MARKOV MODULATED FLUID QUEUES WITH BATCH FLUID ARRIVALS

Hiroyuki Takada

16 citations0/0 files storedJournal of the Operations Research Society of Japan

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

Abstract

In the conventional Markov modulated fluid queue, the buffer content process has a continuous sample path. This paper concerns a Markov modulated fluid queue whose buffer content process may have jumps. This model extends not only the conventional fluid queue but also the M AP/G/1 model. We give a procedure to get a Laplace-Stieltjes transform of the stationary joint distribution of the buffer content and background state. Some numerical examples are presented as well.

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References

1982Stochastic Theory of a Data-Handling System with Multiple Sources 1962The stability of a queue with non-independent inter-arrival and service times 1988Stochastic theory of a fluid model of producers and consumers coupled by a buffer 1994Fluid Models in Queueing Theory and Wiener-Hopf Factorization of Markov Chains 1991Analysis of separable Markov-modulated rate models for information-handling systems 1995Stationary distributions for fluid flow models with or without brownian noise 1991Analysis of separable Markov-modulated rate models for information-handling systems 1989Markov processes whose steady state distribution is matrix-exponential with an application to theGI/PH/1 queue

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