slide1
Download
Skip this Video
Download Presentation
Competitive Queueing Policies for QoS Switches

Loading in 2 Seconds...

play fullscreen
1 / 19

Competitive Queueing Policies for QoS Switches - PowerPoint PPT Presentation


  • 114 Views
  • Uploaded on

Competitive Queueing Policies for QoS Switches. Nir Andelman Yishay Mansour An Zhu TAU TAU Stanford. Outline. Motivation Model description Summary of Previous and new results Non-preemptive queue Two packet types Multiple packet types Preemptive queue lower bound

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Competitive Queueing Policies for QoS Switches' - lisle


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Competitive Queueing

Policies for QoS

Switches

Nir Andelman Yishay Mansour An Zhu

TAU TAU Stanford

outline
Outline
  • Motivation
  • Model description
  • Summary of Previous and new results
  • Non-preemptive queue
    • Two packet types
    • Multiple packet types
  • Preemptive queue lower bound
  • Open Questions
motivation
Motivation
  • Quality of Service
    • Guaranteed performance
    • Limited resources
  • Premium Service
motivation cont
Motivation (cont.)
  • Assured service
    • Relative (not Guaranteed) Performance
    • Different packet priorities (values)
    • High Network Utilization
slide5

Motivation (cont.)

  • Queue management
    • Outgoing port
    • Limited queue space
    • Online packet scheduling

1

1

our model
Our model
  • Input: a stream of valued packets.
  • Actions: either accept or reject a packet
  • Send events: at integer times
  • Benefit = Total value of the packets sent.
  • Main Variations:
    • Non-Preemptive FIFO Queue
    • Preemptive FIFO Queue
    • Delay-Bounded Queue
  • Competitive Analysis: ρ = max {offline/online}
previous results
Previous Results
  • Non-Preemptive Queue
    • (2-1)/ lower bound for 2 values and Analyzes specific policies (AMRR00)
  • Preemptive Queue
    • 2-o(1) competitive greedy algorithm (KLMPSS01)
    • 1.28 lower bound for 2 values (Sviridenko01)
    • 1.30 competitive algorithm for 2 values (LP02)
  • Delay-Bounded Queue (KLMPSS01)
    • 2 competitive greedy algorithm
    • 1.17 lower bound for -uniform bounded delay
    • 1.414  ρ 1.618 for 2-variable bounded delay
    • 1.25  ρ  1.434 for 2-uniform bounded delay
summary of our results
Summary of Our Results
  • Non-preemptive queue
    • Algorithm with ρ = (2-1)/
      • optimal for 2 values
    • tight(er) bounds for previous policies
    • ρ = (ln()) for continuous values
  • Preemptive queue
    • General lower bound of 1.414
    • Exact ρ =1.434 for queue size 2
  • Delay-Bounded queue
    • 1.366  ρ  1.414 for 2-uniform bounded delay
    • ρ = 1.618 for 2-variable bounded delay
non preemptive lower bound 2 values
Non-Preemptive Lower bound - 2 values

1

1

1

1

1

1

1

1

1

1

1

1

1

1

ON

OFF

[From AMRR 2000]

Online accepts xB packets.

Offline accepts B packets.

Ratio is x

slide10

Lower bound- 2 values (cont.)

1

1

1

1

1

1

1

1

1

1

ON

OFF

Online accepts xB low and at most (1-x)B high.

Offline accepts B high value packets.

Ratio is [x+(1-x)]/

lower bound 2 values cont
Lower bound - 2 values (cont.)

Optimize lower bound: x = /(2-1)

Lower bound :   (2-1)/

ratio partition rp policy
Ratio Partition (RP) Policy
  • Always accept high value packets.
  • Each high value packet marks /(-1) low value packets in the queue that arrived before it.
  • Accept a low packet if you can mark it by filling the queue with high value packets.
rp example 1
RP Example (1)

1

1

1

m

1

1

1

m

1

1

m

1

1

m

1

Let  = 2,

Each high value marks 2 low values.

Lemma:

When the queue is full, all packets in it are marked.

slide14

RP Example (2)

1

1

1

1

1

1

1

1

1

Free slots left for (possible) future high values.

rp analysis
RP Analysis
  • Full queue:
    • all low value packets are marked.
  • Online marked packets bound:
    • offline high value packets.
  • Marking parameter balances:
    • accepted low value packets
    • slots for future high value packets.
  • Optimizing the marking parameter givesρ=(2-1)/.
  • Optimal competitive ratio.
continuous values
Continuous Values
  • Create n= ln() sub-queues
  • Sub-queue k accepts values [k-1/n,k/n]
  • Sub-queues take turns in sending
    • Can be simulated by a FIFO queue.
  • Competitive ratio of e ln()
  • Lower bound: ln()+1
preemptive lower bound
Preemptive Lowerbound

i

Z

i-1

B-1

  • Stage i includes:
    • A burst of B-1 i-1 packets followed by one i
    • At the next Z times units, one i packet each unit
  • End with B packets of value k
  • Stop: if B-Z packets are preempted in a stage.
  • Optimize i and Z=B/2
  • the lower bound converges towards 1.414.
  • For B=2 the bound is 1.434.

i-1

i-1

i

i

i

i

open problems
Open Problems
  • Non-Preemptive queue & continuous values
    • Close the constant gap between the upper (e ln()) and lower (ln()+1) bounds
  • Preemptive queue & continuous values
    • Is there a policy which has ρ ≤ 2-ε
  • Delay-Bounded queue:
    • Better than Greedy for delay > 2
ad