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On a generalized finite-capacity storage model

Published online by Cambridge University Press:  14 July 2016

Samuel W. Woolford
Samuel W. Woolford*
Affiliation:
Worcester Polytechnic Institute
*
∗ Postal address: Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, U.S.A.
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Abstract

This paper considers a finite-capacity storage model defined on a Markov chain {Xn ; n = 0, 1, ·· ·}, having state space J ⊆ {1, 2, ·· ·}. If Xn = j, then there is a random ‘input' Vn (j) (a negative input implying a demand) of ‘type' j, having a distribution function Fj (·). We assume that {Vn (j)} is an i.i.d. sequence of random variables, taken to be independent of {Xn } and of {Vn (k)}, for k ≠ j. Here, the random variables Vn (j) represent instantaneous ‘inputs' of type j for our storage model. Within this framework, we establish certain limit distributions for the joint processes (Zn, Xn ) and (Zn, Qn, Ln ), where Zn (defined in (1.2)) is the level of storage at time n, Qn (defined in (1.3)) is the cumulative overflow at time n, and Ln (defined in (1.4)) is the cumulative demand lost due to shortage of supply up to time n. In addition, an expression for the time-dependent distribution of (Zn, Xn ) is obtained.

Keywords

LEVEL OF STORAGEOVERFLOWDEMAND LOSTLIMIT DISTRIBUTION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983, pp. 663 - 674
Copyright
Copyright © Applied Probability Trust 1983 

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