An exhaustive lĕvy storage process with intermittent output

Offer Kella

27 citations0/0 files storedStochastic Models

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

Abstract

We consider a Lĕvy storage model in which the output is shut off every time the system reaches zero, for a length of time which is determined by an arbitrary stopping time with respect to a filtration which may be richer than the one generated by the Lĕvy process. The main contribution is in showing that under suitable conditions, the steady state distribution associated with such a model exhibits a new decomposition property. Namely it can be written as an independent sum of two random variables. One has the distribution associated with a standard reflected Lĕvy process and the other has the steady state distribution of some clearing process (in contrast to excess lifetime or excess number of customers arriving during a vacation). A special case of such a model is the workload process in an M/G/l queue, in particular with the well known T, N and D-policies

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References

1986Queueing systems with vacations ? A survey 1985Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations 1963Queueing Systems with a Removable Service Station 1990Stochastic analysis of computer and communication systems 1968Optimal Operating Policies for M / G /1 Queuing Systems 1971Characterization and Computation of Optimal Policies for Operating an M/G/1 Queuing System with Removable Server 1969Optimal Average-Cost Policy for a Queue with Start-Up and Shut-Down Costs 1989Control Policies for the MX/G/1 Queueing System

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2003A STOCHASTIC CLEARING MODEL WITH A BROWNIAN AND A COMPOUND POISSON COMPONENT 2009Lévy processes with adaptable exponent 2006The M/G/∞ system revisited: finiteness, summability, long range dependence, and reverse engineering 2008ON A QUEUING MODEL WITH SERVICE INTERRUPTIONS 2019Asymptotic independence of regenerative processes with a special dependence structure

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