Minimum Complexity Non-

blocking SwitchingMario Baldi

Politecnico di Torinomario.baldi@polito.it

staff.polito.it/mario.baldi

Yoram OfekUniversità di

Trento

Achille Pattavina

Politecnico di Milano

2IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

Time-Driven SwitchingLow routing complexity

No-header processingLow buffer requirementLow switching complexity

Architecture and controlAligned switchingPre-computed switching fabric configuration

FabricBanyan

4IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

A Potential Problem

5IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

Reservation vectors

As connections/flows are set uptime frames are reserved on each

link.

As more connections/flows are setup …

time cycle

6IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

… more time frames are reservedSince nodes forward packets during the time frame following

their reception …

… the time frames on a link follow the ones on the upstream link.

As more connections/flows are setup on different paths…

7IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

… the reservation vectors grow fuller.

8IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

Still, when setting up a new connection/flow...

… multiple possible schedules may exist.

9IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

However, scheduling may be impossible.

… even though enough capacity is available on all the links.

Not possible

Not possible

Not possible

10IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

Simulation Results

0%

10%

20%

30%

40%

50%

70% 80% 90% 100%

Utilization of bottleneck link B-C [%]

Bloc

king

Pro

babi

lity

[%]

76.8Mbits/s 38.4Mbits/s 25.6Mbits/s 12.8Mbits/s 3.2Mbits/s1000 TFs 64 TFs 32 TFs 16 TFs 1 TF

11IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

Turning the Potential Problem into a Major AdvantageBanyan switching fabric

Minimum complexity: a•N •lgaN

Na {

12IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

Blocking

1

2

3

4

1

2

3

4

But only within the same time frame

13IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

The Intuition

14IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

Simulation ResultsOne Channel per Link

0%

10%

20%

30%

40%

50%

60%

70%

80%

50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100%Average Utilization [%]

Blo

ckin

g Pr

obab

ility

[%]

1 TF 4 TFs 16 TFs 32 TFs 64 TFs 1000 TFs

15IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

Lia’s Theoremv

v: number of vertical replications that ensure the switch to be non-blocking

16IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

Time-space equivalence

Selecting one out of k TFs in a time-driven switch is

equivalent to selecting one out of k vertically replicated

switching fabrics

A time-driven switch with a single Banyan fabric is non-blocking up to a load (k-v)/k

17IP-FLOW Kick-off Meeting – Trento, June 28th, 2004

Ongoing WorkFormal Proof

Basic time-space equivalence theorem

Effect of speed-upSimulation

Validation of analysisBehavior at higher loads

Network of switchesAnalysisSimulation