Alternating renewal processes with instantaneous rewards

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Stochastic Models Pub Date : 2021-10-05 DOI:10.1080/15326349.2021.1975548

Suyono, Ibnu Hadi, Mulyono

引用次数: 0

Abstract

Abstract Consider an alternating renewal process that, over time, alternates between two states (up and down), starting in upstate at time 0. Associated with each up interval a reward which is a function of the interval length. Similarly, we associate with each down interval a reward which depends on the length of it through some function. We call the total reward earned in the time interval an instantaneous alternating renewal reward process. In this article, we derive the probability distribution of the total reward and its expected value. The results are presented in the form of Laplace transforms.

查看原文本刊更多论文

交替更新过程和即时奖励

摘要考虑一个交替的更新过程，随着时间的推移，它在两个状态（向上和向下）之间交替，从时间0开始在北部州。与每个上行间隔相关的奖励是间隔长度的函数。类似地，我们通过一些函数将取决于其长度的奖励与每个向下间隔关联起来。我们将在时间间隔内获得的总奖励称为瞬时交替更新奖励过程。在本文中，我们推导了总报酬及其期望值的概率分布。结果以拉普拉斯变换的形式呈现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Stochastic Models 数学-统计学与概率论

CiteScore

1.30

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastic Models publishes papers discussing the theory and applications of probability as they arise in the modeling of phenomena in the natural sciences, social sciences and technology. It presents novel contributions to mathematical theory, using structural, analytical, algorithmic or experimental approaches. In an interdisciplinary context, it discusses practical applications of stochastic models to diverse areas such as biology, computer science, telecommunications modeling, inventories and dams, reliability, storage, queueing theory, mathematical finance and operations research.