具有k个连续异构服务步骤和暂态休假的M/G/1队列模型

IF 2.3 2区工程技术 Q3 ENGINEERING, INDUSTRIAL

Quality Technology and Quantitative Management Pub Date : 2022-04-26 DOI:10.1080/16843703.2021.1981529

Ali Mohammadi, M. R. Salehi Rad

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引用次数: 4

摘要

摘要研究了一种具有异构服务阶段和休假条件的瞬态队列模型。根据泊松过程，进入者，每次到达按到达顺序在k个阶段依次服务。服务时间遵循一般分布函数。服务完成后，服务器可以以该概率休假，并留在系统中以该概率为其他客户提供服务。对于该模型，我们首先得到了概率生成函数的拉普拉斯变换。在暂态的特殊情况下，得到了系统大小的概率生成函数。通过数值分析得到系统平均尺寸。然后，考虑了模型的灵敏度。

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An M/G/1 queueing model with k sequential heterogeneous service steps and vacations in the transient state

ABSTRACT This article studies a transient state queueing model with sequential heterogeneous service phase and vacations. According to a Poisson process, entrants, each arrival is serviced sequentially in k phases in the order of arrival. The service times follow a general distribution function. Upon completion of the service, the server could take a vacation with the probability and remain in the system to provide service to other customers with the probability . For this model, first, we obtain the Laplace transform of the probability generating functions. The probability generating functions of system sizes are obtained for a special case in the transient state. The mean system size is obtained by using numerical analysis. Then, the sensitivity of the model is considered.

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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.