Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5,...

Abtin KeshavarzianYashar Ganjali

Department of Electrical EngineeringStanford UniversityJune 5, 2002

Cell Switching vs. Packet SwitchingCell Switching vs. Packet Switching

EE384Y: Packet Switch Architectures IIEE384Y: Packet Switch Architectures II

June 5, 2002 Cell Switching vs. Packet Switching 2

MotivationMotivation

Spl

it

Com

bine

2x2 Switch


OutlineOutline

Background: Cells vs. Packets Basic extensions of cell switching

algorithms

Stability of packet switching algorithms Waiting Algorithms Non-waiting Algorithms

Stability under i.i.d. trafficSimulation results


BackgroundBackground

Cell Switching: Fixed length cells 100% throughput using MWM for any

admissible traffic pattern Several “fast” algorithms for i.i.d. traffic

Packet Switching: Packets of different length Scheduling algorithms?


From Cells to PacketsFrom Cells to Packets

Algorithm 1: Consider each packet as a cell with length Lmax and use any cell-based algorithm.

Algorithm 2: Do the same as 1, except renew the input-output matching when all lines are free.

Maximum Packet Length

Current packet

Packet 1

Packet 2

Packet 3


Cell-Based -> Packet-Based

Cell-Based -> Packet-Based

Packet-Based X (PBX): Start with any cell-

based algorithm X At each time slot, keep

all the lines which are in the middle of sending a packet

For all free lines, re-compute a (sub-)matching using algorithm X

a

c

g

e

b

d

h

f


IS Packet-Based XAlways Stable?

IS Packet-Based XAlways Stable?

Under any admissible input traffic


A Counter-exampleA Counter-exampleTime

71 4

5 8

9

32

6

10

A 1,1

A 1,2

A 2,1

A 2,2

3

16

2

4

5


Non-Waiting Algorithms: Renew the matching amongst

free input-output ports at every possible time slot.

Previous example shows that no non-waiting algorithm is stable in general.

Waiting vs. Non-WaitingAlgorithms

Waiting vs. Non-WaitingAlgorithms

1

3

Waiting Algorithms: In some time slots, do not start sending

packets even if the corresponding input-output ports are free.


Stability of Non-Waiting Algorithms

under i.i.d. Traffic

Stability of Non-Waiting Algorithms

under i.i.d. Traffic


PB-MWM: i.i.d. trafficPB-MWM: i.i.d. traffic

a

c

d

b

Lemma: The weight of the matching used by 2

>= weight{MWM at time (n+k)} - 2Nk

1. At time slot n, find MWM

2. Use the same matching for the next k time slots


PB-MWM: i.i.d. trafficPB-MWM: i.i.d. traffic

0 1 2 3

1 - p 1 - p 1 - p

pp

p

p

Start with MWM at state zeroGo back to state 0 with probability at

least p


Stability TheoremStability Theorem

Theorem: PB-MWM is stable for i.i.d. traffic

Theorem: PB-MWM is stable for i.i.d. traffic

Using previous Lemma for PB-MWM &Using the fact that we return to the first

state in a finite number of steps on average,

we can show that E{weight(PB_MWM)} >= weight(MWM) –

const


Simulation ResultsSimulation Results


ConclusionConclusion

1. Non-Waiting PB-X algorithms unstable in general

2. PB-MWM stable for i.i.d. traffic3. PB-MWM performs slightly

better than CB-MWM for low traffic

Questions?

Questions?

Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5,...

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