杂草种子运动的矩阵模型

人类活动(如耕作等)、捕食者活动(如蚂蚁、蚯蚓等)及一些无生命因素(如下雨、冰雪覆盖等),使土壤中的杂草种子在土壤中各个方向上不断运动,运用L eslie矩阵和M arkov链建立了一个具年龄结构的杂草种子在土壤中随时间动态变化的一般矩阵模型.     

Markov链在企业坏账预测中的应用

从随机过程的角度,依据企业应收账款的实际情况,运用M arkov链的理论和方法,构建企业应收账款发生坏账的预测模型,并运用该模型对该企业应收账款中未来可能发生坏账的金额和时间进行预测。     

带干扰的理赔为一般到达的风险模型

本文应用M arkov骨架过程方法,研究了带干扰的理赔为一般到达的保险风险模型,得到了破产时间与破产时刻前后资产盈余的联合分布以及破产时间的分布.     

确定环形Markov链的Q-矩阵

给出了Markov链中任一状态集的逗留时间或击中时间的分布(混合指数分布),以及其分布的各阶微分与Q-矩阵之间的约束方程组.利用该约束关系及环形链结构的先验信息,采用Markov链反演方法证明了:对于有限状态环形Markov链,其Q-矩阵能由其中任意两个相邻状态的逗留时间和击中时间分布唯一决定,并给出了相应的算法.     

SLTBL模型的Bayes分析

利用M arkov cha in M on te C arlo技术对可分离的下三角双线性模型进行B ayes分析.由于参数联合后验密度的复杂性,我们导出了所有的条件后验分布,以便利用G ibbs抽样器方法抽取后验密度的样本.特别地,由于从模型的方向向量的后验分布中直接抽样是困难的,我们特别设计了一个M etropolis-H astings算法以解决该难题.我们用仿真的方法验证了所建议方法的有效性,并成功应用于分析实际数据.     

确定一类带环离子通道门控的转移速率

证明了Markov链中某状态集的生存时间和死亡时间的分布均是混合指数分布,并给出了此分布与转移速率之间的若干约束关系.利用它们证明了:对于文中的带环离子通道门控,四种情形的转移速率都能由其中两个开状态的生存时间和死亡时间分布唯一决定,并给出了相应的算法.而Wagner等指出只有一种情形是可以确定的.     

用Markov链模拟酒店逐月客房利用率的探讨

酒店逐月客房利用率的预测,对于安排来年人员及物质、设备等是至关重要的,也是计算酒店经济利润,进行成本核算不可缺少的参数.由于客人入住是一个随机过程,难以用准确的分布函数来描述,但作出某些合理的假设后,可将其变为平稳随机过程.用M arkov自回归模型可生成模拟未来年的逐月客房利用率系列,以满足酒店规划、计划、市场营销等方面的需要.以乌鲁木齐市伊斯兰酒店为例,用M arkov模型进行了模拟.     

排课问题分组优化决策中的CourseRank

时间表(T im etab ling)问题是NP-完全的,因此很难寻求一个有效的整体优化算法.分组作为重要的优化策略,可以将课程按优先等级逐次分组,每组再采用组合优化方法.通常认为课程的规模是优先等级的决定性因素.然而选课的模式允许学生在一定的范围内选择课程,这就使得课程的关联关系更复杂.该文将课程的关联关系描述为一个M arkov链,进而给出了课程优先度(CourseR ank)的概念.通过对清华大学2002年度学生选课数据的分析和计算,结果表明课程的规模仍然是重要的因素,但并不完全是决定性的.     

经济增长的随机AK模型

本文以经济增长AK模型(模型Ⅰ)作为基本模型,将人口数量作为不确定性的来源,建立了经济增长的随机AK模型(模型Ⅱ).分析了模型Ⅱ解的存在唯一性和M arkov性,探讨了模型Ⅱ的零均衡解的稳定性及资本-劳动比率的动态性质.     

基于特征根方法的M/G_N/1个性化服务排队顾客逗留时间分布函数的数值计算

以多语种便民服务热线为实际应用背景,研究个性化服务M/G_N/1排队系统中顾客逗留时间分布函数的数值计算方法.首先,利用嵌入Markov链技术和Pollaczek-Khintchine变换公式给出顾客逗留时间的Laplace-Stieltjes(LS)变换.其次,根据个性化服务时间分布函数的具体类型,给出上述LS变换的有理函数表达形式.通过求解有理函数分母之具有负实部的零点,即所谓的特征根,最终使用部分分式分解方法和复分析中的留数理论给出顾客逗留时间的概率分布函数.     

Brown运动的逗留时与首中时

设为中的标准Brown运动,对0＜α,记本文求出了X在首中球面之前逗留在Bα内的时间的Laplace变换,在首中之前逗留在Bαb内的时间的Laplace变换以及在首中之前逗留在Bαb内的时间的Laplace变换．作为推论,求出了X关于球面首中时的Laplace变换,逗留在球内总的时间的Laplace变换及逗留在球壳内的总的时间的LaPlace变换．     

Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue

This paper studies the M/G/1 processor-sharing (PS) queue, in particular the sojourn time distribution conditioned on the initial job size. Although several expressions for the Laplace-Stieltjes transform (LST) are known, these expressions are not suitable for computational purposes. This paper derives readily applicable insensitive bounds for all moments of the conditional sojourn time distribution. The instantaneous sojourn time, i.e., the sojourn time of an infinitesimally small job, leads to insensitive upper bounds requiring only knowledge of the traffic intensity and the initial job size. Interestingly, the upper bounds involve polynomials with so-called Eulerian numbers as coefficients. In addition, stochastic ordering and moment ordering results for the sojourn time distribution are obtained. AMS Subject Classification: 60K25, 60E15 This work has been partially funded by the Dutch Ministry of Economic Affairs under the program ‘Technologische Samenwerking ICT-doorbraakprojecten’, project TSIT1025 BEYOND 3G.     

