An exponential semi-markov process, with applications to queueing theory.

Guy Latouche

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

A class of semi-Markov processes is introduced, for which the intervals of time between events are dependent, identically and exponentially distributed random variables. The sequence of correlation coefficients for pairs of intervals is examined, to determine the types of processes which can be so modeled. As an application, such processes are used as input to an exponential server, in order to measure the effect of correlations in the arrival process on the behaviour of the queue.

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1984The caudal characteristic curve of queues 1977The M/M/1 Queue with Randomly Varying Arrival and Service Rates.1967Queues with semi-Markovian arrivals 1978Further Results on the M/M/1 Queue with Randomly Varying Rates.1962Stationary Waiting-Time Distributions for Single-Server Queues 1980Heavy traffic results for single-server queues with dependent (EARMA) service and interarrival times

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