QNQL过程在排队论中的应用──（Ⅱ）：输入过程（成批到达情形）

本文在“相邻两批顾客到达时间间隔独立同分布”这个假定下，讨论成批到达输入过程Ｎ（ｔ）的概率分布问题．     

A Queue with Semi-Markovian Batch Plus Poisson Arrivals with Application to the MPEG Frame Sequence

We consider a queueing system with a single server having a mixture of a semi-Markov process (SMP) and a Poisson process as the arrival process, where each SMP arrival contains a batch of customers. The service times are exponentially distributed. We derive the distributions of the queue length of both SMP and Poisson customers when the sojourn time distributions of the SMP have rational Laplace–Stieltjes transforms. We prove that the number of unknown constants contained in the generating function for the queue length distribution equals the number of zeros of the denominator of this generating function in the case where the sojourn times of the SMP follow exponential distributions. The linear independence of the equations generated by those zeros is discussed for the same case with additional assumption. The necessary and sufficient condition for the stability of the system is also analyzed. The distributions of the waiting times of both SMP and Poisson customers are derived. The results are applied to the case in which the SMP arrivals correspond to the exact sequence of Motion Picture Experts Group (MPEG) frames. Poisson arrivals are regarded as interfering traffic. In the numerical examples, the mean and variance of the waiting time of the ATM cells generated from the MPEG frames of real video data are evaluated.     

生灭型半马氏骨架过程

本文首先引进了生灭型半马氏骨架过程的定义,求出了两骨架时跳跃点τn-1(ω)与τn(ω)之间的嵌入过程X(n)(t,ω)的初始分布及寿命分布.得到了生灭型半马氏骨架过程的一维分布.其次引进了生灭型半马氏骨架过程的数字特征并讨论了它们的概率意义及相互关系.讨论了生灭型半马氏骨架过程的向上和向下的积分型随机泛函.最后讨论了它的遍历性及平稳分布,求出了平均首达时间及平均返回时间.得到了常返和正常返的充分必要条件,求出了在正常返的条件下的平稳分布.     

离散型冲击折扣半马氏决策过程

本文讨论离散型冲击折扣半马氏决策过程，在建立模型后，我们将它化成了一个等价的离散时间马氏决策过程．     

Decomposable jump decision processes

A large class of continuous parameter jump decision processes is considered. Pontryagin's Maximum Principle is used to derive a necessary condition for optimality. An optimal strategy may frequently be obtained explicitly.     

Analysis of channel and disk subsystems in computer systems

The information processing industry has shifted from the conventional mathematical computation to information management. Interactive use of a system with large data bases is now widespread, and the data base has become one of the key factors central to an overall system design. This, in turn, has prompted the development of new peripheral devices.The paper focuses on developing and analyzing stochastic models for disk storage systems. A general model is developed to describe the sequence of operations required for accessing a record on a disk. The model is then used to analyze how technological and architectural changes affect system performance. As concrete examples, performance comparison of IBM 3330 disk system with IBM 3380 disk system will be conducted. All analytical results are validated via simulation.Supported by the National Science Foundation under Grant No. ECS-8404071.     

The robustness of the semi-Markov and delay time single-component inspection models to the Markov assumption

The context of planned preventive maintenance lends itself readilyto probabilistic modelling. Indeed, many of the published theoreticalmodels to be found in the literature adopt a Markov approach,where states are usually ‘operating’, ‘operatingat one of several levels of deterioration’, and ‘failed’.However, most of these models assume the required Markovianproperty and do not address the issue of testing the assumption,or the related task of estimating parameters. It is possiblethat data are inadequate to test the assumption, or that theMarkov property is believed to be not strictly valid, but acceptableas an approximation. In this paper we consider within a specificinspection–maintenance context the robustness of a Markov-basedmodel when the Markov assumption is not valid. This is achievedby comparing the output of an exact delay time model of an inspection–maintenanceproblem with that of a semi-Markov approximation. The importanceof establishing the vadility of the Markov property in the modellingapplication is highlighted. If the plant behaviour is seen tobe nearly Markov, in the case considered the semi-Markov modelgives a good approximation to the exact model. Conversley ifthe Markov assumption is not a good approximation, the semi-Markovmodel can lead to inappropriate advice.     

半马尔可夫过程的极限分布及其推广

本文运用马尔可夫骨架过程的极限理论研究齐次可列半马尔可夫过程,得到其极限分布.当更新间隔的分布不是格子分布时,本文的结果和邓永录等[1]中的结果一致,但采用的方法不同,本文采用的是马尔可夫骨架过程的理论方法,而[1]中采用的是交替更新过程的方法;而且关于更新间隔服从格子分布的情形,[1]中没有研究,而本文给出了结果.最...     

Semi-Markovian decision models with vector-valued reward

The paper deals with vector-valued semi-Markovian decision process (VSMDP). Thereby we derive a suitable definition of the optimal average reward of a VSMDP. We construct an algorithm for improving policies in the vector-valued case.     

Single-Server Queue with Markov-Dependent Inter-Arrival and Service Times

In this paper we study a single-server queue where the inter-arrival times and the service times depend on a common discrete time Markov chain. This model generalizes the well-known MAP/G/1 queue by allowing dependencies between inter-arrival and service times. The waiting time process is directly analyzed by solving Lindley's equation by transform methods. The Laplace–Stieltjes transforms (LST) of the steady-state waiting time and queue length distribution are both derived, and used to obtain recursive equations for the calculation of the moments. Numerical examples are included to demonstrate the effect of the autocorrelation of and the cross-correlation between the inter-arrival and service times. An erratum to this article is available at .