1. Switching Units

2. Types of switching elements
Telephone switches
switch samples
Datagram routers
switch datagrams
ATM switches
switch ATM cells
INPUTS
OUTPUTS
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3. Repeaters, bridges, routers, and gateways
Repeaters/Hubs: at physical level (L1)
Bridges: at datalink level (L2)
based on MAC addresses
discover attached stations by listening
Routers: at network level (L3)
participate in routing protocols
Application level gateways: at application level (L7)
treat entire network as a single hop
Gain functionality at the expense of forwarding speed
for best performance, push functionality as low as possible
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4. Types of services Packet vs. circuit switches
packets have headers and samples don’t
Connectionless vs. connection oriented
connection oriented switches need a call setup
setup is handled in control plane by switch controller
connectionless switches deal with self-contained datagrams
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5. Other switching unit functions
Participate in routing algorithms
to build routing tables
Next Lecture!
Resolve contention for output trunks
buffer scheduling
Previous Lecture!
Admission control
to guarantee resources to certain streams
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6. Requirements
Capacity of switch is the maximum rate at which it can move information, assuming all data paths are simultaneously active
Primary goal: maximize capacity
subject to cost and reliability constraints
Circuit switch must reject call if can’t find a path for samples from input to output
goal: minimize call blocking
Packet switch must reject a packet if it can’t find a buffer to store it awaiting access to output trunk
goal: minimize packet loss
Subgoal: Don’t reorder packets
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7. Internal switching
In a circuit switch, path of a sample is determined at time of connection establishment
No need for a sample header--position in frame is enough
In a packet switch, packets carry a destination field
Need to look up destination port on-the-fly
Datagram
lookup based on entire destination address
Cell
lookup based on VCI – used as an index to a table
Other than that, switching units are very similar
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8. Blocking in packet switches
Can have both internal and output blocking
Internal
no path to output
Example: head of line blocking.
Output
output link busy
If packet is blocked, must either buffer or drop it
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9. Dealing with blocking Overprovisioning Buffers Backpressure
internal links much faster than inputs
Buffers
at input or output
Backpressure
if switch fabric doesn’t have buffers, prevent packet from entering until path is available
Parallel switch fabrics
increases effective switching capacity
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10. Three generations of packet switches
Different trade-offs between cost and performance
Represent evolution in switching capacity, rather than in technology
With same technology, a later generation switch achieves greater capacity, but at greater cost
All three generations are represented in current products
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11. First generation switch
computer
CPU
linecard
linecard
queues in memory
linecard
Most Ethernet switches and cheap packet routers
Bottleneck can be CPU, host-adaptor or I/O bus, depending
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12. Second generation switch
computer
bus
front end processors
or line cards
Port mapping intelligence in line cards
Bottleneck is the bus (or ring)
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13. Third generation switches
Third generation switch provides parallel paths (fabric)
OLC
ILC
NxN
packet
switch
fabric
OUT
OLC IN
ILC
OLC
ILC
control
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14. Third generation (contd.)
Features
self-routing fabric
output buffer is a point of contention
unless we arbitrate access to fabric
potential for unlimited scaling,
as long as we can resolve contention for output buffer
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15. Switching - Fabric

16. Switching: abstract model
Number of connections: from few (4 or 8) to huge (100K)
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17. Multiplexors and demultiplexors
Multiplexor: aggregates sessions
N input lines
Output runs N times as fast as input
Demultiplexor: distributes sessions
one input line and N outputs that run N times slower
Can cascade multiplexors
De-Mux 1 2 N N
MUX
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18. Time division switching
Key idea: when demultiplexing, position in frame determines output link
Time division switching interchanges sample position within a frame:
Time slot interchange (TSI) M U X D E
TSI
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19. Time Slot Interchange (TSI) : example
sessions: (1,3) (2,1) (3,4) (4,2) 1 2 3 4 1 2 2 4 3 1 4 3
Read and write to shared memory in different order
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20. TSI Simple to build. Multicast: easy (why?)
