Estimation of Buffer Overflow Probabilities and Economies of Scale in ATM Multiplexers by Analysis of a Model of Packetized Voice Traffic

Estimation of Buffer Overflow Probabilities and Economies of Scale in ATM M ultiplexers by Analysis of a M odel of Packetized Voice Traffic by Paul J. Farrell We obtain upper bounds on the probability of buffer overflow for an ATM multiplexer of L identical packetized voice sources The multiplexer is modelled by a FCFS single server queue The arrivals at the multiplexer are a homogenous superposition of the arrivals from L independent identical sources, with each source modelled by a copy of a discrete time Markov Chain which we call the Cell Level M odel Throughout, appropriate parameters are scaled with L, to maintain a constant load over all superposition sizes The probability that, the queue-length (q^) of the queue in a finite buffer exceeds the buffer size b, is bounded above by the probability that the queue-length (qL) of the queue m an infinite buffer exceeds length b In order to bound the former above, we find upper bounds or approximations for the latter by using the theory of, • Large Deviations, to determine its asymptotics for large b, • Martingales, to obtain upper bounds, valid for all positive b, • Large Deviations, to determine its asymptotics for large L for time rescaled (proportional to L ) arrival processes These demonstrate the multiplexing gam and economies of scale obtainable from large and small buffers and large multiplexers, respectively Chapter