一类多站循环服务系统的动态与状态转移

探讨具有如下特征的多站循环服务系统：（1）队列容量有限;（2）每次服务对象受限;（3）实施非门限方式。论述的主要内容有：系统与队列运行特点,队列在服务期间的状态转移;队列在周期中的状态与状态转移;系统与队列的有关参量近似于求解。     

状态依赖下的股市正反馈交易

在Sentana和Wadhwani的正反馈模型基础上,本文利用前期涨跌进行状态划分,建立了正反馈交易的Markov状态依赖模型,考察市场中的正反馈交易行为与羊群效应。通过对中国股市的实证研究,可以发现,股价不服从随机游走,在前期股价连续上涨或下跌的情况下,转移概率具有惯性;中国股市存在显著的状态相依的正反馈行为,在前期股价连续上涨的情况下,易激发羊群行为。监管者应注重市场价格的持续变动,投资者可以采用正反馈交易策略。     

关于状态反馈的非线性H∞控制

１一类非线性Ｈ∞控制问题 考虑下述非线性系统：其中为稳定方阵,而关于系统（１·１）的状态反馈 Ｈ控制问题在［１］中被详细地研究了．该问题可表述如下：设法找出一个状态反馈控制器 Ｋ：使得 ｉ） Ｇ／Ｋ具有性质 Ｌ２－ｇａｉｎ）当ｕ＝ Ｋ, ｗ＝ ０时,（１．１）是局部渐近稳定的．这个问题的解可如下导出［１,２］：首先在状态空间定义和相应的Ｈａｍｉｌｔｏｎｉａｎ能量函数再解而得Ｈ∞控制问题的解：本文１９９８年１１月１１日收到２０００年９月２０日收到修改稿．由于Ａ稳定,Ｆ所以当ｗ＝０时,Ｇ是从原点ｘ＝０可及的…     

中国证券市场知情交易概率的动态马尔科夫状态转移模型研究

对指令驱动市场知情交易的研究是近年来的热点问题。常用的EKOP模型存在一些缺陷,本文放宽了EKOP模型关于日内信息均匀释放以及交易者行为独立性的假设,用动态的马尔科夫状态转移模型对该模型进行了改进,并检验了改进后的知情交易概率模型在中国证券市场的适用性。通过模拟数据以及对中国证券市场交易数据的实证研究发现动态的马尔科夫状态转移模型克服了EKOP模型受买卖方数据影响而产生的系统偏误,估计的知情交易概率更符合事后检验。     

一种估算马尔柯夫状态转移概率矩阵的新方法

在现有文献研究的基础上,对马尔柯夫状态转移概率矩阵估算方法又作了进一步研究,根据马尔柯夫状态转移概率矩阵的性质和特点,提出了一种新的估算方法.方法首先构造了一个以相对误差绝对值之和最小为目标,以某一状态转移到其他状态的概率之和等于1以及状态转移概率不小于零为约束条件的优化模型.在此基础上,通过变量替换,将该模型转化为线性规划模型.由于线性规划模型不仅能够求得解析解,而且有现成的求解软件,因此不但便于问题求解,而且更加方便、可靠.最后进行了示例计算,验证了给出的马尔柯夫状态转移概率矩阵优化算法的可行性和正确性.     

基于状态转移模型的条件期望与方差——从2状态到N状态的推广

基于状态转移模型计算的条件期望与方差,可以应用到金融领域,计算和度量市场在不同状态下的收益与风险.Nielson基于2状态转移模型,计算了2状态下股市的收益率的条件期望与方差.然而,实际研究中,常需要用到3状态、甚至多状态的状态转移模型.因此,基于Nielson的研究,从2状态推广到了$N$状态.基于$N$状态转移模型计算了条件期望、条件方差及无条件期望、无条件方差,该结果更具普遍性且形式更为简洁.最后,采用计算期望与方差的方法,分析中国股市收益率与波动率.实证结果表明,中国股市除存在牛市、熊市外,还存在政策市,且其具有`` 低风险,高收益"的特点.利用$N$状态转移模型计算的期望与方差可以更合理地度量金融市场在不同情况下的收益与风险.     

