BBN Notes 2/19/97 Lecture 10 BBN Notes for Lecture 10 (2/19/97)
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Knockout (KO) Switch Cell Loss Analysis

There are two source of cell loss destined output j, :

  1. Knockout (KO) Loss: If in any given time slot, k arrivals occurr for output J with k > L, then (k - L) cells are lost, this is called "knockout loss" or "KO loss".

  2. Buffer Overflow (BO) Loss: If enough cells arrive in some time period at a rate of more than 1 per slot, then the (finite) output buffer can overflow, i.e. buffer overflow or "BO loss" occurs.

1. KO Loss Analysis

KO loss is memoryless. Thus we can make assumptions about arrival process correlation for this part of the analysis.

We compute the probability of loss as follows:

where p = load and the choice of destination is assumed to be independent.

The expected number of lost cells per time slot is given by

The lost cell probability is the expected number of lost cells per time slot at any given output, divided by the average number of cell arrivals per time slot bound for that output. Thus,

2. BO Loss Analysis

Here we can apply our previous results on Output Queuing.

The number of arrivals in time slot i is , and its probability is given by

To apply output queuing, we must assume i.i.d. arrivals (unlike in the KO loss analysis above).

Note: The BO loss analysis in the book gives an upper bound for the BO loss for two reasons:

  1. The book assumes Poisson (or Binomial) arrivals and no KO loss. KO loss is small but could still have an impact on this system due to its burstiness.

  2. For buffer of capacity B,

    where b is defined to be the number of cells in the buffer of the infinite buffer case.

Because of preceding two assumptions, the BO loss analysis in the book gives an upper bound. This, of course, is still quite useful since we are most interested in making sure that loss is below some threshold, which it certainly will be if the upper bound is.

BBN Notes for Lecture 10 (2/19/97)
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Notes taken by Kemal E. Tepe, tepek@rpi.edu, from a lecture by Prof. K.S. Vastola, vastola@ecse.rpi.edu, on February 19, 1997.