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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)
April 3, 2000 Communication Networks 3
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
April 3, 2000 Communication Networks 4
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
April 3, 2000 Communication Networks 5
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)
April 3, 2000 Communication Networks 6
Example - TSI
sessions: (1,2) (2,4) (3,1) (4,3)
4 3 2 12 4 1 3TSI
April 3, 2000 Communication Networks 7
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
April 3, 2000 Communication Networks 8
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
April 3, 2000 Communication Networks 9
Crossbar
Simplest possible space-division switchSimplest possible space-division switch
CrosspointsCrosspoints can be turned on or off
April 3, 2000 Communication Networks 10
Crossbar - example
1
2
3
4
1 2 3 4
sessions: (1,2) (2,4) (3,1) (4,3)
April 3, 2000 Communication Networks 11
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
April 3, 2000 Communication Networks 12
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
April 3, 2000 Communication Networks 13
Time-Space: Example
2 1
3 4
2 1
4 3TSI
31
24
Internal speed = double link speed
time 1
time 2
April 3, 2000 Communication Networks 14
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.
April 3, 2000 Communication Networks 15
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
April 3, 2000 Communication Networks 16
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
April 3, 2000 Communication Networks 17
Example
sessions: (1,3) (2,6) (3,1) (4,4) (5,2) (6,5)
April 3, 2000 Communication Networks 18
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
April 3, 2000 Communication Networks 19
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.
April 3, 2000 Communication Networks 20
Proof
April 3, 2000 Communication Networks 21
Example
Clos(8,2,3)
N=8n=2k=3
4x4
4x4
3x2
3x2
3x2
2x3
2x3
2x3
2x3 4x4 3x2
April 3, 2000 Communication Networks 22
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 ?
April 3, 2000 Communication Networks 23
Recursive constructions - Benes Network
N/2 x N/2
N/2 x N/2
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1
n
1
n
April 3, 2000 Communication Networks 24
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
April 3, 2000 Communication Networks 25
Example 16x16
April 3, 2000 Communication Networks 26
Strict Sense non-Blocking
N/2 x N/2
N/2 x N/2
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.N/2 x N/2
April 3, 2000 Communication Networks 27
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
April 3, 2000 Communication Networks 28
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.
April 3, 2000 Communication Networks 29
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.