Max-Min%20Fair%20Self-Randomized%20Scheduler%20for%20Input-Buffered%20Switches

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Max-Min Fair Self-Randomized Scheduler for
Input-Buffered Switches

• 2004. 5. 11
• ???

2
Outline

• Introduction
• Models and definition
• Instantaneous vs. Total arrival for self
  randomization
• Max-min fair based self-randomized scheduler
• Simulation result

3
Introduction

• 1. Benefit of Input buffered switch
• Input buffered switch architecture become
  dominant architecture for high speed switch
  fabrics
• Their memory BW is lower than alternative
  architecture, such as output-buffered and shared
  memory .
• Memory speed is independent of number of ports
• ? input buffered architecture is scalable both in
  terms of line speed and port numbers.

4
Introduction

• 2. VOQ (virtual output queue)
• Pkt arriving at input i and destined for output j
  are buffered in VOQij
• VOQ resolve HOL blocking in input buffered
  switch. (without VOQ, throughput58.6)

5
Introduction

• 3. MWM (Maximum Weighted matching)
• ?ij average cell arrival rate at input i
• for output j
• ? ?ij lt1 gt traffic is admissible
• If traffic is admissible, MWMs throughput 100
• Deterministic sequential algorithm complex for
  high speed switch

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Introduction

• 4. randomized scheduling algo.
• Low complexity,
• Basic idea instead of deriving scheduling
  matching, to select it from a set of
  predetermined candidates
• Simple randomized procedure obtain or update
  candidate set in every time slot
• Weight backlogged cell
• Randomly selected matching previous time slot
  matching
• Stable but delay

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Introduction

• 5. self-randomized scheduling algo.
• Rely on arrival pattern for generating good
  candidate matchings.
• Shortcomings
• Lower arrival rate, cell arrival occurs very
  rarely, generated candidate matchings are very
  sparse? bad
• We propose to use total cell arrival graph
  instead of instantaneous arrival graph

8
Introduction

• 6. token based max-min fair scheduling algo.
• Allocates BW among flows proportional to their
  weights, if a flow can not utilize its BW then
  residual BW is distributed among others.
• Original max-min fair scheduler categorized as
  deterministic MWM scheduling algo, weight is
  number of tokens allocated to them.

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Introduction

• 7. what we will do in this paper
• We extend idea of max-min fair scheduling algo,
  concept of max-min fair self-randomized
  scheduling algo.
• We use both token generation process arrival
  process ? generating candidate matching
• We use number of tokens number of backlogged
  cells ? weight of link

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Introduction
deterministic ?? matching Weight - backlogged cell
randomized ?? randomly matching previous time matching Weight -backlogged cell
Self-randomized Instead pure random matching, use arrival pattern Weight- backlogged cell
Token based Like deterministic Weight number of token
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Models and Definitions

• 1.Notation
• If input i is matched to output j, corresponding
  VOQ is not empty.
• Matching can be represented by matrix ? ij 1

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Models and Definitions

• 2. Algorithm 1(Tass) (randomized algo.)
• ? S(n) schedule used at time n.
• ? At time n1, choose matching R(n1) uniformly
  at random from set of ?
• ? S(n1)avg max ?S(n),R(n1)
• Every time slot, random matching is generated,
  its weight is compared to weight of matching that
  is used in previous time slot
• Matching with highest weight is selected for
  scheduling
• Stable but poor delay performance

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Models and Definitions

• 3. Algorithm 2 (SERENA) (self- randomized
  algo.)
• ? S(t-1) schedule used at time t-1
• ? A(t)aij(t) denote arrival graph aij(t)1
  indicates arrival aij(t)0 no arrival at time t
• ? S(t) merging A(t) and S(t-1)

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Models and Definitions

• 3. we propose self-randomized schedulers

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Models and Definitions

• First stage
• Memory bank that buffers K previously used
  matchings.
• Selects candidate matching with highest weight
  out of K matchings
• Candidate matching is passed to second stage
• Difference between existed randomized scheduling
  algo. and proposed self-randomized algo.
• Existed process matching that is used in
  previous time slot
• We account matching that are used in K previous
  time slots.
• Saving previous matching and using it as a new
  candidate is main reason for stability of Tass
  algo.

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Models and Definitions

• Second stage
• Generate a candidate matching in self-randomized
  block, merge that matching with candidate
  matching out of first stage
• End result of merging block is scheduling
  matching for that time slot

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Instantaneous vs. Total arrival for
self-randomization

• 1. In SERENA,
• candidate matching is based on instantaneous
  arrivals.
• Weight function is simply number of backlogged
  cells.
• Shortcomings
• Every new arrival gets one chance to be included
  in self-randomized matching.
• if link loses its chance, it should wait for
  another new arrival to get another opportunity.

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Instantaneous vs. Total arrival for
self-randomization

• 2. resolve problem
• We use total arrival graph
• In total graph, there is link for all previous
  cell arrivals that are not scheduled yet.
• Total arrival graph evolution is based on link
  insertions and ejection rules
• Insertion any link with new arrival that is not
  in total arrival graph is added to total arrival
  graph
• Ejection links that are scheduled are removed
  from total arrival graph.

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Instantaneous vs. Total arrival for
self-randomization

• Every cell time matching is extracted from total
  arrival graph.
• Similar to SERENA, for every output port link
  with largest weight is selected from total
  arrival graph.

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Max-Min Fair based Self-Randomized Scheduler

• New class of self-randomized scheduling algo.
  that use set of token values for link weight
  function.
• Token based weight function enables us to do BW
  allocation among different flows based of their
  reserved rates.
• Each flow i has normalized reserved rat or
  priority, wi.

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Max-Min Fair based Self-Randomized Scheduler

• BW allocation is said to be max-min fair if BW
  allotted to a flow can not be improved without
  decreasing that of any other flow having equal or
  less BW.
• BW allocation is max-min fair if it is not
  possible to increase BW of any flow i, without
  hurting another flow j.

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Max-Min Fair based Self-Randomized Scheduler

• In original algorithm,
• Scheduler distributes tokens between eligible
  flows
• Weight of link is min number of allocated tokens
  to it.
• When a link is scheduled, one token is taken out
  of its allocated token buckets.

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Max-Min Fair based Self-Randomized Scheduler

• In our scheme,
• Weight of link is min of tokens allocated to it
  and number of backlogged cells constant B
• Even though number of tokens is not limited by
  number of backlogged cells, weight of link can
  not exceed number of backlogged cell by more than
  constant B.
• Once Cell arrives it does not need to wait for
  scheduler.

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Simulation Results
16X16 input buffered switch
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Simulation Results
K32
Large delay at low rate for B1 ?link is
introduced to self-randomized graph, only when
there is a new arrival for that link. It should
wait for the next cell arrival to get another
chance
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Simulation Results
In B2, performance at low rates is better than
B1, but still average delay plots. Total cell
arrival graph.