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Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet Switch Architectures II
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June 5, 2002 Cell Switching vs. Packet Switching 2 Motivation SplitCombine 2x2 Switch
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June 5, 2002 Cell Switching vs. Packet Switching 3 Outline 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. traffic Simulation results
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June 5, 2002 Cell Switching vs. Packet Switching 4 Background 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?
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June 5, 2002 Cell Switching vs. Packet Switching 5 From Cells to Packets Algorithm 1: Consider each packet as a cell with length L max 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
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June 5, 2002 Cell Switching vs. Packet Switching 6 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
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June 5, 2002 Cell Switching vs. Packet Switching 7 IS Packet-Based X Always Stable? Under any admissible input traffic
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June 5, 2002 Cell Switching vs. Packet Switching 8 A Counter-example Time 714 58 9 3 2 6 10 A 1,1 A 1,2 A 2,1 A 2,2 3 1 6 2 4 5
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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-Waiting Algorithms 1 3 Waiting Algorithms: In some time slots, do not start sending packets even if the corresponding input-output ports are free.
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June 5, 2002 Cell Switching vs. Packet Switching 10 Stability of Non-Waiting Algorithms under i.i.d. Traffic
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June 5, 2002 Cell Switching vs. Packet Switching 11 PB-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
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June 5, 2002 Cell Switching vs. Packet Switching 12 PB-MWM: i.i.d. traffic 0 12 3 1 - p p p p p Start with MWM at state zero Go back to state 0 with probability at least p
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June 5, 2002 Cell Switching vs. Packet Switching 13 Stability Theorem 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
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June 5, 2002 Cell Switching vs. Packet Switching 14 Simulation Results
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June 5, 2002 Cell Switching vs. Packet Switching 15 Simulation Results
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June 5, 2002 Cell Switching vs. Packet Switching 16 Conclusion 1.Non-Waiting PB-X algorithms unstable in general 2.PB-MWM stable for i.i.d. traffic 3.PB-MWM performs slightly better than CB-MWM for low traffic
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