1. Abtin Keshavarzian Yashar Ganjali Department of Electrical Engineering Stanford University June 5, 2002 Cell Switching vs. Packet Switching EE384Y: Packet Switch Architectures II

2. June 5, 2002 Cell Switching vs. Packet Switching 2 Motivation SplitCombine 2x2 Switch

3. 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

4. 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?

5. 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

6. 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

7. June 5, 2002 Cell Switching vs. Packet Switching 7 IS Packet-Based X Always Stable? Under any admissible input traffic

8. 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

9. 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.

10. June 5, 2002 Cell Switching vs. Packet Switching 10 Stability of Non-Waiting Algorithms under i.i.d. Traffic

11. 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

12. 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

13. 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

14. June 5, 2002 Cell Switching vs. Packet Switching 14 Simulation Results

15. June 5, 2002 Cell Switching vs. Packet Switching 15 Simulation Results

16. 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

17. Questions?