeonghoon MoOctober 2004

    Solution of network problemStrategy: design algorithms to implement proportional fairnessSeveral algorithms possible: try to mimic design choices made in existing standards

    Jeonghoon MoOctober 2004

    Primal algorithm

    Jeonghoon MoOctober 2004

    Interpretation of primal algorithmResource j generates feedback signals at rate j(t) signals sent to each user r whose route passes through resource jmultiplicative decrease in flow xr at rate proportional to stream of feedback signals receivedlinear increase in flow xr at rate proportional to wr

    Jeonghoon MoOctober 2004

    Related WorkOptimization Flow Control (S. Low)Window based Model (Mo, Walrand)

    Jeonghoon MoOctober 2004

    Optimization Flow ControlDistributed algorithm to share network resourcesLink algorithm: what to feed backREDSource algorithm: how to reactTCP Tahoe, TCP Reno, TCP Vegas

    Source algLink alg

    Jeonghoon MoOctober 2004

    Welfare maximizationPrimal problem:

    Capacity can be less than real link capacityPrimal problem hard to solve & does not adapt

    Jeonghoon MoOctober 2004

    ModelNetwork:Links l each of capacity clSources s:(L(s), Us(xs), ms, Ms)L(s) - links used by source sUs(xs) - utility if source rate = xs

    Jeonghoon MoOctober 2004

    Distributed SolutionDual problem:

    BW price along path of s

    Given sources can max own benefit individually indeed primal optimal if is dual optimalSolve dual problem!

    Jeonghoon MoOctober 2004

    Distributed Solution (cont)Dual problem:

    Grad projection alg:

    Update rule:

    A distributed computation system to solve the dual problem by gradient projection algorithm

    Jeonghoon MoOctober 2004

    Source Algorithm Decentralized: Source s needs only and

    Jeonghoon MoOctober 2004

    Router (Link) AlgorithmDecentralized Rule of supply and demandAny work-conserving service disciplineSimpleaggregate source rate

    Jeonghoon MoOctober 2004

    Random Exponential Marking (REM)Source algorithmIdentical but does not communicate source rate

    Link algorithmAt update time t, sets price to a fraction of buffer occupancy:

    Theorem: Synchronous convergenceUnder same conditions (with possibly smaller ) : Price update maintains descent direction Gradient estimate converge to true gradientLimit point is primal-dual optimal

    Jeonghoon MoOctober 2004

    REDIdea: early warning of congestionAlgorithmLink:Source (Reno):Bqueuemarking1timewindow

    Jeonghoon MoOctober 2004

    REDIdea: marks for estimation of shadow priceAlgorithmLinkSource

    Global behavior of network of REM: stochastic gradient algorithm to solve dual problemQqueue marking1

    Jeonghoon MoOctober 2004

    Window-based Model [Mo,Walrand]x1 + x2 c1q1(c1 - x1 - x2) = 0w1 = x1 d1 + x1 q1 + x1 q2 xi 0, i = 1, 2, 3qi 0, i = 1, 2, Q = diag{qi }; X = diag{xi }.

    Jeonghoon MoOctober 2004

    Window-based AlgorithmTheorem: [Mowlr98]Then x(t) -> unique weighted -fair point x*Proof:The function (si /wi ) 2iis a Lyapunov functionLet dwidt= - k di siti witi := end-to-end delaysi := wi - xi di - pi

    Jeonghoon MoOctober 2004

    Extensions

    Aggregated Flow ControlQuality of ServiceWireless NetworkMaxnet and Sumnet

    Jeonghoon MoOctober 2004

    Aggregate Flow ControlMotivations:High Capacity of Optical FiberIdea:player are core routers and access routers.access router: regulates the rate of aggregated flowcore router: provide feedbacks to access routers

    Jeonghoon MoOctober 2004

    Quality of ServiceOnly bandwidth is modeled.QoS is affected byloss and delay alsoHow to incorporate other parameters?

    Jeonghoon MoOctober 2004

    Non-Convex Utility Function (Lee04)Considered sigmoidal utility functionNon-convex optimization problem =>duality gap

    (source: J. Lee et. al. Non-convexity Issues, INFOCOM 04)

    Jeonghoon MoOctober 2004

    Non-Convex Utility Functions(source: J. Lee et. al. Non-convexity Issues, INFOCOM 04)Dual Algorithm withSelf-Regulating PropertyWith Self-RegulationWithout Self-Regulation

    Jeonghoon MoOctober 2004

    Wireless Ad-Hoc Network [RAD04]Physical Model:Rate r is an increasing function of SINR.MAC : Each time slot determines power pn,which determines rate xn

    Routing matrix R and flow to path matrix F are given.

    Jeonghoon MoOctober 2004

    Random Topology Results100m x100m grid12 random node, with 6 pairs of transmissions

    Jeonghoon MoOctober 2004

    In the wireless Ad-hoc NetworksThe max-min fair rate allocation of any network has all rates equal to the worst node.

    The capacity maximization objective leads to starving users.

    Proportional Fair Allocation give reasonable trade-off between fairness and efficiency.The worst node does not starve.

    Jeonghoon MoOctober 2004

    MaxNet and SumNetSource takes max(d1,d2,, dN) in the maxnet architectureSource takes sum(d1,d2,,dN) in the sumnet architecture.

    dN

    Destination

    Source

    d1

    Link 2

    Link N

    d2

    Max

    Si

    Link 1

    Goal is not tomaximize network profit or pricing of network services, but to steer network to an efficient operating point where total user utility is maximized.Primal problem is hard to solve because it requires coordination among possibly all sources due to complex coupling through shared linksWhat we would like is a scheme that is distributed (does not require complex coordination among sources), decentralized (using only local information), and naturally adapts to time varying network conditions.

    The key is to look at the dual problem.Our model is very simple.A network is simply a set of links with finite capacities.It is shared by a set of sources. Each source s is characterized by two parameters. L(s) is the set of links source s uses; it can be an arbitrary subset of all links. Us(xs) is the utility attained by source s when it transmits at rate xs.Here is an example..The first term of the dual objective function is separable in sources s, and this is the important term. Lets look at what it is carefully, from the bottom up.Think of p_l as the price per unit bandwidth at link lThen p^s is the link prices summed over all links in the path of s, i.e., p^s is the bandwidth price that source s faces in its path.U_s(x_s) is the uitility of source s when it transmits at rate x_s, p^sx_s is the bandwidth cost in achieving that utility; hence, U_s(x_s) - p^sx_s is the benefit, and B_s(p^s) is the maximum benefit, maximized over transmission rate that lies between the MCR and PCR.

    There are several important points to note:Given the prices p^s, a source s can attempt to maximize its own benefit individually, without having to coordinate with any other sources; hence this maximization can be done distributively.It is also decentralized as a source s needs only its own utility U_s and bandwidth price p^s along its path.In general the result of this individual maximization is not globally optimal, i.e., does not solve the primal problem.By duality however if the bandwidth price is one that solves the dual problem, then indeed individual optimality coincides with social optimality, i.e, x_s(p^s) indeed is primal optimal.

    Hence we will focus on solving the dual problem for p^*. Once we have that the optimal rates come for free through individual maximization of sources.