1 / 14

HOL Blocking analysis

HOL Blocking analysis. based on: Broadband Integrated Networks by Mischa Schwartz. PGF – Probability Generating Functions. Let a be a random variable. The PGF is defined by moment generation. PGF Examples. Poisson distribution Geometric distribution. PGF Examples.

rdoolittle
Download Presentation

HOL Blocking analysis

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. HOL Blocking analysis based on: Broadband Integrated Networks by Mischa Schwartz.

  2. PGF – Probability Generating Functions • Let a be a random variable. • The PGF is defined by • moment generation

  3. PGF Examples • Poisson distribution • Geometric distribution

  4. PGF Examples • Bernoulli distribution • Binomial distribution

  5. M/D/1 Queue n cells in system arrivals q cells in queue • To analyze: consider a slotted time scale k k+1 k-1

  6. M/D/1 Queue k k+1 k-1

  7. Finding p(0)  is the utilization

  8. The buffer statistics

  9. Home assignment • Show that for Poisson arrivals

  10. Remarks • Note that E(n)-E(q)==1-p(0) • The average number in service is 1·Pr(n≥1)=1-p(0) • The time evolution equation for q: • Note that here we cannot simply isolate the terms, we need to be more careful.

  11. HOL blocking analysis at steady state • Assume NxN switch, destinations are uniformly distributed • Packet queues are always full. • Bim = number of packets at the end of time slot m that are blocked for input i. • Aim = number of packets destined to output i moving to the head of the line during the mth time slot at “free” input queues. • Fm= number ofcells transmitted in time slot m.

  12. This is the form of the equation for the number of packets in M/D/1 queue • We analyze the operation of a virtual queue. • Based on home exercise: E[Bim]=02/2(1-0)

  13. Finding the utilization, 0

More Related