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Competitive Queueing Policies for QoS Switches. Nir Andelman Yishay Mansour An Zhu TAUTAUStanford. Outline. Motivation Model description Summary of Previous and new results Non-preemptive queue Two packet types Multiple packet types Preemptive queue lower bound

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Competitive Queueing Policies for QoS Switches

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Competitive queueing policies for qos switches

Competitive Queueing

Policies for QoS

Switches

Nir Andelman Yishay Mansour An Zhu

TAUTAUStanford


Outline

Outline

  • Motivation

  • Model description

  • Summary of Previous and new results

  • Non-preemptive queue

    • Two packet types

    • Multiple packet types

  • Preemptive queue lower bound

  • Open Questions


Motivation

Motivation

  • Quality of Service

    • Guaranteed performance

    • Limited resources

  • Premium Service


Motivation cont

Motivation (cont.)

  • Assured service

    • Relative (not Guaranteed) Performance

    • Different packet priorities (values)

    • High Network Utilization


Competitive queueing policies for qos switches

Motivation (cont.)

  • Queue management

    • Outgoing port

    • Limited queue space

    • Online packet scheduling

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Our model

Our model

  • Input: a stream of valued packets.

  • Actions: either accept or reject a packet

  • Send events: at integer times

  • Benefit = Total value of the packets sent.

  • Main Variations:

    • Non-Preemptive FIFO Queue

    • Preemptive FIFO Queue

    • Delay-Bounded Queue

  • Competitive Analysis: ρ = max {offline/online}


Previous results

Previous Results

  • Non-Preemptive Queue

    • (2-1)/ lower bound for 2 values and Analyzes specific policies (AMRR00)

  • Preemptive Queue

    • 2-o(1) competitive greedy algorithm (KLMPSS01)

    • 1.28 lower bound for 2 values (Sviridenko01)

    • 1.30 competitive algorithm for 2 values (LP02)

  • Delay-Bounded Queue (KLMPSS01)

    • 2 competitive greedy algorithm

    • 1.17 lower bound for -uniform bounded delay

    • 1.414  ρ 1.618 for 2-variable bounded delay

    • 1.25  ρ  1.434 for 2-uniform bounded delay


Summary of our results

Summary of Our Results

  • Non-preemptive queue

    • Algorithm with ρ = (2-1)/

      • optimal for 2 values

    • tight(er) bounds for previous policies

    • ρ = (ln()) for continuous values

  • Preemptive queue

    • General lower bound of 1.414

    • Exact ρ =1.434 for queue size 2

  • Delay-Bounded queue

    • 1.366  ρ  1.414 for 2-uniform bounded delay

    • ρ = 1.618 for 2-variable bounded delay


Non preemptive lower bound 2 values

Non-Preemptive Lower bound - 2 values

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ON

OFF

[From AMRR 2000]

Online accepts xB packets.

Offline accepts B packets.

Ratio is x


Competitive queueing policies for qos switches

Lower bound- 2 values (cont.)

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ON

OFF

Online accepts xB low and at most (1-x)B high.

Offline accepts B high value packets.

Ratio is [x+(1-x)]/


Lower bound 2 values cont

Lower bound - 2 values (cont.)

Optimize lower bound: x = /(2-1)

Lower bound :   (2-1)/


Ratio partition rp policy

Ratio Partition (RP) Policy

  • Always accept high value packets.

  • Each high value packet marks /(-1) low value packets in the queue that arrived before it.

  • Accept a low packet if you can mark it by filling the queue with high value packets.


Rp example 1

RP Example (1)

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Let  = 2,

Each high value marks 2 low values.

Lemma:

When the queue is full, all packets in it are marked.


Competitive queueing policies for qos switches

RP Example (2)

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Free slots left for (possible) future high values.


Rp analysis

RP Analysis

  • Full queue:

    • all low value packets are marked.

  • Online marked packets bound:

    • offline high value packets.

  • Marking parameter balances:

    • accepted low value packets

    • slots for future high value packets.

  • Optimizing the marking parameter givesρ=(2-1)/.

  • Optimal competitive ratio.


Continuous values

Continuous Values

  • Create n= ln() sub-queues

  • Sub-queue k accepts values [k-1/n,k/n]

  • Sub-queues take turns in sending

    • Can be simulated by a FIFO queue.

  • Competitive ratio of e ln()

  • Lower bound: ln()+1


Preemptive lower bound

Preemptive Lowerbound

i

Z

i-1

B-1

  • Stage i includes:

    • A burst of B-1 i-1 packets followed by one i

    • At the next Z times units, one i packet each unit

  • End with B packets of value k

  • Stop: if B-Z packets are preempted in a stage.

  • Optimize i and Z=B/2

  • the lower bound converges towards 1.414.

  • For B=2 the bound is 1.434.

i-1

i-1

i

i

i

i


Open problems

Open Problems

  • Non-Preemptive queue & continuous values

    • Close the constant gap between the upper (e ln()) and lower (ln()+1) bounds

  • Preemptive queue & continuous values

    • Is there a policy which has ρ ≤ 2-ε

  • Delay-Bounded queue:

    • Better than Greedy for delay > 2


Competitive queueing policies for qos switches

The End


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