网络化系统的状态反馈保性能控制

研究了具有随机网络诱导时延且数据包丢失服从马尔可夫链的网络化系统的保性能控制问题．将网络化控制系统建模为具有两种运行模式的马尔可夫跳变线性系统．根据马尔可夫跳变线性系统理论，给出了网络化系统状态反馈保性能控制器存在的充分条件；该保性能控制器为一组线性矩阵不等式的解．通过一个仿真示例说明了本文所提方法的有效性．     

Queueing analysis and optimal control of and systems

We first consider a finite-buffer single server queue where arrivals occur according to batch Markovian arrival process (BMAP). The server serves customers in batches of maximum size ‘b’ with a minimum threshold size ‘a’. The service time of each batch follows general distribution independent of each other as well as the arrival process. We obtain queue length distributions at various epochs such as, pre-arrival, arbitrary, departure, etc. Some important performance measures, like mean queue length, mean waiting time, probability of blocking, etc. have been obtained. Total expected cost function per unit time is also derived to determine the optimal value N^* of N at a minimum cost for given values of a and b. Secondly, we consider a finite-buffer single server queue where arrivals occur according to BMAP and service process in this case follows a non-renewal one, namely, Markovian service process (MSP). Server serves customers according to general bulk service rule as described above. We derive queue length distributions and important performance measures as above. Such queueing systems find applications in the performance analysis of communication, manufacturing and transportation systems.     

Software tools for micro-analysis of programs

The paper proposes and describes several tools enabling their user to estimate the efficiency of Pascal or C-like programs. The approach consists of generating symbolic formulas expressing the efficiency of the programs being analyzed. The formulas are applicable to a variety of compiler-machine configurations. The actual numeric values of the variables in the symbolic formula are determined using linear programming techniques. The proposed approach reduces considerably the amount of benchmarking needed to analyze programs. Several examples are presented showing the applicability of the tools. The effort necessary to implement them is considerably reduced by the combined usage of Prolog and a symbolic formula manipulation package (Maple).     

A tandem queue with general bulk service and servers' “vacation”

This paper analyses two queueing models consisting of two units I and II connected in series, separated by a finite buffer of size N. In both models, unit I has only one exponential server capable of serving customers one at a time and unit II consist of c parallel exponential servers, each of them serving customers in groups according to general bulk service rules. When the queue length in front of unit II is less than the minimum of batch size, the free servers take a vacation. On return from vacation, if the queue length is less than the minimum, they leave for another vacation in the first model, whereas in the second model they wait in the system until they get the minimum number of customers and then start servicing. The steady-state probability vector of the number of customers waiting and receiving service in unit I and waiting in the buffer is obtained for both the models, using the modified matrix geometric method. Numerical results are also presented.     

Statistical multiplexing of VBR sources: A matrix-analytic approach

In this paper we propose a versatile point process as model for a large class of variable bit rate sources and their superpositions. The process belongs to the class of discrete-time batch Markovian arrival processes (D-BMAP). Its use leads to computationally tractable and accurate solutions for various performance measures of the related statistical multiplexer: buffer occupancy distribution, cell loss probability, conditional cell loss probability. Moreover it is shown that the output process of the multiplexer belongs to the same class of processes.     

马氏环境中一般生灭链的灭绝概率及平均吸收时间的计算

将马氏环境中的生灭链 (GBDME)灭绝概率及平均吸收时间的计算 ,推广到马氏环境中一般生灭链 (GB DME) ,得到了关于灭绝概率及平均吸收时间的向量差分方程 .     

Simultaneous ℋ︁2/ℋ︁∞ control of uncertain jump systems with functional time‐delays

This paper presents new results pertaining to the control design of a class of linear uncertain systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state in which the time‐delays are mode dependent. The jumping parameters are modelled as a continuous‐time, discrete‐state Markov process and the uncertainties are norm‐bounded. We construct an appropriate Lyapunov–Krasovskii functional and design a simultaneous ℋ︁₂/ℋ︁_∞ controller which minimizes a quadratic ℋ︁₂ performance measure while satisfying a prescribed ℋ︁_∞‐norm bound on the closed‐loop system. It is established that sufficient conditions for the existence of the simultaneous ℋ︁₂/ℋ︁_∞ controller and the associated performance upper bound are cast in the form of linear matrix inequalities. Simulation results are provided and extension to the case where the jumping rates are subject to uncertainties is presented. Copyright © 2007 John Wiley & Sons, Ltd.     

A binomial approximation of lot yield under Markov modulated Bernoulli item yield

The existing literature that models item-by-item production yield as a Bernoulli process assumes that the intraperiod likelihood of producing an acceptable item is stationary. We investigate the stochastic process that results from relaxing this assumption to account for system deterioration during each production run. More specifically, we consider a Bernoulli yield model with a non-stationary parameter that depends on the deterioration level of the system, which evolves according to a discrete-time Markov chain. For tractability reasons, we construct a simple binomial approximation of the non-stationary process, and compare the two yield distributions both analytically and numerically. Our results suggest that the approximation performs well, even when the deterioration occurs relatively fast, which serves to validate existing (and future) decision models that impose the stationarity assumption.     

Stabilization of discrete-time Markovian jump linear systems via time-delayed and impulsive controllers

This paper discusses the stabilization problem for a class of discrete-time Markovian jump linear systems with time-delayed and impulsive controllers. The delay in the mode signal is assumed to be constant, while that in the system state may be time-varying. First, a hybrid controller with delay and impulses is introduced for the discrete-time stochastic systems. Then, some sufficient conditions are proposed for the design of a hybrid controller such that the closed-loop system is stochastically stable. Finally, a numerical example is provided to illustrate the effectiveness of the proposed result.     

Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays

This paper investigates the stochastic stability of fuzzy Markovian jumping neural networks with mixed delays in mean square. The mixed delays include time-varying delay and continuously distributed delay. By using the Lyapunov functional method, Jensen integral inequality, the generalized Jensen integral inequality, linear convex combination technique and the free-weight matrix method, several novel sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which do not require the differentiability of the activation functions, can be easily checked via Matlab software. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.