Some limit theorems for the general semi-Markov storage model

Author:

Balagopal K.

Abstract

In this paper we treat the general version of the semi-Markov storage model, introduced first by Senturia and Puri: transitions in the state of the system occur at a discrete sequence of time points, described by a two-state semi-Markov process. An input occurs at an instant of transition to state 1 and a demand for release occurs at an instant of transition to state 2. Assuming general distributions for all the variables involved, we show that the dam contents just after the nth input converges properly in distribution as n →∞ under conditions of stability; likewise that after the nth demand. We also show that the demand lost due to shortage of stock, accumulated over instants of demand as well as over time, obeys a strong law and a central limit theorem.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the limit behavior of a multicompartment storage model with an underlying Markov chain;Advances in Applied Probability;1988-03

2. On the limit behavior of certain quantities in a subcritical storage model;Advances in Applied Probability;1985-06

3. On a generalized storage model with moment assumptions;Journal of Applied Probability;1981-06

4. On a generalized storage model with moment assumptions;Journal of Applied Probability;1981-06

5. On limit theorems associated by a storage model;Advances in Applied Probability;1980-06

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