Limit is the time taken to read and write to memory
For 120,000 telephone circuits
Each circuit reads and writes memory once every 125 ms.
Number of operations per second : 120,000 x 8000 x2
each operation takes around 0.5 ns => impossible with current technology
Need to look to other techniques
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21. Space division switching
Each sample takes a different path through the switch, depending on its destination
Crossbar: Simplest possible space-division switch
Crosspoints can be turned on or off i n p u t s
outputs
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22. Crossbar - example inputs output sessions: (1,2) (2,4) (3,1) (4,3) 1 2
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23. Crossbar Advantages: Drawbacks simple to implement simple control
strict sense non-blocking
Multicast
Single source multiple destination ports
Drawbacks
number of crosspoints, N2
large VLSI space
vulnerable to single faults
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24. Time-space switching Precede each input trunk in a crossbar with a TSI
Delay samples so that they arrive at the right time for the space division switch’s schedule
Crosspoint: 4 (not 16)
memory speed : x2 (not x4)
2 1
4 3
MUX 1 2 3 4
TSI
1 2
4 3
DeMux
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25. Finding the schedule Build a routing graph Feasible schedule
nodes - input links
session connects an input and output nodes.
Feasible schedule
Computing a schedule
compute perfect matching. 1 2 3 4
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26. Time-Space: Example time 1 time 2 2 1 2 1 TSI 3 4 4 3 3 2 1 4
2 1
3 4 3 1 2 4
2 1
4 3
TSI
TSI
Internal speed = double link speed
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27. Time-space-time (TST) switching
Allowed to TSI both on input and output
Gives more flexibility => lowers call blocking probability
TSI
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28. Internal Non-Blocking Types
Re-arrangeable
Can route any permutation from inputs to outputs.
Strict sense non-blocking
Given any current connections through the switch.
Any unused input can be routed to any unused output.
Wide sense non-blocking.
There exists a specific routing algorithm, s.t.,
for any sequence of connections and releases,
Any unused input can be routed to any unused output,
assuming all the sequence was served by the routing algorithm.
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29. Circuit switching - Space division
graph representation
transmitter nodes
receiver nodes
internal nodes
Feasible schedule
edge disjoint paths.
cost function
number of crosspoints (complexity of AxB is AB)
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30. Crossbar - example 1 2 3 4 4 1 2 3
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31. Another Example
inputs
outputs
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32. Another Example outputs inputs
sessions: (1,3) (2,6) (3,1) (4,4) (5,2) (6,5)
inputs
outputs
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33. Clos Network Clos(N, n , k) : N - inputs/outputs;
cross-points: 2 (N/n)nk + k(N/n)2
nxk
(N/n)x(N/n)
kxn
2x2
3x3
2x2
N=6
n=2
k=2 N
2x2
3x3
2x2 k
N/n
N/n
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34. Clos Network - strict sense non-blocking
Holds for k  2n-1
Proof Methodology:
Recall: IF [A,B  S and |A|+|B| > |S|] then A∩ B≠Ø
S= The k middle switches
A = middle switches reachable from the inputs
B = middle switches reachable from the outputs
Our case:
|S|=k
|A| ≥ k-(n-1)
|B| ≥ k-(n-1)
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35. Clos Network - strict sense non-blocking
Holds for k  2n-1
Proof:
Consider an idle input and output
Input box connected to at most n-1 middle layer switches
output box connected to at most n-1 middle layer switches
There exists an ”unused" middle switch good for both.
n x k
k x n
n-1
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36. Example Clos(8,2,3) Need to route a new call N=8 n=2 k=3 4x4 3x2 2x3
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37. Clos Network Why is k=n internally blocking? nxk (N/n)x(N/n) kxn N=6
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38. Clos Network - re-arrangable
Holds for k  n
Proof:
Consider the routing graph.
find a perfect matching.
route the perfect matching through a
single middle switch!