Sojourn time distribution in a MAP/M/1 processor-sharing queue

This paper considers the sojourn time distribution in a processor-sharing queue with a Markovian arrival process and exponential service times. We show a recursive formula to compute the complementary distribution of the sojourn time in steady state. The formula is simple and numerically feasible, and enables us to control the absolute error in numerical results. Further, we discuss the impact of the arrival process on the sojourn time distribution through some numerical examples.     

Threshold-based interventions to optimize performance in preemptive priority queues

This paper studies a single-server priority queueing model in which preemptions are allowed during the early stages of service. Once enough service effort has been rendered, however, further preemptions are blocked. The threshold where the change occurs is either a proportion of the service requirement, or time-based. The Laplace–Stieltjes transform and mean of each class sojourn time are derived for a model which employs this hybrid preemption policy. Both preemptive resume and preemptive repeat service disciplines are considered. Numerical examples show that it is frequently the case that a good combination of preemptible and nonpreemptible service performs better than both the standard preemptive and nonpreemptive queues. In a number of these cases, the thresholds that optimize performance measures such as overall average sojourn time are determined. This revised version was published online in June 2006 with corrections to the Cover Date.     

Sojourn time analysis for a cyclic-service tandem queueing model with general decrementing service

A sojourn time analysis is provided for a cyclic-service tandem queue with general decrementing service which operates as follows: starting once a service of queue 1 in the first stage, a single server continues serving messages in queue 1 until either queue 1 becomes empty, or the number of messages decreases to k less than that found upon the server's last arrival at queue 1, whichever occurs first, where 1 ≤ k ≤ ∞. After service completion in queue 1, the server switches over to queue 2 in the second stage and serves all messages in queue 2 until it becomes empty. It is assumed that an arrival stream is Poissonian, message service times at each stage are generally distributed and switch-over times are zero. This paper analyzes joint queue-length distributions and message sojourn time distributions.     

Travel times in queueing networks and network sojourns

We first describe expected values of sojourn times for semi-stationary (or synchronous) networks. This includes sojourn times for units and sojourn times for the entire network. A typical sojourn time of a unit is the time it spends in a sector (set of nodes) while it travels through the network, and a typical network sojourn time is the busy period of a sector. Our results apply to a wide class of networks including Jackson networks with general service times, general Markov or regenerative networks, and networks with batch processing and concurrent movement of units. The results also shed more light on when Little's law for general systems, holds for expectations as well as for limiting averages. Next, we describe the expectation of a unit's travel time on a general route in a basic Markov network process (such as a Jackson process). Examples of travel times are the time it takes for a unit to travel from one sector to another, and the time between two successive entrances to a node by a unit. Finally, we characterize the distributions of the sojourn times at nodes on certain overtake-free routes and the travel times on such routes for Markov network processes.This research was supported in part by the Air Force Office of Scientific Research under contract 89-0407 and NSF grant DDM-9007532.     

First Hitting Time Analysis of the Independence Metropolis Sampler

In this paper, we study a special case of the Metropolis algorithm, the Independence Metropolis Sampler (IMS), in the finite state space case. The IMS is often used in designing components of more complex Markov Chain Monte Carlo algorithms. We present new results related to the first hitting time of individual states for the IMS. These results are expressed mostly in terms of the eigenvalues of the transition kernel. We derive a simple form formula for the mean first hitting time and we show tight lower and upper bounds on the mean first hitting time with the upper bound being the product of two factors: a “local” factor corresponding to the target state and a “global” factor, common to all the states, which is expressed in terms of the total variation distance between the target and the proposal probabilities. We also briefly discuss properties of the distribution of the first hitting time for the IMS and analyze its variance. We conclude by showing how some non-independence Metropolis–Hastings algorithms can perform better than the IMS and deriving general lower and upper bounds for the mean first hitting times of a Metropolis–Hastings algorithm.     

Sojourn time asymptotics in the M/G/1 processor sharing queue

We show for the M/G/1 processor sharing queue that the service time distribution is regularly varying of index -ν, ν non-integer, iff the sojourn time distribution is regularly varying of index -ν. This result is derived from a new expression for the Laplace–Stieltjes transform of the sojourn time distribution. That expression also leads to other new properties for the sojourn time distribution. We show how the moments of the sojourn time can be calculated recursively and prove that the kth moment of the sojourn time is finite iff the kth moment of the service time is finite. In addition, we give a short proof of a heavy traffic theorem for the sojourn time distribution, prove a heavy traffic theorem for the moments of the sojourn time, and study the properties of the heavy traffic limiting sojourn time distribution when the service time distribution is regularly varying. Explicit formulas and multiterm expansions are provided for the case that the service time has a Pareto distribution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Sojourn time problems in feedback queues

A brief survey of the literature on sojourn time problems in single node feedback queueing systems is presented. The derivation of the distribution and moments of the sojourn time of a typical customer in a Markov renewal queue with state dependent feedback is considered in depth. The techniques used relate to the derivation of a first passage time distribution in a particular Markov renewal process. These results are applied to birth-death queues with state dependent feedback. For such models an alternative approach using the theory of Markov chains in continuous time is also examined.     

Some Problems of Local Hitting, Scaling, and Conditioning

The aim of this paper is to convey the basic ideas regarding some local hitting and conditioning properties of random measures. Some very general results are obtainable in the special case of simple point processes. Though much of this theory has no counterpart for general random measures, similar results do exist in two cases of special interest—for local time random measures and for Dawson–Watanabe superprocesses. This is an informal account of some of the basic hitting and conditioning properties common to all three cases. Precise statements and proofs will be provided elsewhere.