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1.
We consider a discrete-time GI-G-1 queueing system with server vacations. Vacations occur whenever the queue becomes empty or whenever a timer expires. When the timer expires one of the following four actions are considered: the server completes transmission of the present packet before leaving for a vacation, the service immediately leaves for a vacation and the interrupted packet's service is either continued, repeated or resampled and repeated after the vacation. Using a probability generating functions approach, we derive various performance measures such as moments of the buffer contents at various time epochs in equilibrium and moments of the packet delay in equilibrium. By means of an example, we then compare the operation modes under consideration. 相似文献
2.
研究一类到达服从一阶离散自回归过程,服务器有可能中断的离散排队系统.着重考虑在到达流具有相关性的情况下,排队系统的性能表现.文章通过概率母函数的方法,得到了系统队长的概率母函数,并由此导出系统平均队长.最后通过数值实验可以看出系统的性能对到达过程的相关性非常敏感. 相似文献
3.
作者通过举例以及理论证明指出目前单时期需求为"离散随机型存储问题"的处理方法所存在的错误,在此基础上引入排队论,并在对单时期需求为"离散随机型存储问题"的盈利数学期望进行研究后,根据盈利期望最大化原则,推导并建立了最佳订购量公式. 相似文献
4.
In analytic queueing theory, Rouche's theorem is frequently used to prove the existence of a certain number of zeros in the domain of regularity of a given function. If the theorem can be applied it leads in a simple way to results concerning the ergodicity condition and the construction of the solution of the functional equation for the generating function of the stationary distribution. Unfortunately, the verification of the conditions needed to apply Rouche's theorem is frequently quite difficult. We prove the theorem which allows to avoid some difficulties arising in applying classical Rouche's theorem to an analysis of queueing models. 相似文献
5.
S. Minkevicius 《Lithuanian Mathematical Journal》2005,45(3):299-314
The modern queueing theory is a powerful tool for a quantitative and qualitative analysis of communication systems, computer
networks, transportation systems, and many other technical systems. The paper is designated to the analysis of queueing systems
arising in the network theory and communications theory (such as the so-called multiphase queueing systems, tandem queues,
or series of queueing systems). We present heavy traffic limit theorems for the full idle time in multiphase queueing systems.
We prove functional limit theorems for values of the full idle time of a queueing system, which is its important probability
characteristic.
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Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 367–386, July–September, 2005. 相似文献
6.
王松建 《数学的实践与认识》2016,(6):165-172
讨论了带有普通类顾客、负顾客和特殊类顾客的M/M/1→M/M/1两级串联排队系统模型,负顾客在一级服务系统中,一对一抵消队尾的普通类顾客(若有),若一级服务系统无普通类顾客,负顾客自动消失,负顾客不进入二级服务系统.特殊类顾客不经过一级服务系统,直接进入二级服务系统等待接受服务.用拟生灭过程和矩阵几何解方法,得到了系统稳态队长的分布,以及系统忙期的分布和顾客逗留时间的分布等相关指标. 相似文献
7.
本文给出了巴拿赫空间中线性差分方程的两个多项式二分性概念, 使其在相应空间中的范数的增长速度不快于指数型增长. 并用实例阐释了相关概念之间的关系. 借助于指数二分性的研究方法讨论了多项式二分性的特征, 所得结论推广了指数稳定性及指数二分性中的一些已有结果. 相似文献
8.
We consider a discrete-time queueing system with a single deterministic server, heterogeneous Markovian arrivals and finite capacity. Most existing techniques model the queueing system using a direct bivariate Markov chain which requires a state space that grows rapidly as the number of customer types increases. In this paper, we define renewal cycles in terms of the input process and model the system occupancy level on each renewal cycle using a one-dimensional Markov chain. We derive the exact joint steady-state probability distribution of both states of input and system occupancy with a considerably reduced state space, which leads to the efficient calculation of overall/individual performance measures such as loss probability and average delay. 相似文献
9.
《随机分析与应用》2013,31(3):703-717
This paper deals with the queueing system M/G r /1 in which customers are served in batches of fixed size r. The author considers the discrete time parameter process, an embedded Markov chain, and the continuous time parameter process, a semi-regenerative process. In both cases, explicit solutions are given for the system size steady-state probabilities in terms of the zeros, inside and/or outside the closed unit ball, of the characteristic equation. Moments are derived and illustrative examples are provided. 相似文献
10.
研究了具有不耐烦顾客的M/M/1休假排队系统,其中休假时间服从位相分布.当顾客在休假时间到达系统,顾客则会因为等待变得不耐烦.服务员休假结束后立刻开始工作.如果在顾客不耐烦时间段内,系统的休假还没有结束,顾客就会离开系统不再回来.建立的模型为水平相依QBD拟生灭过程,通过利用BrightTaylor算法得到系统的稳态概率解.同时还得到一些重要的性能指标.最后通过数据实例验证了我们的结论. 相似文献
11.
若保险赔付工作中赔付人员有限,根据服务人员有限的排队系统的性质,可以研究保险公司所需计提的未决赔款准备金的分布函数.当假设赔付服务工作人员为c个,使用M/M/c/∞和G/M/c/∞排队系统的性质可以得到未决赔款准备金分布函数和年末所需增加计提的未决赔款准备金的分布及其界值.当假设赔付服务工作人员仅一个,使用M/G/1/∞排队系统的性质可以得到此时未决赔款准备金的分布函数.并且在假设损失赔付额取正整数的条件下,得到年末保险公司所需增加计提的未决赔款准备金分布的递推公式.而且通过计算实例表明结论的实用性,及所得到的递推公式在以往难以准确求解未决赔款准备金分布时是十分有效的. 相似文献
12.
A multi-server controllable queueing system with heterogeneous servers is considered. Several monotonicity properties of optimal policies for such a system are proved. 相似文献
13.
This comment is in response to a reply by Scott and Jefferson (Ref. 3) concerning the application of control theory to a queueing problem. 相似文献
14.
考虑一个有一般服务运作和休假时间的M/M/1排队系统。这时服务是非空竭的,也就是说服务员可能在系统有顾客的情形下进入休假,服务员的运作时间和休假时间都为一般分布,且相互独立,使用补充变量的方法,求解出系统稳态队长的母函数,在求解过程中遇到的未知函数po(x),可利用第一类Fredholm积分方程的数值解来确定,最后给出了系统稳态平均队长。 相似文献
15.
S. Minkevičius 《Acta Appl Math》2008,104(3):271-285
The model of an open queueing network in heavy traffic has been developed. These models are mathematical models of computer
networks in heavy traffic. A limit theorem has been presented for the virtual waiting time of a customer in heavy traffic
in open queueing networks. Finally, we present an application of the theorem—a reliability model from computer network practice. 相似文献
16.
研究一类具有三种状态的可修排队模型主算子的豫解集.通过研究该主算子的共轭算子的豫解集得到此主算子的豫解集. 相似文献
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18.
本文对离散马氏可修系统剩余寿命的极限分布进行了研究,指出此分布为几何分布,同时,对一些特殊的马氏可修系统给出其极限分布的参数,并给出了算例。 相似文献
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20.
A work station of a flexible manufacturing system (fms) is modeled as a multi-server queue with finite waiting room. The interarrival/service time distributions have squared coefficients of variations not less than 0.5 and are modeled as Coxian laws of two phases. A recursive scheme is developed to calculate the equilibrium queue length distribution. The model, together with the diffusion approximation model of Part I, can be used to aid the design of fms work stations. 相似文献