基于谱展开方法的一类到达率可变的有限排队系统分析  

An spectral expansion approach to analyzing a fnite queue with variable arrival rate

作　　者：张宏波 周高军 ZHANG Hong-bo;ZHOU Gao-jun(School of Statistics and Mathematics,Henan Finance University,Zhengzhou 450046,China;Digital Technology School,Sias University,Zhengzhou 450003,China)

机构地区：[1]河南财政金融学院统计与数学学院,河南郑州450046 [2]郑州西亚斯学院数字技术产业学院,河南郑州450003

出　　处：《高校应用数学学报（A辑）》2024年第4期404-412,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：河南省高等学校重点科研项目(22B110002)。

摘　　要：该文讨论到达率可变的M/T-SPH/1/N有限排队,其中T-SPH表示可数状态吸收生灭过程吸收时间的分布.当顾客到达时,根据系统中顾客数决定是否进入系统.对该排队模型,首先对文中建立的QBD过程模型,用谱展开方法进行分析,得到了过程联合平稳分布和排队模型的平稳队长分布.另外,由所得结果还进一步得到了QBD过程的矩阵几何解.最后,通过几个数值例子演示了参数变化对排队系统性能指标的影响.Afinite M/T-SPH/1/N queueing model with variable arrival rate is analyzed,where T-SPH denotes the infinite phase type distribution defined on a birth and death process with countably many states.For an arriving customer the probability he decides join the queue depends on the number of customers present in the system.For the queueing system,the established QBD process model can be analyzed by the method of generalized eigenvalues.Using this method,the expression of stationary queue length distribution of the queue is given.Furthermore,the obtained results enable us to give the matrix-geometric solution of the QBD process.Finally,several numerical examples are also presented to illustrate the impact of parameters on performance indexes of the queueing system.

关 键 词：M/T-SPH/1/N排队 有限排队 QBD过程 谱展开方法 矩阵几何解 

分 类 号：O226[理学—运筹学与控制论]