Markov Chain Animation Technique Applied to ATM Bandwidth Derivation and Tandem Switches
The derivation of queue lengths and buffer fills in ATM networks with particular types of cell arrival is known explicitly for some specific cases, but often simulation must be resorted to, which is time consuming and the accuracy is difficult to determine, particularly when one is considering cell losses or CDV around the 10-8 level. We describe an alternative technique which involves iteration of the Markov transition and state probabilities for a queue; we have called this Animation. Its principle is simply that of repetitively applying the appropriate Markov chain transition matrix to the current queue length probabilities to produce a new set of probabilities. In the case of a known cell sequence arrival the transition matrix changes for each iteration to reflect the arrival probability. Animation presents some numerical difficulties and techniques are described to overcome these. The specific application described is the derivation of equivalent bandwidth of cell patterns resulting from ATM policing or shaping, and the transit of these cells through networks containing multiple switching stages.
KeywordsATM bandwidth policing queuing switching
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- J M Griffiths, L G Cuthbert “Very Selective ATM Statistical Filter” Electronics Letters, vol 32, No 7 28 March 96Google Scholar