Packet Scheduling/Arbitration in Virtual Output Queues and Others

1
Packet Scheduling/Arbitration in Virtual Output
Queuesand Others
2
Key Characteristics in Designing Internet
Switches and Routers

1. Scalability in terms of line rates
2. Scalability in terms of number of interfaces
   (port numbers)

3
Switch/Router Architecture Comparison
http//www.lightreading.com/document.asp?doc_id47
959
4
Head-of-Line Blocking
Blocked!
Blocked!
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(No Transcript)
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(No Transcript)
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Crossbar Switches Virtual Output Queues

• Virtual Output Queues
• At each input port, there are N queues each
  associated with an output port
• Only one packet can go from an input port at a
  time
• Only one packet can be received by an output port
  at a time
• It retains the scalability of FIFO input-queued
  switches (no memory bandwidth problem)
• It eliminates the HoL problem with FIFO input
  Queues

8
Virtual Output Queues
9
VOQs How Packets Move
VOQs
Scheduler
10
Crossbar Scheduler in VOQ Architecture

• Memory b/w2R

• Can be quite complex!

11
Question do more lanes help?

• Answer it depends on the scheduling

Head of Line Blocking
VOQs with Bad Scheduling
Good Scheduling? Ayalon depends on traffic
matrix
12
Crossbar Scheduler in VOQ Architecture
Which packets I can send during each
configuration of the crossbar
13
Switch core architecture
Port 1
Scheduler (Like the Processor of A Computer)
Port 256
14
Basic Switch Model
S(n)
L11(n)
A11(n)
1
1
D1(n)
A1(n)
A1N(n)
AN1(n)
DN(n)
AN(n)
N
N
ANN(n)
LNN(n)
15
Some definitions
3. Queue occupancies
16
Some possible performance goals
When traffic is admissible
17
VOQ Switch Scheduling

• The VOQ switch scheduling can be represented by a
  bipartite graph
• The left-hand side nodes of the bipartite graph
  are the input ports
• The right-hand side nodes of the bipartite graph
  are the output ports
• The edges between the nodes are requests for
  packet transmission between input ports and
  output ports.

A
1
B
2
3
C
4
D
5
E
6
F
18
Maximum size bipartite match

• Intuition maximizes instantaneous throughput

L11(n)gt0
Maximum Size Match
LN1(n)gt0
Bipartite Match
Request Graph
19
Network flows and bipartite matching
A
1
B
2
Sink t
Source s
3
C
4
D
5
E
6
F

• Finding a maximum size bipartite matching is
  equivalent to solving a network flow problem with
  capacities and flows of size 1.

20
Network Flows
a
c
Source s
Sink t
b
d

• Let GV,E be a directed graph with capacity
  cap(v,w) on edge v,w.
• A flow is an (integer) function, f, that is
  chosen for each edge so that f(v,w) lt cap(v,w).
• We wish to maximize the flow allocation.

21
A maximum network flow exampleBy inspection
a
c
Source s
Sink t
b
d
Step 1
22
A maximum network flow example
Step 2
a
c
10, 10
Source s
Sink t
10, 10
1
10, 10
1
10, 1
b
d
10, 1
1, 1
Flow is of size 101 11
23
Ford-Fulkerson method of augmenting paths

1. Set f(v,w) -f(w,v) on all edges.
2. Define a Residual Graph, R, in which res(v,w)
   cap(v,w) f(v,w)
3. Find paths from s to t for which there is
   positive residue.
4. Increase the flow along the paths to augment them
   by the minimum residue along the path.
5. Keep augmenting paths until there are no more to
   augment.

