The Annals of Applied Probability

A Markovian storage model

António Pacheco and N. U. Prabhu

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Abstract

We investigate a storage model where the input and the demand are additive functionals on a Markov chain J. The storage policy is to meet the largest possible portion of the demand. We first derive results for the net input process embedded at the epochs of transitions of J, which is a Markov random walk. Our analysis is based on a Wiener-Hopf factorization for this random walk; this also gives results for the busy period of the storage process. The properties of the storage level and the unsatisfied demand are then derived.

Article information

Source
Ann. Appl. Probab., Volume 6, Number 1 (1996), 76-91.

Dates
First available in Project Euclid: 18 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1034968066

Digital Object Identifier
doi:10.1214/aoap/1034968066

Mathematical Reviews number (MathSciNet)
MR1389832

Zentralblatt MATH identifier
0863.60096

Subjects
Primary: 60K330 60J15 60J25: Continuous-time Markov processes on general state spaces

Keywords
Additive functional busy period communication systems integral equation Markov-additive processes Markov random walk storage models Wiener-Hopf factorization

Citation

Pacheco, António; Prabhu, N. U. A Markovian storage model. Ann. Appl. Probab. 6 (1996), no. 1, 76--91. doi:10.1214/aoap/1034968066. https://projecteuclid.org/euclid.aoap/1034968066


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References

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  • DEPARTAMENTO DE MATEMATICA, SCHOOL OF OPERATIONS RESEARCH INSTITUTO SUPERIOR TECNICO AND INDUSTRIAL ENGINEERING ´ TECHNICAL UNIVERSITY OF LISBON CORNELL UNIVERSITY AV. ROVISCO PAIS RHODES HALL 1096 LISBOA CODEX ITHACA, NEW YORK 14853-3801 PORTUGAL E-mail: questa@orie.cornell.edu E-mail: apecheco@math.ist.utl.pt

The Institute of Mathematical Statistics

The Annals of Applied Probability

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