Inequalities between time and customer averages for HNB(W)UE arrival processes

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Applied Probability Pub Date : 2024-03-21 DOI:10.1017/jpr.2023.120

Shigeo Shioda, Kana Nakano

引用次数: 0

Abstract

We show that for arrival processes, the ‘harmonic new better than used in expectation’ (HNBUE) (or ‘harmonic new worse than used in expectation’, HNWUE) property is a sufficient condition for inequalities between the time and customer averages of the system if the state of the system between arrival epochs is stochastically decreasing and convex and the lack of anticipation assumption is satisfied. HNB(W)UE is a wider class than NB(W)UE, being the largest of all available classes of distributions with positive (negative) aging properties. Thus, this result represents an important step beyond existing result on inequalities between time and customer averages, which states that for arrival processes, the NB(W)UE property is a sufficient condition for inequalities.

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HNB(W)UE 到达过程的时间和客户平均值之间的不等式

我们证明，对于到达过程，如果系统在到达历时之间的状态是随机递减和凸的，并且满足缺乏预期假设，那么 "谐波新值优于预期用过的值"（HNBUE）（或 "谐波新值劣于预期用过的值"，HNWUE）特性就是系统时间平均值和客户平均值之间不等式的充分条件。与 NB(W)UE 相比，HNB(W)UE 的范围更广，是所有具有正（负）时效特性的分布中最大的一类。因此，这一结果比关于时间与客户平均值不等式的现有结果迈出了重要的一步，现有结果指出，对于到达过程，NB(W)UE 属性是不等式的充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.