24
Example of Residual Graph
a
c
10, 10
10, 10
1
10, 10
s
t
10
1
10
b
d
1
Flow is of size 10
Residual Graph, R
res(v,w) cap(v,w) f(v,w)
a
c
10
10
10
1
t
s
10
1
10
b
d
1
Augmenting path
25
Example of Residual Graph
a
c
10, 10
10, 10
1
10, 10
s
t
10
1
10
b
d
1
Flow is of size 10
Residual Graph, R
res(v,w) cap(v,w) f(v,w)
a
c
10
10
10
1
t
s
10
1
10
b
d
1
Augmenting path
26
Example of Residual Graph
Step 2
a
c
10, 10
s
t
10, 10
1
10, 10
1
10, 1
b
d
10, 1
1, 1
Flow is of size 101 11
Residual Graph
a
c
10
s
t
10
10
1
1
1
1
b
d
9
1
9
Augmenting path
27
Example of Residual Graph
Step 3
a
c
10, 9
s
t
10, 10
1, 1
10, 10
1, 1
10, 2
b
d
10, 2
1, 1
Flow is of size 102 12
Residual Graph
a
c
10
s
t
10
10
1
2
1
2
b
d
8
1
8
28
An other Example Ford-Fulkerson method
find augmenting path p
f0
Gf
G
12
a
b
16
20
9
4
s
10
t
7
13
4
11
c
d
29
An other Example Ford-Fulkerson method
find augmenting path p
f4
Gf
G
12
12
a
b
a
b
16
20
16
20
9
9
4
s
10
t
4
s
10
t
7
7
4
4/13
4/4
4
4
4/11
9
c
d
c
d
7
30
An other Example Ford-Fulkerson method
find augmenting path p
f16
Gf
G
12/12
12
a
b
a
b
8
4
12/16
12/20
12
12
9
9
4
s
10
t
4
s
10
t
7
7
4
4/13
4/4
4
4
4/11
9
c
d
c
d
7
31
An other Example Ford-Fulkerson method
find augmenting path p
f23
Gf
G
12/12
12
a
b
a
b
1
4
12/16
19/20
12
19
9
9
4
s
10
t
4
s
10
t
7/7
7
11
11/13
4/4
4
11/11
2
c
d
c
d
11
No more augmenting path
Maximum Flow is 23
32
An example for Flow Obvious solution
Total flow 10, Sub-optimal solution!
33
Flow algorithm Optimal version
Total flow 10 9 19 units!
9
34
Complexity of network flow problems

• In general, it is possible to find a solution by
  considering at most V.E paths, by picking
  shortest augmenting path first.
• There are many variations, such as picking most
  augmenting path first.
• The complexity of the algorithm is less when the
  graph is bipartite
• There are techniques other than the
  Ford-Fulkerson method.

35
Ford - Fulkerson Algorithm 1
Network flows and bipartite matching
Finding a maximum size bipartite matching is
equivalent to solving a network flow problem with
capacities and flows of size 1.
sink
1
2
3
4
5
6
a
b
c
d
e
f
source
36
Ford - Fulkerson Algorithm 2
sink
Increasing the flow by 1.
1
2
3
4
5
6
a
b
c
d
e
f
source
37
Ford - Fulkerson Algorithm 3
sink
Increasing the flow by 1.
1
2
3
4
5
6
a
b
c
d
e
f
source
38
Ford - Fulkerson Algorithm 4
sink
Increasing the flow by 1.
1
2
3
4
5
6
a
b
c
d
e
f
source
39
Ford - Fulkerson Algorithm 5
sink
Increasing the flow by 1.
1
2
3
4
5
6
a
b
c
d
e
f
source
40
Ford - Fulkerson Algorithm 6
sink
Increasing the flow by 1.
1
2
3
4
5
6
a
b
c
d
e
f
source
41
Ford - Fulkerson Algorithm 7
sink
Augmenting flow along the augmenting path.
1
2
3
4
5
6
a
b
c
d
e
f
source
42
Ford - Fulkerson Algorithm 8
sink
Maximum flow found! Thus maximum matching found.
1
2
3
4
5
6
a
b
c
d
e
f
source
43
Complexity of Maximum Matchings

• Maximum Size/Cardinality Matchings
• Algorithm by Dinic O(N5/2)
• Maximum Weight Matchings
• Algorithm by Kuhn O(N3logN)
• ftp//dimacs.rutgers.edu/pub/netflow/matching/
• (contains code for maximum size/weighting
  algorithms)
• In general
• Hard to implement in hardware
• Slooooow.

