1. Analysis and Simulation of a Fair Queueing Algorithm A. Demers, S. keshav, and S. Shenker Wireless/Mobile Network Lab 임상택

2. Table of Contents Introduction Fair Queueing – Motivation – Definition of algorithm – Properties of Fair Queueing Flow Control Algorithms Simulations Discussion

3. 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)

4. 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

5. 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

6. R(t) : the number of rounds made in the round-robin up to time t N ac (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 t 0 will have its last bit serviced P rounds later – At time t, R(t) = R(t 0 ) + P t i α : arrival time at the gateway that packet i belonging to flow α S i α, F i α : values of R(t) when the packet started and finished service P i α : packet size F i α = S i α + P i α, S i α = MAX(F i-1 α, R(t i α )) Since R(t) is a strictly monotonically increasing function, the ordering of F i α 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.

7. A natural Way to emulate BR algorithm – F i α define the sending order of the packets – The smallest value of F i α Promptness allocation – Give more promptness (less delay) to users who utilize less than their fair share of bandwidth – B i α, nonnegative parameter δ B i α = S i α + P i α, S i α = MAX(F i-1 α, R(t i α )-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(t i α )<=F i-1 α, flow α is active ⇒ δ is irrelevant and B i α depends only on the finishing number of the previous packet R(t i α )>F i-1 α, flow α is inactive ⇒ δ = 0, B i α = P i α + R(t i α ) ⇒ δ = ∞, B i α = P i α + F i-1 α 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

8. Properties of Fair Queueing

9. Flow Control Algorithms

10. Simulations

11. Discussion