摘要
多类顾客的共享排队系统是排队论中一个既重要又困难的研究方向,它在计算机网络、生产制造系统与交通网络等领域中有着许多重要的实际应用.近年来,国外学者对多类顾客的共享排队系统已经开展了一些关键性的研究工作,给出了稳态联合队长的母函数,由此可以得到稳态联合队长的一阶矩和二阶矩.然而,由这个母函数反演来提供多类顾客共享排队系统的稳态联合队长的直接表达式却是一个多年来的困难问题.基于此,本文利用信息论中的最大熵原理,提供了一个高精度的近似表达式,其中这个近似表达式与它的精确表达式能够保证前三阶矩是相同的.另一方面,针对这个近似表达式,本文实现了它的有效数值计算,并通过数值算例分析了这个近似表达式中的重要因子是如何依赖于系统的原始参数.因此这个近似表达式对于推进多类顾客共享排队系统的实际应用具有重要的理论意义,同时本文的方法与结果不仅为研究多类顾客的共享排队系统提供了一条新的重要途径,而且为如何将信息理论应用于排队系统、排队网络以及更一般的随机模型研究提供了理论依据与技术支撑.
The discriminatory processor sharing queues with multiple classes of customers(abbreviatedas DPS queues)are an important but dicult research direction in queueing theory,and it has manyimportant practical applications in the elds of,such as,computer networks,manufacturing systems,transportation networks,and so forth.Recently,researchers have carried out some key work for the DPSqueues.They gave the generating function of the steady-state joint queue lengths,which leads to the rsttwo moments of the steady-state joint queue lengths.However,using the generating function to provideexplicit expressions for the steady-state joint queue lengths has been a dicult and challenging problem formany years.Based on this,this paper applies the maximum entropy principle in the information theoryto providing an approximate expression with high precision,and this approximate expression can have thesame rst three moments as those of its exact expression.On the other hand,this paper gives ecientlynumerical computation by means of this approximate expression,and analyzes how the key variables ofthis approximate expression depend on the original parameters of this queueing system in terms of somenumerical experiments.Therefore,this approximate expression has important theoretical signi cance topromote practical applications of the DPS queues.At the same time,not only do the methodology andresults given in this paper provide a new line in the study of DPS queues,but they also provide thetheoretical basis and technical support for how to apply the information theory to the study of queueingsystems,queueing networks and more generally,stochastic models.
作者
李泉林
马静宇
李超然
樊瑞娜
LI Quanlin;MA Jingyu;LI Chaoran;FAN Ruina(School of Economics and Management Sciences, Yanshan University, Qinhuangdao, 066004, China)
出处
《应用概率统计》
CSCD
北大核心
2018年第4期399-415,共17页
Chinese Journal of Applied Probability and Statistics
基金
国家自然科学基金项目(批准号:71471160
71671158)
河北省自然科学基金项目(批准号:G2017203277)资助
关键词
多类顾客的共享排队系统
信息论
最大熵原理
稳态联合队长
discriminatory processor sharing queues with multiple classes of customers
information theory
maximum entropy principle
steady-state joint queue lengths
作者简介
通讯作者:马静宇,E-mail:mjy0501@126.com.
