EE384Y: Packet Switch Architectures II
Cell Switching vs. Packet Switching
Abtin Keshavarzian
Yashar Ganjali
Department of Electrical Engineering
Stanford University
June 5, 2002
Split
Combine
Motivation
2x2 Switch
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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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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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From Cells to Packets
 Algorithm 1: Consider each packet as a
cell with length Lmax and use any cellbased algorithm.
Maximum Packet Length
Current packet
 Algorithm 2: Do the same as 1, except
renew the input-output matching when all
lines are free.
Packet 1
Packet 2
Packet 3
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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, recompute a (sub-)matching
using algorithm X
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a
b
c
d
e
f
g
h
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Under any admissible input traffic
IS Packet-Based X
Always Stable?
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A Counter-example
Time
A 1,1
A 1,2
A 2,1
A 2,2
5
3
8
2
10
6
1
4
7
9
53
2
6
14
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Waiting vs. Non-Waiting
Algorithms
 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.
3
1
 Waiting Algorithms:
 In some time slots, do not start sending
packets even if the corresponding input-output
ports are free.
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Stability of
Non-Waiting Algorithms
under
i.i.d. Traffic
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PB-MWM: i.i.d. traffic
1. At time slot n,
find MWM
2. Use the same
matching for
the next k time
slots
a
d
c
b
Lemma: The weight of the matching used by 2
>=
weight{MWM at time (n+k)} - 2Nk
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PB-MWM: i.i.d. traffic
 Start with MWM at state zero
 Go back to state 0 with probability at
least p
1-p
1-p
p
0
p
1
1-p
3
2
p
p
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Stability Theorem
 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
Theorem: PB-MWM is stable for
i.i.d. traffic
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Simulation Results
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Simulation Results
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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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Questions?