带有止步和状态相依的M/Ej/1/N排队系统的矩阵解法

研究了带有止步和服务率依赖于状态的M/Ej/1/N排队系统.顾客到达系统时,以一定的概率选择进入系统或止步(不进入系统).顾客接受服务的服务率依赖于系统中的顾客数,当系统中的顾客数不超过临界值k时,服务员慢速服务;否则,服务员快速服务.利用分块矩阵的方法,推出了稳态概率向量所满足的矩阵形式的迭代公式,给出了稳态概率的表达式和计算过程.作为特例,考虑了N=4时系统稳态概率的计算.在此基础上,还求出了系统的一些性能指标,并建立了以临界值k为控制变量的费用模型.通过数值分析,求出了使费用函数最小的最优临界值k*,并进一步研究了模型参数对最优临界值和最优费用的影响.     

带有止步和状态相依的M/Ej/1/N排队系统的矩阵解法

研究了带有止步和服务率依赖于状态的M/Ej/1/N排队系统.顾客到达系统时,以一定的概率选择进人系统或止步(不进人系统).顾客接受服务的服务率依赖于系统中的顾客数,当系统中的顾客数不超过临界值k时,服务员慢速服务;否则,服务员快速服务.利用分块矩阵的方法,推出了稳态概率向量所满足的矩阵形式的迭代公式,给出了稳态概率的表达式和计算过程.作为特例,考虑了N=4时系统稳态概率的计算.在此基础上,还求出了系统的一些性能指标,并建立了以临界值k为控制变量的费用模型.通过数值分析,求出了使费用函数最小的最优临界值k*,并进一步研究了模型参数对最优临界值和最优费用的影响.     

多状态概率转移模型在医院住院管理系统的应用

在医院现代化管理的进程中，医院管理者需要经常了解医院病人的流动情况，尤其是住院病人。根据部门反馈的信息，综合分析，对病人的收容和病床的使用安排作出科学的管理决策。本文试用随机过程理论分析医院住院管理系统，建立了医院住院管理系统的多状态概率转移模型（简称ＨＱＭ模型），并分析了住院管理系统的几个优化指标。     

随机混合动态系统的状态反馈控制

针对一类以有限齐次马氏链δ(k)作为切换信号的随机混合系统,首先,通过构造随机混合Lyapunov函数,得到整个随机混合系统渐近稳定的充分条件.然后,引入可调转移概率等相关概念,通过对有限齐次马氏链δ(k)及各子系统加入控制,以实现状态反馈控制.进一步,得到随机混合闭环系统渐近稳定的充分条件.     

M/G/1/N vacation model with varying E-limited service discipline

We define and analyze anM/G/1/N vacation model that uses a service discipline that we call theE-limited with limit variation discipline. According to this discipline, the server provides service until either the system is emptied (i.e. exhausted) or a randomly chosen limit ofl customers has been served. The server then goes on a vacation before returning to service the queue again. The queue length distribution and the Laplace-Stieltjes transforms of the waiting time, busy period and cycle time distributions are found. Further, an expression for the mean waiting time is developed. Several previously analyzed service disciplines, including Bernoulli scheduling, nonexhaustive service and limited service, are special cases of the general varying limit discipline that is analyzed in this paper.     

Analysis of the M/G/1 queue with exponentially working vacations—a matrix analytic approach

In this paper, an M/G/1 queue with exponentially working vacations is analyzed. This queueing system is modeled as a two-dimensional embedded Markov chain which has an M/G/1-type transition probability matrix. Using the matrix analytic method, we obtain the distribution for the stationary queue length at departure epochs. Then, based on the classical vacation decomposition in the M/G/1 queue, we derive a conditional stochastic decomposition result. The joint distribution for the stationary queue length and service status at the arbitrary epoch is also obtained by analyzing the semi-Markov process. Furthermore, we provide the stationary waiting time and busy period analysis. Finally, several special cases and numerical examples are presented.     

