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1.
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.  相似文献   

2.
在文中,我们首先给出由马氏过程的一些跳跃时刻形成的简单点过程的有限维分布族弱收敛到泊松过程的相应分布族的条件,并讨论了有限维分布族弱收敛到泊松过程相应分布族的平稳马氏排队系统的话务过程,其次,我们证明了GI/M/1排队系统的离去过程的有限维分布族在重话务的情况下弱收敛到泊松过程的相应分布族。  相似文献   

3.
本文我们给出了基于神经元网络的随机过程的条件分位数的均方收敛速度.无论是在独立同分布情况下还是在平稳混合(α-混合β-混合)的情况下,我们都给出了相应的结果.结果与基于神经元网络的回归估计的收敛速度相同.采用的技术同Zhang(1998)一致.  相似文献   

4.
本文研究一维可压缩Navier-Stokes-Vlasov耦合模型在空间周期区域上初值问题整体解的渐近行为;证明随着时间发展,流体速度和粒子宏观平均速度以指数速率收敛到同一个常速度,并且粒子分布函数关于速度变量的紧支集以指数速率收缩到一个点集.  相似文献   

5.
孙六全  周勇 《数学学报》1998,41(5):1113-1120
本文在左截断右删失模型下获得了乘积限过程和累积失效率过程的振动模和Lipschitz-12模的强一致收敛的精确速度.作为定理的应用,推导了各种核密度估计和失效率估计的强一致收敛的精确速度.  相似文献   

6.
本文主要研究了顾客一般独立批到达、指数批服务、缓冲器容量有限的单个服务器的排队系统,本文首先使用补充变量和嵌入马氏链的方法,在部分拒绝和全部拒绝情形下,得到系统排队队长的稳态分布,进而得到相应的性能指标,如系统的平均排队长、平均等待时间、损失概率等.其次对等待时间进行了分析.  相似文献   

7.
该文在M/M/c排队驱动系统中加入工作休假策略,研究了单重工作休假多服务台排队驱动的流体模型.利用拟生灭过程和矩阵几何解法得到驱动系统稳态队长分布.构建净输入率结构,导出流体模型的稳态联合分布函数满足的的矩阵微分方程组,进而利用Laplace-Stieltjes变换(LST)方法得到稳态下缓冲器库存量的空库概率及均值表达式.最后,给出模型在多信道无线Mesh网下的应用,通过数值例子展示参数变化对系统性能指标的影响.  相似文献   

8.
曹成铉 《应用数学》1999,12(1):110-114
本文给出了G/G/1排队系统的离去过程的有限维分布弱收敛到泊松过程的有限维分布的条件,特别给出了生灭排队系统及G/M/1排队系统的离去过程的有限维分布弱收敛到泊松过程的有限维分布的简单条件.  相似文献   

9.
本文主要对具有启动时间和休假可中断策略的流体排队模型进行经济学分析.假设当流体到达系统时,以其观察到的缓冲器状态为依据来计算个体净收益,进而决定是否进入缓冲器排队.基于以上条件,对该模型从经济学角度展开分析,在完全可视和几乎可视两种情况下分别讨论了:当只考虑个体收益时流体的止步策略及单位时间内社会收益达到最优时流体的止步策略.通过对该排队模型进行相关分析,给个体和决策者提出相应合理化建议,以实现收益最优.  相似文献   

10.
在有负顾客到达可清空优先权排队中的全部顾客的机制下,研究了M_1,M_2/G_1,G_2/1重试排队系统.假设两类顾客的到达分别服从独立的泊松过程,如服务器忙,优先级高的顾客则排队等候服务,而优先级低的顾客只能进入Orbit中进行重试,直到重试成功.此外,假设负顾客的到达服从Poisson过程,当负顾客到达系统时,若发现服务台忙,将带走正在接受服务的顾客及优先权队列中的顾客.若服务台空闲,则负顾客立即消失,对系统没有任何影响.应用补充变量及母函数法给出了该模型的稳态解的拉氏变换表达式.  相似文献   

