Throughput of Internally Buffered Crossbar Switch - PowerPoint PPT Presentation

About This Presentation
Title:

Throughput of Internally Buffered Crossbar Switch

Description:

Contents. Motivation. High throughput performance crossbar switch ... CQ. 4. Motivations. Classic results: ~58.3%(blocking) and ~63%(non-blocking) ... – PowerPoint PPT presentation

Number of Views:254
Avg rating:3.0/5.0
Slides: 42
Provided by: sunda7
Learn more at: https://web.stanford.edu
Category:

less

Transcript and Presenter's Notes

Title: Throughput of Internally Buffered Crossbar Switch


1
Throughput of Internally Buffered Crossbar Switch
Thursday, October 22, 2020
Mingjie Lin mingjie_at_stanford.edu www.stanford.edu/
mingjie
2
Contents
  • Motivation
  • High throughput performance crossbar switch
  • What is the impact of crosspoint buffer on
    throughput of crossbar switch?
  • Problem Statement and Notations
  • The structure of a internally buffered crossbar
    switch (IBCS)
  • Two cases 1. With blocking, 2. Without blocking
  • Markov Chain model
  • Analysis approach
  • Results summary

3
Background
IQ
OQ
Switching Fabric
CQ
4
Motivations
Classic results 58.3(blocking) and
63(non-blocking) throughput for IQ crossbar
switch
5
Motivations
What will happen to the throughput if we add
Crosspoint buffer?
6
Contents
  • Motivation
  • High throughput performance crossbar switch
  • What is the impact of crosspoint buffer on
    throughput of crossbar switch?
  • Problem Statement and Notations
  • The structure of a internally buffered crossbar
    switch (IBCS)
  • Two cases 1. With blocking, 2. Without blocking
  • Markov Chain model
  • Analysis approach
  • Results summary

7
The structure of an internally buffered crossbar
switch (IBCS)
  • Input Traffic i.i.d uniform Bernoulli type,
    independent at each input.
  • Scheduling Algorithm (2 phases in 1 time slot)
  • Buffer In Phase For each input queue i, each
    HOL packet goes to its destined crosspoint buffer
    cell if it is vacant.
  • Buffer Out Phase For each output port j,
    randomly pick one cell from all occupied
    crosspoint buffer cells, and output its packet.

8
Throughput Analysis
2 Cases 1. Non-Blocking Mode 2.
Blocking Mode
9
Throughput Analysis
  • 2 Cases
  • 1. Non-Blocking Mode
  • 2. Blocking Mode
  • Idea
  • Using Markov Chain to model the crossbar switch
    behavior.

10
Notation
Internal buffer cell
Input queue at input port I
For any column of buffer cells, the probability
of having k packets in total at
time n state transition
probability of Markov chain
model.
11
Contents
  • Motivation
  • High throughput performance crossbar switch
  • What is the impact of crosspoint buffer on
    throughput of crossbar switch?
  • Problem Statement and Notations
  • The structure of a internally buffered crossbar
    switch (IBCS)
  • Two cases 1. With blocking, 2. Without blocking
  • Markov Chain model
  • Analysis approach
  • Results summary

12
Observation
  • Symmetry
  • a) traffic b) switching fabric
    structure

13
Observation
  • Symmetry
  • a) traffic b) switching fabric
    structure
  • 2. During each time slot, if there is at least 1
    packet in B,j, then there will be a packet to
    output

14
Observation
  • Symmetry
  • a) traffic b) switching fabric
    structure
  • 2. During each time slot, if there is at least 1
    packet in B,j, then there will be a packet to
    output
  • 3. Saturation Throughput

15
Markov Chain
16
Derivation
17
Key Equation
Total probability
18
Key Equation
Total probability
19
Key Equation (cont.)
N linear equations
20
IBCS without blocking
Solution of transition probability
21
IBCS without blocking (cont.)
Solve those N linear equations, we can compute
through for any N.
22
IBCS without blocking (cont.)
Solve those N linear equations, we can compute
through for any N. Question what happens to
throughput if N goes to infinity?
23
IBCS without blocking (cont.)
We know
24
IBCS without blocking (cont.)
We know
when
25
IBCS without blocking (cont.)
Therefore
26
IBCS without blocking (cont.)
Add them up
finally
27
IBCS without blocking (cont.)
Which leads to
28
IBCS with blocking
Markov chain model, however, state space too
large to manage
29
IBCS with blocking
Markov chain model, however, state space too
large to manage What is key difference between
with blocking and without blocking?
30
IBCS with blocking
Markov chain model, however, state space too
large to manage What is key difference between
with blocking and without blocking? What is
thoughput if N goes to infinity?
31
IBCS with blocking (cont.)
32
IBCS with blocking (cont.)
33
IBCS with blocking (cont.)
when
Therefore
finally
34
Contents
  • Motivation
  • High throughput performance crossbar switch
  • What is the impact of crosspoint buffer on
    throughput of crossbar switch?
  • Problem Statement and Notations
  • The structure of a internally buffered crossbar
    switch (IBCS)
  • Two cases 1. With blocking, 2. Without blocking
  • Markov Chain model
  • Analysis approach
  • Results summary

35
Results Summary
36
Results Summary (cont.)
37
Results Summary (cont.)
  1. Crosspoint buffer cells have a significant impact
    on throughput of crossbar switch Symmetry.

38
Results Summary (cont.)
  1. Crosspoint buffer cells have a significant impact
    on throughput of crossbar switch Symmetry.
  2. Without crosspoint buffer, throughput will
    decrease while N increases, the opposite is true
    for ICBS.

39
Results Summary (cont.)
  1. Crosspoint buffer cells have a significant impact
    on throughput of crossbar switch Symmetry.
  2. Without crosspoint buffer, throughput will
    decrease while N increases, the opposite is true
    for ICBS.
  3. When N goes infinity, throughput of crossbar
    switch without crosspoint buffer will converge to
    63 without HOL blocking, but ICBSs will
    converge to 100.

40
Results Summary (cont.)
  1. Crosspoint buffer cells have a significant impact
    on throughput of crossbar switch Symmetry.
  2. Without crosspoint buffer, throughput will
    decrease while N increases, the opposite is true
    for ICBS.
  3. When N goes infinity, throughput of crossbar
    switch without crosspoint buffer will converge to
    63 without HOL blocking, but ICBSs will
    converge to 100.
  4. When N goes infinity, throughput of crossbar
    switch without crosspoint buffer will converge to
    58 without HOL blocking, but ICBSs will
    converge to 100.

41
Thank you!
Write a Comment
User Comments (0)
About PowerShow.com