Imbedded Markov chain analysis of single server bulk queues

U. Narayan Bhat

34 citations0/0 files storedJournal of the Australian Mathematical Society

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

Abstract

Summary In this paper results from Fluctuation Theory are used to analyse the imbedded Markov chains of two single server bulk-queueing systems, (i)with Poisson arrivals and arbitrary service time distribution and (ii) with arbitrary inter-arrival time distribution and negative exponential service time. The discrete time transition probailities and the equilibrium behaviour of the queue lengths of the systems have been obtained along with distributions concerning the busy periods. From the general results several special cases have been derived.

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References

1953Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain 1954On Queueing Processes with Bulk Service 1959Imbedded Markov Chain Analysis of a Waiting-Line Process in Continuous Time 1959A Contribution to the Theory of Bulk Queues 1962An Elementary Queueing Problem 1961A Bulk-Service Queueing Problem with Variable Capacity 1962The General Bulk Queue as a Hilbert Problem

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1985The Factorization of Queueing Equations and Their Interpretation 1982Time-Inhomogenous Bulk Server Queue in Discrete Time: A Transportation Type Problem 2002Restricted Admissibility of Batches into anM/G/1 Type Bulk Queue with Modified Bernoulli Schedule Server Vacations 1973A note on the MX/GY/1, K bulk queueing system 1970Some Results for Bulk-Arrival Queues with State-Dependent Service Times 1970A Feedback Queueing System With Batch Arrivals, Bulk Service, and Queue-Dependent Service Time

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