带抢占优先权和同步多重工作休假的M/M/c排队模型  

The M/M/c Queueing Model with Preemptive Priority and Multiple Synchronous Working Vacation

作　　者：马占友[1] 王文博[1] 郑晓铭 MA Zhanyou;WANG Wenbo;ZHENG Xiaoming(School of Science, Yanshan University, Qinhuangdao Hebei 066004, Chin)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《重庆师范大学学报（自然科学版）》2018年第3期96-100,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.61472342);河北省自然科学基金(No.A2014203096;No.G2013203169);河北省高等学校自然科学研究重点项目(No.ZD2017079);燕山大学青年教师基金(No.13LGA017);河北省高等学校科学技术研究青年基金(No.QN2016016);校级硕士研究生创新项目(No.2017XJSS045)

摘　　要：【目的】为了丰富随机休假排队理论,在经典M/M/c排队模型的基础上,研究带抢占优先权和多重工作休假的M/M/c排队模型。【方法】利用拟生灭过程和矩阵几何解的方法,得到了系统稳态队长分布的矩阵几何形式,进而求出系统中Ⅰ级、Ⅱ级顾客的平均队长、Ⅱ级顾客消失的概率等性能指标,最后举例进行验证。【结果】得到了带抢占优先权和多重工作休假的M/M/c排队模型。【结论】所得结果描绘出参数变化对系统性能指标的影响,并得到使社会利益达到最大的最优参数。[Purposes]In order to enrich the queueing theory of random vacations,the M/M/c queueing model with preemptive priority and multiple working vacations is studied. There are two types of customers,when the high-priority customer arrives at the system,if partial servers are occupied by low-priority customers and there is no free server,the new arriving high-priority customer will preempt the service of the low-priority customer at the head of the queue. When all servers are occupied by the high-priority customers,the new arriving high-priority customer will disappear. [Methods]According to the state transition rate matrix,the distribution of the queueing length in the boundary state is obtained by using the quasi birth-and-death process and the method of matrix-geometric solution,the matrix geometric form of the system steady-state distribution is analyzed. [Findings]The expressions of performance measures such as the system average queue length and the serving rate of the servers are given. [Conclusions]Finally,by analyzing some numerical examples,the influence of the parameters on the system performance measures and the optimal parameter which leads to the maximal social benefit are obtained.

关 键 词：抢占优先权 工作休假 稳态分布 优化 

分 类 号：O226[理学—运筹学与控制论]