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# Analysis and Simulation of a Fair Queueing Algorithm A. Demers, S. keshav, and S. Shenker - PowerPoint PPT Presentation

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 AlgorithmA. Demers, S. keshav, and S. Shenker

Wireless/Mobile Network Lab

임상택

• Introduction

• Fair Queueing

• Motivation

• Definition of algorithm

• Properties of Fair Queueing

• Flow Control Algorithms

• Simulations

• Discussion

• 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)

• 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 time t

Discussion time t