44
Maximum size bipartite match

• Intuition maximizes instantaneous throughput
• for uniform traffic.

L11(n)gt0
Maximum Size Match
LN1(n)gt0
Bipartite Match
Request Graph
45
Why doesnt maximizing instantaneous throughput
give 100 throughput for non-uniform traffic?
Three possible matches, S(n)
46
Maximum weight matching
S(n)

• Weight could be length of queue or age of packet
• Achieves 100 throughput under all traffic
  patterns

L11(n)
A11(n)
A1(n)
D1(n)
1
1
A1N(n)
AN1(n)
AN(n)
DN(n)
ANN(n)
N
N
LNN(n)
L11(n)
Maximum Weight Match
LN1(n)
Bipartite Match
Request Graph
47
Packet Scheduling/Arbitration in Virtual Output
Queues Maximal Matching Algorithms
48
Maximum Matching in VOQ Architecture
49
Complexity of Maximum Matchings

• Maximum Size/Cardinality Matchings
• Algorithm by Dinic O(N5/2)
• Maximum Weight Matchings
• Algorithm by Kuhn O(N3logN)
• In general
• Hard to implement in hardware
• Slooooow.

50
Maximal Matching

• A maximal matching is a matching in which each
  edge is added one at a time, and is not later
  removed from the matching.
• i.e., No augmenting paths allowed (they remove
  edges added earlier) like by inspection.
• No input and output are left unnecessarily idle.

51
Example of Maximal Size Matching
A
1
A
1
B
2
B
2
3
C
3
C
4
4
D
D
5
E
5
E
6
6
F
F
Maximum Matching
Maximal Matching
52
Comments on Maximal Matchings

• In general, maximal matching is much simpler to
  implement, and has a much faster running time.
• A maximal size matching is at least half the size
  of a maximum size matching.
• A maximal weight matching is defined in the
  obvious way.
• A maximal weight matching is at least half the
  size of a maximum weight matching.

53
PIM Maximal Size Matching Algorithm Performance
and Properties

• It is among the very first practical schedulers
  proposed for VOQ architectures (used by DEC).
• It is based on having arbiters at the inputs and
  outputs
• It iterates the following steps until no more
  requests can be accepted (or for a given number
  of iterations)
• Request Each unmatched input sends a request to
  every output for which it has a queued cell
• Grant (outputs) If an unmatched output receives
  any request, it grants one by randomly selecting
  a request uniformly over all requests.
• Accept (inputs) If an unmatched input receives a
  grant, it accepts one by selecting an output
  randomly among those granted to this input.

54
Implementation of the parallel maximal matching
algorithms

• Grant Arbiters

• Request Arbiters

55
Implementation of the parallel maximal matching
algorithms (another similar way)
56
PIM Maximum Size Matching Algorithm Performance
and Properties
PIM 1st Iteration

• Step 1 Request

• Random selection

• Random selection

• Step 2 Grant

• Step 3 Accept

57
PIM Maximum Size Matching Algorithm Performance
and Properties
PIM 2nd Iteration

• Step 1 Request

1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
1
1
2
2

• Step 2 Grant

3
3

• Step 3 Accept

4
4
58
Traffic Types to evaluate Algorithms
Uniform traffic
Unbalanced traffic
Hotpot traffic
59
Parallel Iterative Matching
PIM with a single iteration
60
Parallel Iterative Matching
PIM with 4 iterations
61
Parallel Iterative MatchingAnalytical Results
Number of iterations to converge
62
PIM Maximum Size Matching Algorithm Performance
and Properties

• It is a fair algorithm servicing inputs
• Can have 100 throughput under uniform traffic
• It converges in logN iterations to a maximal size
  matching
• It has a very poor performance (63 throughput)
  with 1 iteration because of its inability to
  desynchronize the output pointers
• It is not easy to build random arbiters in
  hardware
• The best iterative maximal size matching
  algorithm takes O(N2logN) serial or O(log N)
  parallel time steps.
• If the number of iterations is constant, then it
  can be implemented in constant time (that is why
  it is practical) however the hardware design is
  not trivial.

