带有反馈机制的单服务台排队系统的泛函重对数律

本文考虑了一个带有贝努里反馈机制的单服务台排队系统.我们将该系统的一些数量指标如队长过程,忙期过程,负荷过程的泛函重对数律的问题转化为一个反射布朗运动相关的问题,利用已有的布朗运动的重对数率的结果,刻画了队长过程,忙期过程,负荷过程的重对数律.     

高负荷下非强占优先排队网络系统中队长过程的扩散逼近

本文是在高负荷下非强占优先排除网络系统中给出了队长过程的扩散逼近 .证明了其队长过程的扩散极限是半鞅反射的布朗运动 .     

高负荷下带重尾服务强占优先排队的扩散逼近

考虑的排队系统是单服务台,顾客的初始到来是依泊松过程来到服务台,顾客的服务时间是重尾分布,服务的原则是强占优先服务.在高负荷条件下对此模型进行研究,获得了系统中的负荷过程,离去过程和队长过程的扩散逼近.     

多通道Assembly-like排队系统的强逼近

借助于强逼近理论和修正系统，本文较为详细地研究了多路到达、多服务台Ａｓｓｅｍｂｌｙ－ｌｉｋｅ排队系统，得到了队长过程、离去过程、负荷和虚等待时间过程的强逼近定理。     

每个节点具有多服务台的Jackson网络流体逼近的收敛速度

研究一个每个节点具有多服务台的Jackson网络.在服务强度为1的条件下,研究了Jackson网络的泛函重对数率与其流体逼近的收敛速度,证明了如果该网络的外部到达过程,服务过程有泛函重对数率,且在流体变换下以指数速度收敛到其相应的流体模型,则其队长过程、负荷过程、忙期过程等也具有相应的性质.     

基于Min(N,D)-策略的M/G/1排队系统的队长分布及最优策略

考虑基于Min(N,D)-策略的M/G/1排队系统,运用全概率分解技术和拉普拉斯变换工具,获得了队长瞬态分布的拉普拉斯变换的递推表达式和稳态队长分布的递推表达式,进一步通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并阐述了稳态队长分布的表达式在系统容量优化设计中的重要价值.最后,建立了费用模型,对最优Min(N,D)-策略与单一的最优N-策略和单一的最优D-策略进行了比较分析.     

具有两阶段服务和服务台故障M/M/1/N多重休假排队系统

研究了具有两阶段服务和服务台故障的M/M/1/N多重休假排队系统.利用马尔可夫过程理论建立了系统稳态概率方程组,并利用分块矩阵解法,得到了稳态概率的矩阵解.然后由此得出了系统的平均队长、平均等待队长等性能指标.     

具有Min(N,D,V)-策略控制的M/G/1排队系统

研究服务员具有多重休假和系统采取Min(N,D,V)-策略控制的M/G/1排队系统,运用全概率分解技术和拉普拉斯变换工具,研究了系统队长的瞬态分布和稳态分布,得到了队长瞬态分布的拉普拉斯变换的表达式和稳态队长分布的递推表达式,同时给出了稳态队长的随机分解结果和附加队长分布的显示表达式.进一步讨论了当N→∞,或D→∞,或p{V=∞}=1,或p{V=0}=1的一些特殊情况.最后,在建立系统费用结构模型的基础上,导出了系统长期单位时间的期望费用的显示表达式,并通过数值实例不但确定了使得系统在长期单位时间内的期望费用最小的联合控制策略(N~*,D~*),而且与单一的最优N~*-控制策略和D~*-控制策略进行了比较.     

生产流水线中的排队问题

本文讨论产品以Poisson过程到达,有K道加工工序,每加工点是有限容量且服务服从指数分布带受阻的排队网络,并给出了平稳条件和在平稳条件下以三节点组合逼近方法得到平均队长．     

具有多类顾客的单服务台流体逼近的收敛速度

本文研究了—个具有多类顾客到达的单服务台排队系统．在流体变换下,我们知道排队模型以概率1在紧集上一致收敛到相应的流体模型．在一致收敛拓扑下,如果到达过程,服务过程在流体变换下以指数速度收敛到相应的流体过程,我们证明了在流体变换下的排队系统中的各个参量以指数速度收敛到流体模型中相应的参量,这些参量包括队长过程,负荷过程,逗留时间过程,离去过程,闲期过程等．     

On the fluid approximation for a multiclass queue under non-preemptive SBP service discipline

A multi-class single server queue under non-preemptive static buffer priority (SBP) service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length and busy time processes. Furthermore, we prove that the convergence rate of the fluid approximation for the queue length and busy time processes is exponential for large N. Additionally, a sufficient condition for stability is obtained.     

The acquisition queue

We propose a new queueing model named the acquisition queue. It differs from conventional queueing models in that the server not only serves customers, but also performs acquisition of new customers. The server has to divide its energy between both activities. The number of newly acquired customers is uncertain, and the effect of the server’s acquisition efforts can only be seen after some fixed time period δ (delay). The acquisition queue constitutes a (δ+1)-dimensional Markov chain. The limiting queue length distribution is derived in terms of its probability generating function, and an exact expression for the mean queue length is given. For large values of δ the numerical procedures needed for calculating the mean queue length become computationally cumbersome. We therefore complement the exact expression with a fluid approximation. One of the key features of the acquisition queue is that the server performs more acquisition when the queue is small. Together with the delay, this causes the queue length process to show a strongly cyclic behavior. We propose and investigate several ways of planning the acquisition efforts. In particular, we propose an acquisition scheme that is designed specifically to reduce the cyclic behavior of the queue length process. This research was financially supported by the European Network of Excellence Euro-NGI. The work of the second author was supported in part by a TALENT grant from the Netherlands Organisation for Scientific Research (NWO).     

Fluid approximation and its convergence Rate for GI/G/1 queue with vacations

A GI/G/1 queue with vacations is considered in this paper.We develop an approximating technique on max function of independent and identically distributed(i.i.d.) random variables,that is max{ηi,1 ≤ i ≤ n}.The approximating technique is used to obtain the fluid approximation for the queue length,workload and busy time processes.Furthermore,under uniform topology,if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate,we prove by the...     

Some results for the queues Mx/M/c and GIx/ G/c

We develop for the queue M^x/M/c an upper bound for the mean queue length and lower bounds for the delay probabilities (that of an arrival group and that of an arbitrary customer in the arrival group). An approximate formula is also developed for the general bulk-arrival queue GI^x/G/c. Preliminary numerical studies have indicated excellent performance of the results.     

一类重入型网络在优先服务原则下的扩散近似

本文研究了一类重入型网络在优先服务原则下的扩散近似,运用随机分析方法,证明了标准化队长过程的C-紧性．在优先服务原则下,给出了这类网络的标准化队长过程扩散近似存在的充分条件．