AN M/M/1 QUEUE SUBJECT TO DIFFERENTIATED VACATION WITH PARTIAL INTERRUPTION AND CUSTOMER IMPATIENCE

IF 2.3 2区工程技术 Q3 ENGINEERING, INDUSTRIAL

Quality Technology and Quantitative Management Pub Date : 2021-11-02 DOI:10.1080/16843703.2021.1892907

Vijayashree K. V., A. K

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引用次数: 6

Abstract

ABSTRACT In this work, we consider an M/M/1 queueing model subject to differentiatedvacations. When the server is idle, he takes a break for a specific duration(termed Type I vacation). Upon completing the vacation, he takes another short break if the server stillfinds an empty system (termed as Type IIvacation). Both types of vacation follow an exponential distribution. As TypeI vacation persists for an extended period, it is reasonable to assume that theservice continues during this vacation by an alternate server at a slower rate,unlike the Type II vacation. Also, Type II being a shorter duration vacation,we assume that the Type II vacation is interrupted when the queue size reaches a predefined threshold value. Further, the arriving customers willwait only for a fixed duration of time, and if the service is incomplete by then,they leave the system permanently. We obtain an exact analytical expressionfor the transient state probabilities using Laplace transform, generatingfunctions, and continued fraction methodology. We also derive some useful measuresof effectiveness like the time-dependent mean and variance andillustrate their variations graphically.

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具有部分中断和顾客不耐烦的差异化休假的m / m /1队列

在本文中，我们考虑一个具有微分假期的M/M/1排队模型。当服务器空闲时，他会休息一段特定的时间(称为Type I vacation)。在完成假期后，如果服务器仍然发现一个空系统(称为Type IIvacation)，他将进行另一次短暂的休息。两种类型的假期都遵循指数分布。由于TypeI假期持续了一段较长的时间，因此可以合理地假设，与typeii假期不同，在此假期期间，服务将由备用服务器以较慢的速度继续提供。此外，Type II是一个持续时间较短的假期，我们假设当队列大小达到预定义的阈值时，Type II假期被中断。此外，到达的客户只会等待一段固定的时间，如果到那时服务还没有完成，他们就会永久地离开系统。我们利用拉普拉斯变换、生成函数和连分式方法得到了暂态概率的精确解析表达式。我们还推导了一些有用的有效性度量，如时间相关的均值和方差，并以图形方式说明了它们的变化。

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

Quality Technology and Quantitative Management ENGINEERING, INDUSTRIAL-OPERATIONS RESEARCH & MANAGEMENT SCIENCE

CiteScore

5.10

自引率

21.40%

发文量

审稿时长

>12 weeks

期刊介绍： Quality Technology and Quantitative Management is an international refereed journal publishing original work in quality, reliability, queuing service systems, applied statistics (including methodology, data analysis, simulation), and their applications in business and industrial management. The journal publishes both theoretical and applied research articles using statistical methods or presenting new results, which solve or have the potential to solve real-world management problems.