Article1993

Marked point processes as limits of Markovian arrival streams

234 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Point processes and geometric inequalities

Abstract

A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that asm→∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.

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References

1991New results on the single server queue with a batch markovian arrival process 1986Comparison Methods for Queues and Other Stochastic Models.1984Comparison Methods for Queues and Other Stochastic Models 1976Stochastic Processes in Queueing Theory 1990A single-server queue with server vacations and a class of non-renewal arrival processes 1985Queues and Point Processes.1980The N/G/1 queue and its detailed analysis

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