6 Switch Fabric

Switching - Fabric

An Engineering Approach to Computer NetworkingAn Engineering Approach to Computer Networking

April 3, 2000 Communication Networks 2

Switching

Number of connections: from few (4 or 8) to huge (100K)


Switching - Basic Assumptions

continuous streamscontinuous streams

telephone connectionstelephone connections no burstsno bursts no buffersno buffers

connections changeconnections change

multicastmulticast

BlockingBlocking externalexternal internalinternal

re-arrangeablere-arrangeable strict sense non-blockingstrict sense non-blocking wide sense non-blockingwide sense non-blocking


Multiplexors and demultiplexors

Multiplexor: aggregates sessions Multiplexor: aggregates sessions N input linesN input lines Output runs N times as fast as inputOutput runs N times as fast as input

Demultiplexor: distributes sessionsDemultiplexor: distributes sessions

one input line and N outputs that run N times slowerone input line and N outputs that run N times slower Can cascade multiplexorsCan cascade multiplexors


Time division switching Key idea: when demultiplexing, position in frame determines Key idea: when demultiplexing, position in frame determines

output limkoutput limk

Time division switching interchanges sample position within a Time division switching interchanges sample position within a frame: time slot interchange (TSI)frame: time slot interchange (TSI)


Example - TSI

sessions: (1,2) (2,4) (3,1) (4,3)

4 3 2 12 4 1 3TSI


TSI

Simple to build.Simple to build.

MulticastMulticast

Limit is the time taken to read and write to memoryLimit is the time taken to read and write to memory

For 120,000 circuitsFor 120,000 circuits need to read and write memory once every 125 microsecondsneed to read and write memory once every 125 microseconds each operation takes around 0.5 ns => impossible with current each operation takes around 0.5 ns => impossible with current

technologytechnology Need to look to other techniquesNeed to look to other techniques


Space division switching

Each sample takes a different path through the switch, Each sample takes a different path through the switch, depending on its destinationdepending on its destination


Crossbar

Simplest possible space-division switchSimplest possible space-division switch

CrosspointsCrosspoints can be turned on or off


Crossbar - example

1

2

3

4

1 2 3 4

sessions: (1,2) (2,4) (3,1) (4,3)


Crossbar

Advantages:Advantages: simple to implementsimple to implement simple controlsimple control strict sense non-blockingstrict sense non-blocking

DrawbacksDrawbacks number of crosspoints, Nnumber of crosspoints, N22

large VLSI spacelarge VLSI space vulnerable to single faultsvulnerable to single faults


Time-space switching

Precede each input trunk in a crossbar with a TSIPrecede each input trunk in a crossbar with a TSI

Delay samples so that they arrive at the right time for the space Delay samples so that they arrive at the right time for the space division switch’s scheduledivision switch’s schedule

2 1

4 3

MUX

MUX

1

2

3

4


Time-Space: Example

2 1

3 4

2 1

4 3TSI

31

24

Internal speed = double link speed

time 1

time 2


Finding the schedule

Build a graphBuild a graph nodes - input linksnodes - input links session connects an input and output nodes.session connects an input and output nodes.

Feasible scheduleFeasible schedule

Computing a scheduleComputing a schedule compute perfect matching.compute perfect matching.


Time-space-time (TST) switching

Allowed to flip samples both on input and output trunkAllowed to flip samples both on input and output trunk

Gives more flexibility => lowers call blocking probabilityGives more flexibility => lowers call blocking probability


Circuit switching - Space division

graph representationgraph representation transmitter nodestransmitter nodes receiver nodesreceiver nodes internal nodesinternal nodes

Feasible scheduleFeasible schedule edge disjoint paths.edge disjoint paths.

cost functioncost function number of crosspointsnumber of crosspoints internal nodesinternal nodes


Example

sessions: (1,3) (2,6) (3,1) (4,4) (5,2) (6,5)


Clos Network

Clos(N, n , k)N - inputs/outputs;

nxk (N/n)x(N/n) kxn

N=6n=2k=2

3x3

3x3

2x2

2x2

2x2

2x2

2x2

2x2


Clos Network - strict sense non-blocking

Holds for k >= 2n-1Holds for k >= 2n-1

Proof:Proof: Consider and idle input and outputConsider and idle input and output Input box connected to at most n-1 middle layer switchesInput box connected to at most n-1 middle layer switches output box connected to at most n-1 middle layer switchesoutput box connected to at most n-1 middle layer switches There exists a "free" middle switch.There exists a "free" middle switch.


Proof


Example

Clos(8,2,3)

N=8n=2k=3

4x4

4x4

3x2

3x2

3x2

2x3

2x3

2x3

2x3 4x4 3x2


Clos Network - rearrangable

Holds for k >= nHolds for k >= n

Proof:Proof: Consider all input and outputConsider all input and output find a perfect matching.find a perfect matching. route the perfect matchingroute the perfect matching remaining network is Clos(N-n,n-1,k-1)remaining network is Clos(N-n,n-1,k-1)

summary:summary: smaller circuitsmaller circuit weaker guaranteeweaker guarantee

Mulicast ?Mulicast ?


Recursive constructions - Benes Network

N/2 x N/2

N/2 x N/2

.

.

.

.

.

.

1

n

1

n


Benes Networks

Size:Size: F(N) = 4N + 2F(N/2) = 4N log NF(N) = 4N + 2F(N/2) = 4N log N

RearrangableRearrangable Clos network with k=2 n=2Clos network with k=2 n=2

SymmetrySymmetry

Example.Example.

proofproof


Example 16x16


Strict Sense non-Blocking

N/2 x N/2

N/2 x N/2

.

.

.

.

.

.N/2 x N/2


Properties

Size:Size: F(N) = 4N + 3F(N/2) = 4NF(N) = 4N + 3F(N/2) = 4N1.581.58

strict sense non-blockingstrict sense non-blocking Clos network with k=3 n=2Clos network with k=3 n=2

Better parameters:Better parameters: k=sqrt{N} and n=sqrt{N}k=sqrt{N} and n=sqrt{N} recursive size sqrt{N} x sqrt{N}recursive size sqrt{N} x sqrt{N} Circuit size N logCircuit size N log2.582.58 N N


Cantor Networks

m copies of Benes network.m copies of Benes network.

For m >= log N its strict sense non-blockingFor m >= log N its strict sense non-blocking

Network size N logNetwork size N log22 N N

Example Example

Proof.Proof.


Advanced constructions

There are networks of size N log N.There are networks of size N log N. the constants are huge!the constants are huge!

Basic paradigm also applies to large packet switches.Basic paradigm also applies to large packet switches.

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6 Switch Fabric