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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (6): 812-822.doi: 10.3969/j.issn.1005-3085.2015.06.003

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具有阀值策略的$M/M/2/K$多重休假排队系统

李  惠,  岳德权   

  1. 燕山大学理学院，秦皇岛  066004
  • 收稿日期:2014-06-23 接受日期:2014-12-18 出版日期:2015-12-15 发布日期:2016-02-15
  • 基金资助:
    国家自然科学基金(71071133).

An $M/M/2/K$ Queuing System with Threshold Policy and Multiple Vacations

LI Hui,   YUE De-quan   

  1. College of Science, Yanshan University, Qinhuangdao 066004
  • Received:2014-06-23 Accepted:2014-12-18 Online:2015-12-15 Published:2016-02-15
  • Supported by:
    The National Natural Science Foundation of China (71071133).

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摘要： 本文研究了带有阀值策略的服务器不同的$M/M/2/K$异步多重休假排队系统．第一个服务器在服务完一个顾客后，若发现系统中无等待的顾客，则立刻开始休假．当系统中等待的顾客数小于阀值时，第二个服务器开始休假．论文通过深入研究该系统的性能，为决策者提供一些参考．利用矩阵分析的方法，求出了系统的平稳概率向量和排队指标的解析表达式．最后，我们构造了一个费用模型，并分析了各参数对系统最小费用和最优阀值的影响．

关键词: 排队系统, 阀值策略, 异步休假, 矩阵分析, 费用模型

Abstract:

This paper studies an $M/M/2/K$ queuing system with a threshold policy and asynchronous multiple vacations, where the service rates of two servers are not identical. At the completion instant of a service, the first server will take a vacation if there is no waiting customer, while the other server starts a vacation when the number of customers in the waiting line is less than the threshold value. The main purpose of this paper is to provide guidence for decision makers through detailed research on the performance of this system. Using the matrix analysis method, we obtain the stationary probability vectors and analytical expressions of the queue indexes. Finally, we establish a cost model which analyzes the influence of defferent parameters on the minimum cost and optimal threshold value of the system.

Key words: queuing system, threshold policy, asynchronous multiple vacations, matrix analytic, cost model

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