{"title":"Aging Properties of Actual and Virtual Waiting Times in the GI|G|1|∞ Queuing Model","authors":"R. Chitchyan","doi":"10.1134/s0361768823090049","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The article considers a single-channel non-Poisson queuing model GI|G|1|<b>∞</b> with a FIFO “first-in-first-out” service discipline in stationary conditions and system load intensity less than one. One of the important concepts of the mathematical theory of reliability is the property of increasing the hazard rate (IHR) of homogeneous elements forming reliability systems, otherwise called the aging property. This problem is also of importent for the queuing theory. Two independent in the aggregate and independent of each other sequences: sequence of the waiting times before the start of servicing of actual calls and sequence of the waiting times of virtual calls, starting at time <i>t</i>, or, more precisely, sequence of the durations of the time intervals starting at time t and ending at the moment when the system is free from calls received into the system until time t, are considered. Using the properties of ladder points and ladder heights, as well as applying formulas of Takac’s, Cohen’s and Hook’s, it proved that the widely used in the theory of random walks two above-mentioned sequences of random variables are IHR.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Programming and Computer Software","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s0361768823090049","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
The article considers a single-channel non-Poisson queuing model GI|G|1|∞ with a FIFO “first-in-first-out” service discipline in stationary conditions and system load intensity less than one. One of the important concepts of the mathematical theory of reliability is the property of increasing the hazard rate (IHR) of homogeneous elements forming reliability systems, otherwise called the aging property. This problem is also of importent for the queuing theory. Two independent in the aggregate and independent of each other sequences: sequence of the waiting times before the start of servicing of actual calls and sequence of the waiting times of virtual calls, starting at time t, or, more precisely, sequence of the durations of the time intervals starting at time t and ending at the moment when the system is free from calls received into the system until time t, are considered. Using the properties of ladder points and ladder heights, as well as applying formulas of Takac’s, Cohen’s and Hook’s, it proved that the widely used in the theory of random walks two above-mentioned sequences of random variables are IHR.
摘要 本文研究了一个单通道非泊松排队模型 GI|G|1|∞，该模型在静止条件下具有先进先出（FIFO）的 "先进先出 "服务规则，系统负载强度小于 1。可靠性数学理论的一个重要概念是构成可靠性系统的同质元素的危险率（IHR）增加的特性，又称老化特性。这个问题对排队理论也很重要。我们考虑了两个总体上独立且相互独立的序列：从时间 t 开始的实际呼叫服务开始前的等待时间序列和虚拟呼叫等待时间序列，或者更确切地说，从时间 t 开始到系统在时间 t 之前没有收到呼叫时结束的时间间隔的持续时间序列。利用阶梯点和阶梯高度的特性，以及应用塔卡克公式、科恩公式和胡克公式，证明了随机游走理论中广泛使用的上述两个随机变量序列是 IHR。
期刊介绍：
Programming and Computer Software is a peer reviewed journal devoted to problems in all areas of computer science: operating systems, compiler technology, software engineering, artificial intelligence, etc.
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