Analysis and simulation of a fair queueing algorithm a demers s keshav and s shenker
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Analysis and Simulation of a Fair Queueing Algorithm A. Demers, S. keshav, and S. Shenker. Wireless/Mobile Network Lab 임상택. Table of Contents. Introduction Fair Queueing Motivation Definition of algorithm Properties of Fair Queueing Flow Control Algorithms Simulations Discussion.

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Analysis and simulation of a fair queueing algorithm a demers s keshav and s shenker

Analysis and Simulation of a Fair Queueing AlgorithmA. Demers, S. keshav, and S. Shenker

Wireless/Mobile Network Lab

임상택


Table of contents
Table of Contents

  • Introduction

  • Fair Queueing

    • Motivation

    • Definition of algorithm

    • Properties of Fair Queueing

  • Flow Control Algorithms

  • Simulations

  • Discussion


Introduction
Introduction

  • The rapid growth, in both use and size, of computer networks ⇒ methods of congestion control

  • Congestion control

    • At the source point ⇒ flow control algorithms

    • At the gateway point ⇒ routing and queueing algorithms

  • Queueing algorithms can be though of as allocating three nearly independent quantities

    • Bandwidth(which packets get transmitted)

    • Promptness(when do those packets get transmitted)

    • Buffer space(which packets are discarded by the gateway)


Fair queueing
Fair Queueing

  • Motivation

    • The requirement that the queueing algorithm allocate bandwidth and buffer space fairly

    • Nagle’s Fair Queueing flaw

      • The gateway should provide service that does not depend on a packet’s time of arrival

      • lack of consideration of packet lengths( long packets get more bandwidth than short packets, not fairly.)

    • Max-min fairness criterion


  • Definition of algorithm

    • It is simple to Allocate buffer space fairly

      • by dropping packets, when necessary from the flow with the largest queue

    • Allocate bandwidth fairly

      • Pure Round-robin service fails to guarantee a fair allocation ⇒ Because of variations in packet sizes

      • Bit-by-bit round robin (BR) fashion ( as in a head-of-queue processor sharing discipline )

        • Allocates fairly ⇒ Since at every instant in time each flow is receiving its fair share


  • R(t) : the number of rounds made in the round-robin up to time t

  • Nac(t) : the number of active sessions that have bits in their queue at time t

  • μ : the line-speed of the gateway’s outgoing line

  • A Packet of size P whose first bit gets serviced at time t0 will have its last bit serviced P rounds later

    • At time t, R(t) = R(t0) + P

  • tiα : arrival time at the gateway that packet i belonging to flow α

  • Siα, Fiα : values of R(t) when the packet started and finished service

  • Piα: packet size

    Fiα = Siα + Piα , Siα = MAX(Fi-1α , R(tiα))

  • Since R(t) is a strictly monotonically increasing function, the ordering of Fiα values is the same as the ordering of the finishing times

  • Bit-by-bit round robin is unrealistic ⇒ Emulate this algorithm by packet-by-packet transmission scheme.


  • A natural Way to emulate BR algorithm time t

    • Fiα define the sending order of the packets

    • The smallest value of Fiα

  • Promptness allocation

    • Give more promptness (less delay) to users who utilize less than their fair share of bandwidth

    • Biα , nonnegative parameter δ

      Biα = Siα + Piα , Siα = MAX(Fi-1α , R(tiα)-δ)

    • Sending order is determined by the B’s, not the F’s

    • This gives slightly faster service to packets that arrive at an inactive conversation

    • Two extreme cases δ = 0 and δ = ∞

      • R(tiα)<=Fi-1α , flow α is active ⇒ δ is irrelevant and Biα depends only on the finishing number of the previous packet

      • R(tiα)>Fi-1α , flow α is inactive

        • δ = 0, Biα = Piα + R(tiα)

        • δ = ∞, Biα = Piα + Fi-1α

  • Buffer space

    • When the queue is full and new packet arrives, the last packet from the source using the most buffer space is dropped

    • When packet is dropped, F’s and S’s unchanged

      • Small penalty for ill-behaved hosts




Simulations
Simulations time t


Discussion
Discussion time t


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