remaining network is Clos(N-N/n,n-1,k-1)
summary:
smaller circuit
weaker guarantee
Multicast ? 1 2 3 4
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39. Recursive Construction: basis
The basic element:
The dimension: r=0
The two states:
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40. Recursive Construction: Benes Network
r-1 dimension
N/2 size
r-1 dimension
N/2 size
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41. Example 16x16
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42. Benes Networks Symmetry Size: Rearrangable Proof I:
F(N) = 2(N/2)*4 + 2F(N/2) = O(N log N)
Rearrangable
Clos network with k=2 n=2
Proof I:
Build routing graph.
Find 2 matchings
route one in the upper Benes and the other in the lower.
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43. Greedy permutation routing
Start with an arbitrary node i1
set i1 to upper.
At the output, o1 , a new constraint,
set o2 to lower.
Continue until no new constraint.
Completing a cycle.
Continue until done.
Solve for the upper and lower Benes recursively.
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44. Example: Benes Network for r=2I1 1 2 3 4 5 6 7 8 I2
level 0 switches
level 2r switches
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45. Example ) 1 2 3 4 5 6 7 8 1 5 6 8 4 2 3 7 ( I1 I2 level 0 switches ) I1 1 2 3 4 5 6 7 8 I2
level 0 switches
level 2r switches
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46. Example ) 1 2 3 4 5 6 7 8 1 5 6 8 4 2 3 7 ( I1 I2 level 0 switches ) I1 1 2 3 4 5 6 7 8 I2
level 0 switches
level 2r switches
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47. Example ) 1 2 3 4 5 6 7 8 1 5 6 8 4 2 3 7 ( I1 I2 level 0 switches ) I1 1 2 3 4 5 6 7 8 I2
level 0 switches
level 2r switches
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48. Example ) 1 2 3 4 5 6 7 8 1 5 6 8 4 2 3 7 ( I1 I2 level 0 switches ) I1 1 2 3 4 5 6 7 8 I2
level 0 switches
level 2r switches
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49. Strict Sense non-Blocking
N/2 x N/2 . .
N/2 x N/2
N/2 x N/2
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50. Properties Size: Better parameters: F(N) = 2N*6 + 3F(N/2) = O( N1.58 )
strict sense non-blocking
Clos network with k=3 n=2
Better parameters:
n=sqrt{N}, k=2sqrt{N}-1
recursive size sqrt{N} x sqrt{N}
Circuit size N log2.58 N
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51. Cantor Networks m copies of Benes network.
For m = log N its strict sense non-blocking
Network size N log2 N
Example
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52. Cantor Network
m=4
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53. Proof Sketch: Benes network:
2 log N -1 layers,
N/2 nodes in layer.
Middle layer= layer log N -1
Consider the middle layer of the Benes Networks.
There are Nm/2 nodes in in all of them combined.
Bound (from below) the number of nodes reachable from an input and output.
If the sum is more than Nm/2:
There is an intersection
there has to be a route.
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54. Proof Sketch: Let A(k) = number of nodes reachable at level k. A(0)=m
A(1)= 2A(0)-1
A(2)=2A(1)-2
A(k)=2A(k-1) - 2k-1 = 2k A(0) - k 2k-1
A(log N -1) = Nm/2 - (log N -1) N/4
Need that: 2A(log N -1) > Nm/2.
2[Nm/2 - (log N -1) N/4] > Nm/2.
Hold for m> log N-1.
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55. Advanced constructions
There are networks of size O(N log N).
the constants are huge!
Basic paradigm also applies to large packet switches.
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56. Proof Sketch: Let A(k) = number of nodes reachable at level k. A(0)=m
A(1)= 2A(0)-1
A(2)=2A(1)-2
A(k)=2A(k-1) - 2k-2 = 2k-1 A(1) - (k-1) 2k-2
A(log N) = Nm/2 - (log N -1) N/4
Need that: 2A(log N) > Nm/2.
Hold for m> log N-1.
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