Analysis of MAP/PH_1,PH_2/1 queue with vacations and optional secondary services

Srinivas R. Chakravarthy

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Analysis of MAP/PH_1,PH_2/1 queue with vacations and optional secondary services

机译：带有假期和可选辅助服务的MAP / PH_1，PH_2 / 1队列分析

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摘要

In this paper we study a queueing model in which the customers arrive according to a Markovian arrival process (MAP). There is a single server who offers services on a first-come-first-served basis. With a certain probability a customer may require an optional secondary service. The secondary service is provided by the same server either immediately (if no one is waiting to receive service in the first stage) or waits until the number waiting for such services hits a pre-determined threshold. The model is studied as a QBD-process using matrix-analytic methods and some illustrative examples are discussed.

机译：在本文中，我们研究了一种排队模型，在该模型中，客户根据马尔可夫到达过程（MAP）到达。有一个服务器以先到先得的方式提供服务。客户很有可能需要可选的辅助服务。辅助服务由同一服务器立即提供（如果没有人在第一阶段等待接收服务），或者等待直到等待此类服务的次数达到预定阈值。使用矩阵分析方法将模型作为QBD过程进行研究，并讨论了一些说明性示例。

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来源
《Applied Mathematical Modelling》 |2013年第21期|8886-8902|共17页
作者
Srinivas R. Chakravarthy;
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作者单位

Department of Industrial and Manufacturing Engineering, Kettering University, Flint, MI 48504, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Markovian arrival process; Queueing; Effective service time; Vacation; Secondary batch services; Phase type distribution;

机译：马尔可夫到达过程;排队;有效服务时间;假期;二级批处理服务;相型分布;

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1. ANALYSIS OF AN MMAP/PH_1, PH_2/N/∞ QUEUEING SYSTEM OPERATING IN A RANDOM ENVIRONMENT [J] . Chesoong KIM, Alexander DUDIN, Sergey DUDIN, International Journal of Applied Mathematics and Computer Science . 2014,第3期

机译：随机环境中运行的MMAP / PH_1，PH_2 / N /∞排队系统的分析
2. Optimization of the (MAP_1, MAP_2)/(PH_1, PH_2)/N retrial queue model of wireless cellular networks with channel allocation [J] . Zonghao Zhou, Yijun Zhu Computers and Electrical Engineering . 2013,第6期

机译：具有信道分配的无线蜂窝网络的（MAP_1，MAP_2）/（PH_1，PH_2）/ N重试队列模型的优化
3. Analysis of a non-Markovian single server batch arrival queueing system of compulsory three stages of services with fourth optional stage service, service interruptions and deterministic server vacations [J] . P. Vignesh, S. Srinivasan, S. Maragatha Sundari International Journal of Operational Research . 2019,第1期

机译：第四个可选阶段服务，服务中断和确定性服务器假期的强制三个阶段的非马洛维亚单服务器批量到达排队系统分析
4. Analysis on preemptive priority retrial queue with two types of customers, balking, optional re-service, single vacation and service interruption [C] . S Yuvarani, M C Saravanarajan International Conference on Science, Engineering the Technology . 2018

机译：具有两种客户的抢占优先级重审队列分析，废弃，可选重新服务，单假和服务中断
5. Modeling an M/M/1 Queue with Unreliable Service and a Working Vacation [D] . ?Patterson, Joshua K. 2019

机译：建模的 M / M / 1排队不可靠的服务和一个工作休假
6. Finite Buffer GI/M(n)/1 Queue with Bernoulli-Schedule Vacation Interruption under N-Policy [O] . P. Vijaya Laxmi, V. Suchitra 2014

机译：N策略下带有Bernoulli-Schedule假期中断的有限缓冲区GI / M（n）/ 1队列
7. Analysis of an M[X]/(G1,G2)/1 retrial queueing system with balking, optional re-service under modified vacation policy and service interruption [O] . P. Rajadurai, M.C. Saravanarajan, V.M. Chandrasekaran 2014

机译：分析m [X] /（G1，G2）/ 1重审排队系统，在改进的休假政策和服务中断下进行无人值守，可选的重新服务

Analysis of MAP/PH_1,PH_2/1 queue with vacations and optional secondary services

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