HOL Blocking analysis

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HOL Blocking analysis

• based on
• Broadband Integrated Networks by Mischa Schwartz.

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PGF Probability Generating Functions

• Let a be a random variable.
• The PGF is defined by
• moment generation

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PGF Examples

• Poisson distribution
• Geometric distribution

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PGF Examples

• Bernoulli distribution
• Binomial distribution

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M/D/1 Queue
n cells in system
arrivals
q cells in queue

• To analyze consider a slotted time scale

k
k1
k-1
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M/D/1 Queue
k
k1
k-1
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Finding p(0)
? is the utilization
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The buffer statistics
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Home assignment

• Show that for Poisson arrivals

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Remarks

• Note that E(n)-E(q)?1-p(0)
• The average number in service is 1Pr(n1)1-p(0)
• The time evolution equation for q
• Note that here we cannot simply isolate the
  terms, we need to be more careful.

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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 of cells transmitted in time slot m.

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• 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 EBim?02/2(1-?0)

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Finding the utilization, ?0