11.
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...  相似文献   

12.
We consider the long-range dependent cumulative traffic generated by the superposition of constant rate fluid sources having exponentially distributed inter start times and Pareto distributed durations with finite mean and infinite variance. We prove a sample path large deviation principle when the session start time intensity is increased and the processes are centered and scaled appropriately. Properties of the rate function are investigated. We derive a sample path large deviation principle for a related family of stationary queue length processes. The large deviation approximation of the steady-state queue length distribution is compared with the corresponding empirical distribution obtained by a computer simulation. MSC 2000 Classifications: Primary 60F10; Secondary 60K25, 68M20, 90B22  相似文献   

13.
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.  相似文献   

14.
Using stochastic dominance, in this paper we provide a new characterization of point processes. This characterization leads to a unified proof for various stability results of open Jackson networks where service times are i.i.d. with a general distribution, external interarrivai times are i.i.d. with a general distribution and the routing is Bernoulli. We show that if the traffic condition is satisfied, i.e., the input rate is smaller than the service rate at each queue, then the queue length process (the number of customers at each queue) is tight. Under the traffic condition, the pth moment of the queue length process is bounded for allt if the p+lth moment of the service times at all queues are finite. If, furthermore, the moment generating functions of the service times at all queues exist, then all the moments of the queue length process are bounded for allt. When the interarrivai times are unbounded and non-lattice (resp. spreadout), the queue lengths and the remaining service times converge in distribution (resp. in total variation) to a steady state. Also, the moments converge if the corresponding moment conditions are satisfied.  相似文献   

15.
We consider the long-range dependent cumulative traffic generated by the superposition of constant rate fluid sources having exponentially distributed intra start times and Pareto distributed durations with finite mean and infinite variance. We prove a sample path moderate deviation principle when the session intensity is increased and the processes are centered and scaled appropriately. The governing rate function is known from large deviation principles for the tail probabilities of fractional Brownian motion. We derive logarithmic tail asymptotics for associated queue length processes when the traffic loads an infinite buffer with constant service rate. The moderate deviation approximation of steady-state queue length tail probabilities is compared to those obtained by computer simulations.  相似文献   

16.
Using a bounding technique, we prove that the fluid model of generalized Jackson network (GJN) with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence rate are embodied by the queue length, workload, and busy time processes.  相似文献   

17.
We consider a process associated with a stationary random measure, which may have infinitely many jumps in a finite interval. Such a process is a generalization of a process with a stationary embedded point process, and is applicable to fluid queues. Here, fluid queue means that customers are modeled as a continuous flow. Such models naturally arise in the study of high speed digital communication networks. We first derive the rate conservation law (RCL) for them, and then introduce a process indexed by the level of the accumulated input. This indexed process can be viewed as a continuous version of a customer characteristic of an ordinary queue, e.g., of the sojourn time. It is shown that the indexed process is stationary under a certain kind of Palm probability measure, called detailed Palm. By using this result, we consider the sojourn time processes in fluid queues. We derive the continuous version of Little's formula in our framework. We give a distributional relationship between the buffer content and the sojourn time in a fluid queue with a constant release rate.  相似文献   

18.
本文研究成批到达排队系统中队长过程的随机比较问题.利用随机比较方法我们对成批到达指数服务的多服务台排队系统进行分析,得到了该排队系统中队长过程的随机比较以及队长函数关于时间的凹性和凸性.同时我们也给出了成批到达一般服务的单服务台排队系统队长过程、稳态队长的随机比较以及队长函数关于时间的凹性和凸性.  相似文献   

19.
We consider a general QBD process as defining a FIFO queue and obtain the stationary distribution of the sojourn time of a customer in that queue as a matrix exponential distribution, which is identical to a phase-type distribution under a certain condition. Since QBD processes include many queueing models where the arrival and service process are dependent, these results form a substantial generalization of analogous results reported in the literature for queues such as the PH/PH/c queue. We also discuss asymptotic properties of the sojourn time distribution through its matrix exponential form.  相似文献   

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