无标度网络上队列资源分配研究

研究了节点队列资源有限的条件下,无标度网络上的信息流动力学过程,发现了网络由自由流通到拥塞的相变现象,提出了一种基于节点度的队列资源分配模型.模型的核心是使节点i的队列长度与kβi成正比(ki为节点i的度,β为分配参数).仿真结果表明,在网络使用最短路径算法进行信息包传送的条件下,β近似等于1.25时队列资源分配最合理,网络容量最大,且该最佳值与队列总资源多少以及网络的规模无关.     

弹性分组环网的分组延时性能研究

本文采用了M/G/1/K排队模型对Darwin标准草案中建议的弹性分组环网的分组传输延时进行了性能分析,结果表明不同优先级的业务等待延时不同,高优先级分组在网络中传输延时最低,中优先级分组的延时仅略低于低优先级分组,当网络规模增加时,这种差距逐渐减小甚至可以忽略;并且从理论上推导出网络最大吞吐量,这对于制定相关标准、设计和规划实用网络具有重要指导作用.     

直觉判断矩阵的弱传递性与加型一致性研究

定义了直觉判断矩阵的有向图和有向路概念,证明在一定的条件下直觉判断矩阵的有向图有唯一有向路.利用该结论给出一个简洁的排序方法,并指出这种方法的不足之处.通过反例说明了直觉判断矩阵已有的加型一致性概念与弱传递性概念之间没有必然强弱关系.根据直觉模糊数的得分值和精确度值,利用效用的思想给出直觉判断矩阵加型一致性的新定义,并证明了新定义的加型一致性具有弱传递性.针对一般的直觉判断矩阵, 运用新定义的加型一致性概念以及偏差函数的方法给出了求解直觉判断矩阵的直觉模糊数型权重的模型,并通过算例验证了决策方法的实用性.     

Sorting Using Complete Subintervals and the Maximum Number of Runs in a Randomly Evolving Sequence

We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a string of 0’s, and then evolves by changing each 0 to 1, with the n changes done in random order. What is the maximal number of runs of 1’s? We give asymptotic results for the distribution and mean. It turns out that, as in many problems involving a maximum, the maximum is asymptotically normal, with fluctuations of order n ^1/2, and to the first order well approximated by the number of runs at the instance when the expectation is maximized, in this case when half the elements have changed to 1; there is also a second order term of order n ^1/3. We also treat some variations, including priority queues and sock-sorting. The proofs use methods originally developed for random graphs.     

A difference equation approach for analysing a batch service queue with the batch renewal arrival process

We consider an infinite buffer single server queue wherein customers arrive according to the batch renewal arrival process and are served in batches following the random serving capacity rule. The service-batch times follow exponential distribution. This model has been studied in the past using the embedded Markov chain technique and probability generating function. In this paper we provide an alternative yet simple methodology to carry out the whole analysis which is based on the supplementary variable technique and the theory of difference equations. The procedure used here is simple in the sense that it does not require the complicated task of constructing the transition probability matrix. We obtain explicit expressions of the steady-state system-content distribution at pre-arrival and arbitrary epochs in terms of roots of the associated characteristic equation. We also present few numerical results in order to illustrate the computational procedure.     

Relationships between characteristics in periodic Poisson queues

We study single server periodic queues in the day equilibrium conditions. The following characteristics of interest are considered at time of dayt: V^p(t)-the work load, L^p(t)-the number of customers and u^p(t)-the departure rate. We give relationships between E[V^p(t)], E[L^p(t)] and u^p(t). We also prove that E[V^p(t)] < and E[L^p(t)] < provided the second moment of the service time is finite.     

The interdeparture-time distribution for each class in the ∑ i M i /G i /1 queue

A stationary queueing system is described in which a single server handles several competing Poisson arrival streams on a first-come first-served basis. Each class has its own generally distributed service time characteristics. The principal result is the Laplace-Stieltjes transform, for each class, of the interdeparture time distribution function. Examples are given and applications are discussed.     

Discrete-time queues with discretionary priorities

In this paper, we consider a discrete-time two-class discretionary priority queueing model with generally distributed service times and per slot i.i.d. structured inputs in which preemptions are allowed only when the elapsed service time of a lower-class customer being served does not exceed a certain threshold. As the preemption mode of the discretionary priority discipline, we consider the Preemptive Resume, Preemptive Repeat Different, and Preemptive Repeat Identical modes. We derive the Probability Generating Functions (PGFs) and first moments of queue lengths of each class in this model for all the three preemption modes in a unified manner. The obtained results include all the previous works on discrete-time priority queueing models with general service times and structured inputs as their special cases. A numerical example shows that, using the discretionary priority discipline, we can more subtly adjust the system performances than is possible using either the pure non-preemptive or the preemptive priority disciplines.     

带有Bernoulli反馈的多级适应性休假的Geo/G/1排队系统分析

考虑带有Bernoulli反馈的多级适应性休假的Geo/G/1离散时间排队系统.通过引入服务员忙期和使用一种简洁的分解方法,讨论了队长的瞬时分布,得到了在任意时刻n队长为j的概率关于时刻n的z-变换的递推式,及队长平稳分布的递推式,且证明了稳态队长的随机分解性质.最后,给出了在特殊情形下相应的一些结果和数值计算实例.     

Scheduling networks of queues: Heavy traffic analysis of a simple open network

We consider a queueing network with two single-server stations and two types of customers. Customers of type A require service only at station 1 and customers of type B require service first at station 1 and then at station 2. Each server has a different general service time distribution, and each customer type has a different general interarrival time distribution. The problem is to find a dynamic sequencing policy at station 1 that minimizes the long-run average expected number of customers in the system.The scheduling problem is approximated by a dynamic control problem involving Brownian motion. A reformulation of this control problem is solved, and the solution is interpreted in terms of the queueing system in order to obtain an effective sequencing policy. Also, a pathwise lower bound (for any sequencing policy) is obtained for the total number of customers in the network. We show via simulation that the relative difference between the performance of the proposed policy and the pathwise lower bound becomes small as the load on the network is increased toward the heavy traffic limit.