A queueing system with a fixed accumulation level, random server capacity and capacity dependent service time

Author:

Dshalalow Jewgeni H.1,Tadj Lotfi2

Affiliation:

1. Department of Applied Mathematics, Florida Institute of Technology, Melbourne 32901, FL, USA

2. Department of Operations Research, Florida Institute of Technology, Melbourne 32901, FL, USA

Abstract

This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at leastrthe server takes a batch of sizerand processes it a random time arbitrarily distributed. If the queueing level is less thanrthe server idles until the queue accumulatesrcustomers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size.The objective of the paper is the stationary distribution of queueing process which is studied via semi-regenerative techniques. An ergodicity criterion for the process is established and an explicit formula for the generating function of the distribution is obtained.

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

Cited by 12 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Sojourn-Time Distribution for $$Geo/G^{a,b}/1$$ Queue with Batch Service;International Journal of Applied and Computational Mathematics;2023-12

2. Sojourn-time Distribution for $$M/G^a/1$$ Queue with Batch Service of Fixed Size - Revisited;Methodology and Computing in Applied Probability;2022-06-08

3. Effect of the server capacity distribution on the optimal control of a bulk service queueing system;Chaos, Solitons & Fractals;2003-12

4. On an M/G/1 quorum queueing system under T-policy;Journal of the Operational Research Society;2003-05

5. Explicit Solution of a Quorum Queueing System;Stochastic Analysis and Applications;2003-01-05

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3