63
RRM Maximum Size Matching Algorithm Performance
and Properties

• Round Robin Matching (RRM) is easier to implement
  that PIM (in terms of designing the I/O
  arbiters).
• The pointers of the arbiters move in
  straightforward way
• It iterates the following steps until no more
  requests can be accepted (or for a given number
  of iterations)
• Request. Each input sends a request to every
  output for which it has a queued cell.
• Grant. If an output receives any requests, it
  chooses the one that appears next in a fixed,
  round-robin schedule starting from the highest
  priority element. The output notifies each input
  whether or not its request was granted. The
  pointer gi to the highest priority element of the
  round-robin schedule is incremented (modulo N) to
  one location beyond the granted input. If no
  request is received, the pointer stays unchanged.

64
RRM Maximum Size Matching Algorithm Performance
and Properties

• Accept. If an input receives a grant, it accepts
  the one that appears next in a fixed, round-robin
  schedule starting from the highest priority
  element. The pointer ai to the highest priority
  element of the round-robin schedule is
  incremented (modulo N) to one location beyond the
  accepted output. If no grant is received, the
  pointer stays unchanged.

65
RRM Maximal Matching Algorithm (1)
Step 1 Request
66
RRM Maximal Matching Algorithm (2)
Step 2 Grant
67
RRM Maximal Matching Algorithm (2)
68
RRM Maximal Matching Algorithm (2)
69
RRM Maximal Matching Algorithm (2)
70
RRM Maximal Matching Algorithm (3)
0 3 1 2
71
RRM Maximal Matching Algorithm (3)
0 3 1 2
72
RRM Maximal Matching Algorithm (3)
0 3 1 2
73
Poor performance of RRM Maximal Matching Algorithm
0 1 0 1 ..
0
0
0 1 0 1 ..
1
1
50 Throughput
74
iSLIP Maximum Size Matching Algorithm
Performance and Properties

• It is a scheduler used in most VOQ switches
  (e.g., Cisco).
• It is exactly like RRM algorithm with the
  following change
• Grant. If an output receives any requests, it
  chooses the one that appears next in a fixed,
  round-robin schedule starting from the highest
  priority element. The output notifies each input
  whether or not its request was granted. The
  pointer gi to the highest priority element of the
  round-robin schedule is incremented (modulo N) to
  one location beyond the granted input if and only
  if the grant is accepted in (Accept phase) .

75
iSLIP Maximum Size Matching Algorithm
iSlip 1st Iteration

• Step 1 Request

4 1 3 2
1
1
2
2
3
3
4
4
4 1 3 2
1 4 2 3

• Step 2 Grant

4 1 3 2

• Step 3 Accept

76
iSLIP Maximum Size Matching Algorithm
iSlip 2nd Iteration

• Step 1 Request

1
1
1
1
4 1 3 2
2
2
2
2
3
3
3
3
4
4
4
4
1
1
1 4 2 3
2
2

• Step 2 Grant

3
3
4 1 3 2

• Step 3 Accept

4
4

• No change

77
Simple Iterative Algorithms iSlip
Step 1 Request
78
Simple Iterative Algorithms iSlip
Step 2 Grant
79
Simple Iterative Algorithms iSlip
80
Simple Iterative Algorithms iSlip
Step 3 Accept
0
0
1
1
0 3 1 2
2
2
3
3
81
Simple Iterative Algorithms iSlip
Step 3 Accept
0
0
1
1
0 3 1 2
2
2
3
3
82
Simple Iterative Algorithms iSlip
83
Simple Iterative Algorithms iSlip
Step 3 Accept
0
0
1
1
0 3 1 2
2
2
3
3
84
Simple Iterative Algorithms iSlip
Step 3 Accept
0
0
1
1
0 3 1 2
2
2
3
3
85
iSLIP Implementation
Programmable Priority Encoder
1
1
State
Decision
log2N
N
Grant
Accept
2
2
Grant
Accept
N
log2N
N
N
Grant
Accept
log2N
N
86
Hardware Design
Layout of the 256 bits Priority Encoder
87
Hardware Design
Layout of 256 bits grant arbiter
88
FIRM Maximum Size Matching Algorithm Performance
and Properties

