The M/G/1 queue with instantaneous bernoulli feedback

Ralph L. Disney · Donald C. McNickle · Burton Simon

48 citations0/0 files storedNaval Research Logistics Quarterly

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Advanced Queuing Theory Analysis Probability and Statistical Research Age of Information Optimization

Abstract

Abstract In this paper we are concerned with several random processes that occur in M/G/1 queues with instantaneous feedback in which the feedback decision process is a Bernoulli process. Queue length processes embedded at various times are studied. It is shown that these do not all have the same asymptotic distribution, and that in general none of the output, input, or feedback processes is renewal. These results have implications in the application of certain decomposition results to queueing networks.

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References

1957Networks of Waiting Lines 1993An introduction to queueing theory 1963A Single-Server Queue with Feedback 1973Introduction to Queueing Theory 1979Characterizations of Poisson traffic streams in Jackson queueing networks

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1984Stationary queue-length and waiting-time distributions in single-server feedback queues 1982On Markov Jump Processes Imbedded at Jump Epochs and Their Queueing-Theoretic Applications 1983Queues with delayed feedback 1981A note on sojourn times in M/G/1 queues with instantaneous, bernoulli feedback 2021Cost Analysis and Optimization of Machine Repair Model with Working Vacation and Feedback–Policy 1991Sojourn times in vacation and polling systems with Bernoulli feedback 1982Application of level crossing analysis to discrete state processes in queueing systems

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