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Analysis and Simulation of a Fair Queueing Algorithm A. Demers, S. keshav, and S. ShenkerPowerPoint Presentation

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 AlgorithmA. 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

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

- 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

- It is simple to Allocate buffer space fairly

- 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

- Properties of Fair Queueing time t

Flow Control Algorithms time t

Simulations time t

Discussion time t

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