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![Page 1: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/1.jpg)
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
![Page 2: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/2.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 2
MotivationMotivation
Spl
it
Com
bine
2x2 Switch
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June 5, 2002 Cell Switching vs. Packet Switching 3
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
![Page 4: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/4.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 4
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?
![Page 5: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/5.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 5
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
![Page 6: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/6.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 6
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
![Page 7: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/7.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 7
IS Packet-Based XAlways Stable?
IS Packet-Based XAlways Stable?
Under any admissible input traffic
![Page 8: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/8.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 8
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
![Page 9: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/9.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 9
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.
![Page 10: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/10.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 10
Stability of Non-Waiting Algorithms
under i.i.d. Traffic
Stability of Non-Waiting Algorithms
under i.i.d. Traffic
![Page 11: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/11.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 11
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
![Page 12: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/12.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 12
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
![Page 13: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/13.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 13
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
![Page 14: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/14.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 14
Simulation ResultsSimulation Results
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June 5, 2002 Cell Switching vs. Packet Switching 15
Simulation ResultsSimulation Results
![Page 16: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/16.jpg)
June 5, 2002 Cell Switching vs. Packet Switching 16
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
![Page 17: Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet.](https://reader036.fdocuments.us/reader036/viewer/2022062422/56649f1b5503460f94c30150/html5/thumbnails/17.jpg)
Questions?
Questions?