• It is exactly like iSLIP with a very small yet
  significant modification.
• Grant (outputs) If an unmatched output receives
  a request, it grants the one that appears next in
  a fixed, round-robin schedule starting from the
  highest priority element. The output notifies
  each input whether or not its request is granted.
  The pointer to the highest priority element of
  the round-robin schedule is incremented beyond
  the granted input. If input does not accept the
  pointer is set at the granted one.

89
Simple Iterative Algorithms FIRM
Step 3 Accept
90
Pointer Synchronization

• Why this is good this small change prevents the
  output arbiters from moving in lock-step (being
  synchronized pointing to the same input)
  leading to a dramatic improvement in performance.
• If several outputs grant the same input, no
  matter how this input chooses, only one match can
  be made, and the other outputs will be idle.
• To get as many matches as possible, it's better
  that each output grants a different input.
• Since each output will select the highest
  priority input if a request is received from this
  input, it's better to keep the output pointers
  desynchronized (pointing to different locations).

91
iSLIP Maximal Matching Algorithm
0 1 0 1 ..
0
0
0 0 1 0 ..
1
1
100 Throughput
92
Pointer Synchronization Differences between
RRM, iSlip FIRM
93
Differences between RRM, iSlip FIRM
RRM iSlip FIRM FIRM
Input No grant unchanged unchanged unchanged unchanged
Input Granted one location beyond the accepted one one location beyond the accepted one one location beyond the accepted one one location beyond the accepted one
Output No request unchanged unchanged unchanged unchanged
Output Grant accepted one location beyond the granted one one location beyond the granted one one location beyond the granted one one location beyond the granted one
Output Grant not accepted one location beyond the previously granted one unchanged unchanged the granted one
94
General remarks

• Since all of these algorithms try to approximate
  maximum size matching, they can be unstable under
  non-uniform traffic
• They can achieve 100 throughput under uniform
  traffic
• Under a large number of iterations, their
  performance is similar
• They have similar implementation complexity

95
Input QueueingLongest Queue First orOldest Cell
First



Queue Length
Weight
100



Waiting Time
1
1
1
1
1
2
10
2
2
2
1

w
e
i
g
h
t
M
a
x
i
m
u
m
3
3
3
3
1
10
4
4
4
4
1
96
Input QueueingWhy is serving long/old queues
better than serving maximum number of queues?

• When traffic is uniformly distributed, servicing
  themaximum number of queues leads to 100
  throughput.
• When traffic is non-uniform, some queues become
  longer than others.
• A good algorithm keeps the queue lengths
  matched, and services a large number of queues.

97
Maximum/Maximal Weight Matching

• 100 throughput for admissible traffic (uniform
  or non-uniform)
• Maximum Weight Matching
• OCF (Oldest Cell First) wcell waiting time
• LQF (Longest Queue First)winput queue occupancy
• LPF (Longest Port First)wQL of the source port
  Sum of QL form the source port to the
  destination port
• Maximal Weight Matching (practical algorithms)
• iOCF
• iLQF
• iLPF (comparators in the critical path of iLQF
  are removed )

98
Maximal Weight Matching Algorithms iLQF

• Request. Each unmatched input sends a request
  word of width bits to each output for which it
  has a queued cell, indicating the number of cells
  that it has queued to that output.
• Grant. If an unmatched output receives any
  requests, it chooses the largest valued request.
  Ties are broken randomly.
• Accept. If an unmatched input receives one or
  more grants, it accepts the one to which it made
  the largest valued request. Ties are broken
  randomly.

