Scheduling for Communication and Processing Networks

Scheduling for Communication and Processing Networks

Jean WalrandEECS

University of California, Berkeley

CORNELL, 4/25/2011

Ref: Jiang-Walrand: Scheduling and Congestion Control for Communication and Processing Networks. Morgan-Claypool 2010

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WiFi Network

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WiFi Network

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WiFi Network

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WiFi Network

How to schedule transmissions?How many active nodes?

Hard to organize.Answer: Try at random!

Norman Abramson

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WiFi Network

Backoff timers;Random initial valueFreeze timer when

channel is busyTransmit when timer

runs out

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WiFi Network

Backoff timers;Random initial valueFreeze timer when

channel is busyTransmit when timer

runs out

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WiFi Network

This scheme is called CSMACarrier Sense Multiple Access

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WiFi Network

Collisions are possible:

When initial timer valuesare very similar.

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WiFi Network

To reduce chances ofcollision:

When retransmittinga packet, nodes

select initial value of timer in a range that is

twice as wide.

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WiFi Network

This scheme is calledExponential Backoff

Thus, WiFi usesCSMA with

Exponential Backoff

Metcalfe &Boggs

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WiFi Network

CSMA with Exponential Backoffworks pretty well.

About 50% efficient…Most users are happy.

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Ad Hoc Network

Why not transmitdirectly?

More efficient(parallel transmissions,

lower power,…)

Multi-hop to reach destination.If no infrastructure.

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Ad Hoc NetworkHow to schedule transmissions?

WiFi scheme?

Very unfair to nodes with many neighbors.

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WiFi scheme?Very unfair to nodes

with many neighbors.

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WiFi scheme?Very unfair to nodes

with many neighbors.

Also, oblivious to requirementsof the different nodes.

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Adaptive CSMA

Replace Exponential Backoff by Queue-Based Backoff

Libin Jiang

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Adaptive CSMA

A node with a bigger backlog should choose its random backoff in a smaller range. Stuff to send

Backoff timers

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Adaptive CSMA

The node with a bigger backlog will get a higher throughput.

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Adaptive CSMA

Adjust R so that the link transmits fast enough.

Let R = 1/(average timer value) = rate of transmission attempts

Backlog increases increase R.Backlog decreases decrease R.

R1

R3

R2

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Adaptive CSMA

Adjust R so that the link transmits fast enough.

Let R = 1/(average timer value) = rate of transmission attempts

Backlog increases increase R.Backlog decreases decrease R.

R1

R3

R2

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Adaptive CSMAHow to choose the values of R?

Do we need to know all the backlogs?

Could some nodes starve other nodes?

Can such a scheme be efficient and fair?

No

No

Yes

R = Exp{a.Backlog}

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Dual AlgorithmComplex Problem: Congestion ControlSimple Solution: TCP: AIMD

Max Sj Uj(xj) s.t. Rate on link k < Ck

Dual algorithm Local Solution- Each link k posts a price rk ≈ its backlog- Each user j chooses xj to maximize utility - price Uj(xj) – Skrk1{j uses k}

Frank Kelly

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Dual AlgorithmMuch subsequent work; backpressure protocols (see references)

Related idea: Maximize drift of Lyapunov function (see references)

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Dual AlgorithmComplex Problem: Scheduling Conflicting LinksSimple Solution: MWM (Maximum Weighted Matching)

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MWM

At any time, the links in the maximal independent set with the largest sum of queue lengths transmit.

Conflicting nodes: At any time, either {2} or {1, 3} can transmit. Maximal Independent Sets.

12

3

or

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MWM

At any time, the links in the maximal independent set with the largest sum of queue lengths transmit.Two problems:1) Finding out the backlogs of other nodes;2) Finding the independent set with maximum

sum.

Property: Stabilizes the queues. [Tassiulas, Ephremides 92]

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Dual AlgorithmComplex Problem: Random AccessSimple Solution: Adaptive CSMA

Max H(p(R)) s.t. sj > lj

Service rate at node jEntropy of distribution of independent setsDual Algorithm Local Solution

Rj updated based on backlog of j

Rj ≈ Exp{aXj}

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Example

Network

Queue Lengths

Time

λ = 0.98*(convex combination of maximal independent sets)

†

†0.2*{1, 3} + 0.3*{1, 4, 6} + 0.3*{3, 5} + 0*{2, 4} +

0.2*{2, 5}

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Congestion Control + Scheduling

• Links want to maximize the “total utility” u1(λ1) + u2(λ2) + u3(λ3)

• Congestion control + scheduling[Adjust arrival rates]

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Congestion Control + SchedulingNode i maximizes

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•Approach: Q-CSMA + input rate control•Fact: (Essentially) achieves maximum utility

Congestion Control + SchedulingNode i maximizes

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Congestion Control + Scheduling + Routing

Wireless links, with interference(Here, assume that transmitters interfere with each other via carrier sensing.)

