{"title":"Marginal and joint distribution of inter-departure times for a PH/PH/c queue","authors":"Ruth Sagron , Yoav Kerner","doi":"10.1016/j.peva.2023.102383","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we introduce the Laplace–Stieltjes transform (LST) of the inter-departure time distribution in a <em>PH/PH/c</em> queue, and the two-dimensional joint LST of two consecutive inter-departure times to construct their correlation structure. We exploit the properties of phase-type (PH) random variables, as well as the steady-state distribution of the underlying continuous-time Markov chain in a <em>PH/PH</em>/<em>c</em> queue to construct these LSTs. We demonstrate our approach through numerical examples, while validating the results. Later, we analyze the correlation between two consecutive inter-departure times for various <em>PH/PH/c</em> queues. We observe that, if the fundamental elements of the queue have high (low) variability, then the correlation is positive (negative).</p></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"163 ","pages":"Article 102383"},"PeriodicalIF":1.0000,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0166531623000536/pdfft?md5=b3ce45055b5a49cf2750969c2b7c7d10&pid=1-s2.0-S0166531623000536-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Performance Evaluation","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166531623000536","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, HARDWARE & ARCHITECTURE","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we introduce the Laplace–Stieltjes transform (LST) of the inter-departure time distribution in a PH/PH/c queue, and the two-dimensional joint LST of two consecutive inter-departure times to construct their correlation structure. We exploit the properties of phase-type (PH) random variables, as well as the steady-state distribution of the underlying continuous-time Markov chain in a PH/PH/c queue to construct these LSTs. We demonstrate our approach through numerical examples, while validating the results. Later, we analyze the correlation between two consecutive inter-departure times for various PH/PH/c queues. We observe that, if the fundamental elements of the queue have high (low) variability, then the correlation is positive (negative).
期刊介绍：
Performance Evaluation functions as a leading journal in the area of modeling, measurement, and evaluation of performance aspects of computing and communication systems. As such, it aims to present a balanced and complete view of the entire Performance Evaluation profession. Hence, the journal is interested in papers that focus on one or more of the following dimensions:
-Define new performance evaluation tools, including measurement and monitoring tools as well as modeling and analytic techniques
-Provide new insights into the performance of computing and communication systems
-Introduce new application areas where performance evaluation tools can play an important role and creative new uses for performance evaluation tools.
More specifically, common application areas of interest include the performance of:
-Resource allocation and control methods and algorithms (e.g. routing and flow control in networks, bandwidth allocation, processor scheduling, memory management)
-System architecture, design and implementation
-Cognitive radio
-VANETs
-Social networks and media
-Energy efficient ICT
-Energy harvesting
-Data centers
-Data centric networks
-System reliability
-System tuning and capacity planning
-Wireless and sensor networks
-Autonomic and self-organizing systems
-Embedded systems
-Network science
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