99
Maximal Weight Matching Algotithms iLQF

• The i-LQF algorithm has the following properties
• Property 1. Independent of the number of
  iterations, the longest input queue is always
  served.
• Property 2. As with i-SLIP, the algorithm
  converges in at most logN iterations.
• Property 3. For an inadmissible offered load, an
  input queue may be starved.

100
Maximal Weight Matching Algotithms iOCF

• The i-OCF algorithm works in similar fashion to
  iLQF, and has the following properties
• Property 1. Independent of the number of
  iterations, the cell that has been waiting the
  longest time in the input queues (it must at the
  head of the queue)
• Property 2. As with i-LQF, the algorithm
  converges in at most logN iterations.
• Property 3. No input queue can be starved
  indefinitely.
• Property 4. It is difficult to keep time stamps
  on the cells.

101
iLQF - Implementation
102
iLQF - Implementation
Complicated hardware
103
Other research efforts

• Packet-based arbitration
• Exhaustive-based arbitration
• Numerous other efforts

104
Packet Scheduling/Arbitration in Virtual Output
QueuesRandomized Algorithmsand Others
105
Input-Queued Packet Switch
(?i ?i,j lt 1 ?j ?i,j lt 1)
Xi,j
106
Bipartite Graph and Matrix
inputs
1
2
3
outputs
3
2
1
107
Stability of Scheduling

• DefinitionLet Xi,j(t) be the number of packets
  queued at input i for output j at time-slot t.
  Then an algorithm is stable iff

108
Motivation

• Networking problems suffer from the curse of
  dimensionality
• algorithmic solutions do not scale well
• Typical causes
• size large number of users or large number of
  I/O
• time very high speeds of operation
• A good deterministic algorithm exists (Max Flow),
  but
• it needs state information, and state is too
  big
• it starts from scratch in each iteration

109
Randomization

• Randomized algorithms have frequently been used
  in many situations where the state space (e.g.,
  different number of connections between input and
  output N!) is very large
• Randomized algorithms
• are a powerful way of approximating the optimal
  solution
• it is often possible to randomize deterministic
  algorithms
• this simplifies the implementation while
  retaining a (surprisingly) high level of
  performance
• The main idea is
• to simplify the decision-making process
• by basing decisions upon a small, randomly chosen
  sample of the state
• rather than upon the complete state

110
Randomizing Iterative Schemes (e.g., iSLIP)

• Often, we want to perform some operation
  iteratively
• Example find the heaviest matching in a switch
  in every time slot
• Since, in each time slot
• at most one packet can arrive at each input
• and, at most one packet can depart from each
  output
• the size of the queues, or the state of the
  switch, doesnt change by much between successive
  time slots
• so, a matching that was heavy at time t will
  quite likely continue to be heavy at time t1
• This suggests that
• knowing a heavy matching at time t should help in
  determining a heavy matching at time t1
• there is no need to start from scratch in each
  time slot

111
Summarizing Randomized Algorithms

• Randomized algorithms can help simplify the
  implementation
• by reducing the amount of work in each iteration
• If the state of the system doesnt change by much
  between iterations, then
• we can reduce the work even further by carrying
  information between iterations
• The big pay-off is
• that, even though it is an approximation, the
  performance of a randomized scheme can be
  surprisingly good

112
Randomized Scheduling Algorithms Example

• Consider a 3 x 3 input-queued switch
• input traffic is Bernoulli IID and ?ij a/3
  for all i, j, and a lt 1
• This is admissible
• note there are a total of 6 ( 3!) possible
  service matrices

113
Random Scheduling Algorithms

• In time slot n, let S(n) be equal to one of the 6
  possible matchings independently and uniformly at
  random
• Stability of Random
• Consider L11(n), the number of packets in VOQ11
• arrivals to VOQ11 occur according to A11(n),
  which is Bernoulli IID
• input rate ?11 a/3
• this queue gets served whenever the service
  matrix connects input 1 to output 1
• There are 2 service matrices that connect input 1
  to output 1
• since Random chooses service matrices u.a.r.,
  input 1 is connected to output 1
• 1. for a fraction of time 2/6 1/3 --- the
  service rate between input1 and output1
• E(L11(n)) lt iff ?11 lt 1/3 ? a lt 1
• This random algorithm is stable.