Goal: maximize total utility of flowsCongestion control, scheduling, and routing

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Node [1]: If (9 - 5)C(g) > (9 - 3)C(b): [1] -> [3]; Else: [1] -> [2] Let b[1] = max{(9 - 5)C(g), (9 - 3)C(b)} Let T[1] be exponentially distributed with rate Exp{ αb[1] }

[1] [2]

[3]Node [2]: If (8 - 4)C(d) > (3 - 0)C(c): (d); Else: (c) Let b[2] = max{(8 - 4)C(d), (3 - 0)C(c)} Let T[2] be exponentially distributed with rate Exp{ αb[2] }


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[1] [2]

[3]

Then, use CSMA with those backoff delays.Also, A chooses x that maximizes UA(x) - β10x; B chooses y s.t....

Fact: (Essentially) achieves maximum utility


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Multipath routing allowed

Unicast S2 -> D2Anycast S1 to any D1


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Summary• Each node:• Adjusts incoming rate: maximize u(λ) - λβX• Calculates, for every flow

backpressure = link rate * (trans. Q - receiver Q)• Chooses flow with max. backpressure B• Generates backoff with mean = 1/exp{αB}• Then uses CSMA• Fact: (Essentially) maximizes sum of utilities

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StatusCompatibility with TCPB: Using max S(log(1 + x)) [Srikant]Reduce Delays: B+: Placeholder packets, virtual arrivalsRouting: C+: Avoid long pathsCollisionsWithout hidden nodes: A: [Srikant et al., LJ-JW]With hidden nodes: B: Using RTS/CTS; [Kim et al.]Unreliable links: AChanging links: CMulticast, Unicast: AImplementations: Promising examples (Rhee, Chiang, …)

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Processing Networks

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Processing NetworksTask: 1 from queue 1; Task B: 1 from all queues; Task C: 1 from queue 3

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MWM

T = 0

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MWM

T = 1-

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MWM

T = 1

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MWM

T = 2-

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MWM

T = 2

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MWM

T = 3-

Maximum Weighted Matching is not stable.

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DWM: Use MWM based on Virtual Queues

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T = 0-


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T = 0


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T = 1-


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T = 1


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T = 2-


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T = 2


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T = 3-


Deficit Maximum Weighted Matching is stable.[Proof: Lyapunov argument.]

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ConclusionsAdaptive-CSMA is throughput optimalDelays: Not perfect, but can be improvedExtends to congestion control and routingKey idea: Maximize entropyApproach applies to other distributed allocation problems:

Power allocationPeer selectionVCG auctions

Processing Networks: MWM DWM

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ReferencesCSMA & Product-Form

R.R. Boorstyn et al, 1987X. Wang & K. Kar, 2005S. Liew et al., 2007

MWMTassiulas & Ephremides, 1992

Primal-Dual Decomposition of NUMKelly et al., 1998, Low-Lapsley, Low-Tang, …Chiang-Low-Calderbank-Doyle, 2007

Backpressure Protocols + NUM Lin & Shroff, 2004 Neely-Modiano-Li; Eryilmaz-Srikant; Stolyar 2005

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ReferencesAdaptive-CSMA

Jiang-Walrand 2008/09, Shah, Proutiere, Chiang, …Improvements of Adaptive-CSMA

Ni-Tan-Srikant 2009, Jiang-Ni-Leconte-Srikant-JW 2010Adaptive-CSMA with collisions

Ni-Srikant; Jiang-Walrand; Liu et al. 2009Implementations

Warrier-Ha-Wason-Rhee, 2008*Lee-Lee-Yi-Chong-Proutiere-Chiang, 2009

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ReferencesMonographs

Jiang-Walrand. Scheduling and Congestion Control for Wireless and Processing Networks. Morgan-Claypool 2010.Neely. Stochastic Network Optimization with Application to Communication and Queueing Systems. Morgan Claypool 2010.Pantelidou-Ephremides. Scheduling in Wireless Networks. NOW, 2011

Documents

Scheduling for Communication and Processing Networks