Symmetric queues served in cyclic order

Consider a symmetrical system of n queues served in cyclic order by a single server. It is shown that the stationary number of customers in the system is distributed as the sum of three independent random variables, one being the stationary number of customers in a standard M/G/1 queue. This fact is used to establish an upper bound for the mean waiting time for the case where at most k customers are served at each queue per visit by the server. This approach is also used to rederive the mean waiting times for the cases of exhaustive service, gated service, and serve at most one customer at each queue per visit by the server.     

Selecting batch size in discrete-time two-phase queuing system

This paper discusses the modeling and analysis of a discrete-time two-phase queuing system. Packets arrive at the system according to a Bernoulli process and receive batch service in the first queue and individual service in the second queue. We study the queue length, average waiting time of packets in the first queue and the effect of batch size on the waiting time.     

Admission control of a service station when the arrivals are internal

All studies in the admission control of a service station make decisions at arrival epochs. When arrivals are internal and are rejected from a queue, the rejected jobs have to be routed to other stations in the system. However the system will not know whether a job will be admitted to a queue or not until its arrival epoch to that queue. Thus, the system has to react dynamically and agilely to the decisions made at a specific queue and may try several queues before finding a queue that admits the job. This paper remedies these difficulties by changing the decision epochs of the admission control from arrival epochs to departure epochs with the actions of switching (keeping) the arrival stream on or off. Thus upstream stations will have information on the admission status of their downstream stations all the time. It is proved that the optimal policy for this revised admission control system is of control limit type for an M/G/1 queue. Comparisons of the optimal values and optimal policies for the admission controls made at arrival epochs and at departure epochs are included in the paper.     

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.     

动态输入率和服务率设定下的M/M/c模型扩展及其应用

为了解决M/M/c模型中恒定输入率和服务率假设与现实现象不符的问题,本文提出了随系统状态变化的输入概率和服务度,并通过新输入概率与平均输入率以及新服务度与平均服务率的结合分别构造了动态输入率和服务率。基于上述动态输入率和动态服务率,建立了依赖系统当前状态的状态转移过程,从状态转换强度方面优化了排队理论及其度量模型,同时,设计了结合系统实际的后确定法求解动态输入率与服务率的相关参数,从而构建了扩展M/M/c模型。由于输入率和服务率的动态性,扩展M/M/c模型具有比原排队论模型更广的适用范围和精度更高的模拟结果。最后,通过一个生活实例对新模型的有效性和实用性进行验证。     

成批到达排队系统的随机比较

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．     

TheM/G/1 queue with processor sharing and its relation to a feedback queue

The central model of this paper is anM/M/1 queue with a general probabilistic feedback mechanism. When a customer completes his ith service, he departs from the system with probability 1–p(i) and he cycles back with probabilityp(i). The mean service time of each customer is the same for each cycle. We determine the joint distribution of the successive sojourn times of a tagged customer at his loops through the system. Subsequently we let the mean service time at each loop shrink to zero and the feedback probabilities approach one in such a way that the mean total required service time remains constant. The behaviour of the feedback queue then approaches that of anM/G/1 processor sharing queue, different choices of the feedback probabilities leading to different service time distributions in the processor sharing model. This is exploited to analyse the sojourn time distribution in theM/G/1 queue with processor sharing.Some variants are also considered, viz., anM/M/1 feedback queue with additional customers who are always present, and anM/G/1 processor sharing queue with feedback.     

A two-queue model with Bernoulli service schedule and switching times

In this paper, we present a detailed analysis of a cyclic-service queueing system consisting of two parallel queues, and a single server. The server serves the two queues with a Bernoulli service schedule described as follows. At the beginning of each visit to a queue, the server always serves a customer. At each epoch of service completion in the ith queue at which the queue is not empty, the server makes a random decision: with probability p_i, it serves the next customer; with probability 1-p_i, it switches to the other queue. The server takes switching times in its transition from one queue to the other. We derive the generating functions of the joint stationary queue-length distribution at service completion instants, by using the approach of the boundary value problem for complex variables. We also determine the Laplace-Stieltjes transforms of waiting time distributions for both queues, and obtain their mean waiting times. This revised version was published online in June 2006 with corrections to the Cover Date.