114
Random Scheduling Algorithms

• Instability of Random
• Now suppose ?ii a for all i and ?ij 0 for
• clearly, this is admissible traffic for all a lt 1
  
• but, under Random, the service rate at VOQ11 is
  1/3 at best
• hence VOQ11 and the switch will be unstable as
  soon as
• Stability (or 100 throughput) means it is stable
  under all admissible traffic!

115
Obvious Randomized Schemes

• Choose a matching at random and use it as the
  schedule
• doesnt give 100 throughput (already shown)

• Choose 2 matchings at random and use the heavier
  one as the schedule
• Choose N matchings at random and use the heaviest
  one as the schedule

• None of these can give 100 throughput !!

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Iterative Randomized Scheme(Tassiulas)

• Say M is the matching used at time t
• Let R be a new matching chosen uniformly at
  random (u.a.r.) among the N! different matchings
• At time t1, use the heavier of M and R
• Complexity is very low O(1) iterations
• This gives 100 throughput !
• note the boost in throughput is due to memory
  (saving previous matchings)
• But, delays are very large

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Finer Observations

• Let M be schedule used at time t
• Choose a good random matching R
• M Merge(M,R)
• M includes best edges from M and R
• Use M as schedule at time t1
• Above procedure yields algorithm called LAURA
• There are many other small variations to this
  algorithm.

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Merging Procedure
3
1
2
2
3
3
2
4
2
1
Merging
X
R
3-12-22
W(X)12
W(R)10
2-12-4-1
M
W(M)13
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Can we avoid having schedulers altogether !!!
123
Recap Two Successive Scaling Problems
124
IQ Arbitration Complexity

• Scaling to 160Gbps
• Arbitration Time 3.2ns
• Request/Grant Communication BW 280Gbps

• Two main alternatives for scaling
• Increase cell size
• Eliminate arbitration

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Desirable Characteristics for Router Architecture

• Ideal OQ
• 100 throughput
• Minimum delay
• Maintains packet order
• Necessary able to regularly connect any input to
  any output
• What if the world was perfect? Assume Bernoulli
  iid uniform arrival traffic...

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Round-Robin Scheduling

• Uniform non-bursty traffic gt 100 throughput
• Problem traffic is non-uniform bursty

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Two-Stage Switch (I)
External Outputs
Internal Inputs
External Inputs
First Round-Robin
Second Round-Robin
128
Two-Stage Switch (I)
External Outputs
Internal Inputs
External Inputs
First Round-Robin
Second Round-Robin
129
Two-Stage Switch Characteristics
External Outputs
Internal Inputs
External Inputs
Cyclic Shift
Cyclic Shift

• 100 throughput
• Problem unbounded mis-sequencing

130
Two-Stage Switch (II)
New
N3 instead of N2
131
Expanding VOQ Structure
Solution expand VOQ structure by distinguishing
among switch inputs
132
What is being done in practice(Cisco for example)

• They want schedulers that achieve 100 throughput
  and very low delay (Like MWM)
• They want it to be as simple as iSLIP in terms of
  hardware implementation
• Is there any solution to this !!!!!

133
Typical Performance of ISLIP-like Algorithms
PIM with 4 iterations
134
What is being done in practice(Cisco for example)
Company Switching Capacity Switch Architecture Fabric Overspeed
Agere 40 Gbit/s-2.5 Tbit/s Arbitrated crossbar 2x
AMCC 20-160 Gbit/s Shared memory 1.0x
AMCC 40 Gbit/s-1.2 Tbit/s Arbitrated crossbar 1-2x
Broadcom 40-640 Gbit/s Buffered crossbar 1-4x
Cisco 40-320 Gbit/s Arbitrated crossbar 2x