Time to Start a Crowded Period in a Finite-Buffer Queue with Poisson Input Flow and General Processing Times

机译：在具有泊松输入流和一般处理时间的有限缓冲区队列中开始拥挤时段的时间

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A finite-capacity queueing model with Poisson input flow and generally distributed processing times of jobs is considered. An idea of a crowded period is introduced, namely the time period in the system operation during which the number of jobs present in the system is continually greater than or equal the fixed level M > 0. A system of integral equations for the tail cumulative distribution function of the time to start a crowded period is derived, conditioned by the number of jobs present in the accumulating buffer before the start moment. A solution of the equivalent system written for Laplace transforms is found using the linear algebraic approach.

机译：考虑具有泊松输入流和作业的一般分布处理时间的有限容量排队模型。引入了拥挤周期的概念，即系统运行中系统中存在的作业数量连续大于或等于固定水平M> 0的时间段。尾部累积分布的积分方程组根据开始时刻之前累积缓冲区中存在的作业数量，得出开始拥挤时间段的时间函数。使用线性代数方法可以找到为拉普拉斯变换编写的等效系统的解决方案。

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来源
《Finite difference methods: theory and applications》|2018年|329-336|共8页
会议地点 Lozenetz(BG)
作者
Wojciech M. Kempa;
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作者单位

Institute of Mathematics, Silesian University of Technology, 23 Kaszubska Street, 44-100 Gliwice, Poland;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Crowded period; Finite buffer; Poisson process; Single-server queue; Transient state;

机译：拥挤的时期有限缓冲泊松过程单服务器队列；暂态;

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1. THE ANALYSIS OF A DISCRETE TIME FINITE-BUFFER QUEUE WITH WORKING VACATIONS UNDER MARKOVIAN ARRIVAL PROCESS AND PH-SERVICE TIME [J] . Qingqing Ye, Liwei Liu, Tao Jiang, RAIRO operations research . 2020,第3期

机译：马尔科夫到达过程下与PH维修时间下工作假期的离散时间有限缓冲队列分析
2. Discrete-time single-server finite-buffer queues under discrete Markovian arrival process with vacations [J] . U.C. Gupta, S.K. Samanta, R.K. Sharma, Performance Evaluation . 2007,第1期

机译：带休假的离散马尔可夫到达过程下的离散时间单服务器有限缓冲区队列
3. A Unified Approach to Analyze the Discrete-time Finite-buffer Queue with Batch-Markovian Arrival Process Under Partial- and Whole-batch Acceptance Strategies [J] . U. C. Gupta, S. K. Samanta, M. L. Chaudhry Электронное моделирование: Науч.-теорет. журн. . 2006,第5期

机译：分批和整批接受策略下具有批马尔可夫到达过程的离散时间有限缓冲队列的统一分析方法
4. Time to Start a Crowded Period in a Finite-Buffer Queue with Poisson Input Flow and General Processing Times [C] . Wojciech M. Kempa International Conference on Finite Difference Methods . 2019

机译：时间在有限缓冲区队列中启动拥挤时期，使用泊松输入流量和一般处理时间
5. Occurrence and duration of queue overflow for heavy tail interarrival times. [D] . Mao, XueJun. 2006

机译：大量尾部到达时间，队列溢出的发生和持续时间。
6. Factorized time-dependent distributions for certain multiclass queueing networks and an application to enzymatic processing networks [O] . W.H. Mather, J. Hasty, L.S. Tsimring, -1

机译：某些多种子队排队网络的分解时间依赖性分布以及酶处理网络的应用
7. Many server queueing processes with Poisson input and exponential service times [O] . Samuel Karlin, James McGregor 1958

机译：许多服务器排队进程，具有泊松输入和指数服务时间
8. The Queue with Poisson Input and General Service Times, Treated as a Branching Process [R] . Neuts, M. F. 1966

机译：具有泊松输入和一般服务时间的队列作为分支过程处理

Time to Start a Crowded Period in a Finite-Buffer Queue with Poisson Input Flow and General Processing Times

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