BMAP/G/1/∞ system with last come first served probabilistic priority

Consideration was given to the BMAP/G/1/∞ single-server queuing system with batch Markov arrivals, arbitrary servicing, finite-capacity buffer, and last come first served probabilistic priority. Equations for determination of the stationary probabilities of states and stationary characteristics associated with the time of customer sojourn in the system were determined.     

A class of systems of bilinear integral Volterra equations of the first kind of the second order

A class of bilinear systems of integral Volterra equations of the first kind related to the problem of automatic control of a nonlinear dynamic system (object) with unknown structure and vector input and output is studied. Algorithms for an analytic solution to corresponding bilinear systems and its numerical approximation are developed. A special character of the algorithms is illustrated by model examples.     

On the properties of the identically singular Lagrange problem

We consider the identically singular Lagrange problem of the calculus of variations. It is investigated how the conjugate points and the Jacobi equation index are related to the solvability conditions of the appropriate matrix Riccati equation and the reducibility of the functional to a perfect square. The criterion of the trajectory variation smallness at a small variation of the functional in the neighborhood of the extremal is obtained.     

Control of complex ecological-economic systems

The paper is devoted to developing methods for control of ecological-economic systems consisting of three hierarchically subordinate subjects of control. In describing the dynamics of a system state, equations in partial derivatives that are solved numerically according to a semi-implicit scheme of the finite-difference method are used. To achieve its main goal (maintenance of an ecological subsystem in stable state), the subject of control of the upper level applies different control methods. Methods of hierarchical control (motivation, enforcement, and persuasion) that differ in the direction of action (on the objective function or domain of admissible controls) are proposed; examples of their use are represented and a comparative analysis of the obtained results is made.     

Minimum of power consumption in the problem of oscillation damping

Consideration was given to minimization of the L ¹-norm of control of the linear oscillatory system. For consumption of the energy resources required to damp oscillations, bilateral estimates were obtained.     

基于联系数的位置不确定性数据UCNK-Means聚类算法

摘要位置不确定性数据的聚类是一个新的不确定性数据聚类问题。其聚类方法主要包括获取对象的概率密度函数,通过积分计算对象间的期望距离来进行聚类分析和以区间数表示对象,通过区间数的系列运算来进行聚类分析这两大类。前者存在概率密度函数获取困难、计算复杂、实用性不强的缺陷;后者在区间数转化为实数过程中,忽略了区间数变化范围对聚类效果的影响,其聚类质量不佳。鉴于此,提出一种基于联系数的不确定对象聚类新算法UCNK-Means。该算法用联系数巧妙地表示不确定性对象,并专门定义了对象间的联系距离,运用联系数态势值比较联系距离大小,克服了现有算法的不足。仿真实验表明,UCNK-Means具有聚类精度高、计算复杂度低、实用性强的特点。     

Convergence Results of the Biconjugate Residual Algorithm for Solving Generalized Sylvester Matrix Equation

In this article, we investigate a variant of the biconjugate residual (BCR) algorithm to solve the generalized Sylvester matrix equation which includes the well‐known Lyapunov, Stein and Sylvester matrix equations. We show that the BCR algorithm with any (special) initial matrix pair can smoothly compute the (least Frobenius norm) solution pair of the generalized Sylvester matrix equation within a finite number of iterations in the absence of round‐off errors. Finally the accuracy and effectiveness of the BCR algorithm in comparison to some existing algorithms are demonstrated by two numerical examples.     

A fuzzy reasoning and fuzzy-analytical hierarchy process based approach to the process of railway risk information: A railway risk management system

Risk management is becoming increasingly important for railway companies in order to safeguard their passengers and employees while improving safety and reducing maintenance costs. However, in many circumstances, the application of probabilistic risk analysis tools may not give satisfactory results because the risk data are incomplete or there is a high level of uncertainty involved in the risk data. This article presents the development of a risk management system for railway risk analysis using fuzzy reasoning approach and fuzzy analytical hierarchy decision making process. In the system, fuzzy reasoning approach (FRA) is employed to estimate the risk level of each hazardous event in terms of failure frequency, consequence severity and consequence probability. This allows imprecision or approximate information in the risk analysis process. Fuzzy analytical hierarchy process (fuzzy-AHP) technique is then incorporated into the risk model to use its advantage in determining the relative importance of the risk contributions so that the risk assessment can be progressed from hazardous event level to hazard group level and finally to railway system level. This risk assessment system can evaluate both qualitative and quantitative risk data and information associated with a railway system effectively and efficiently, which will provide railway risk analysts, managers and engineers with a method and tool to improve their safety management of railway systems and set safety standards. A case study on risk assessment of shunting at Hammersmith depot is used to illustrate the application of the proposed risk assessment system.     

Tradeoffs in process strategy games with application in the WDM reconfiguration problem

We consider a variant of the graph searching games that models the routing reconfiguration problem in WDM networks. In the digraph processing game, a team of agents aims at processing, or clearing, the vertices of a digraph D. We are interested in two different measures: (1) the total number of agents used, and (2) the total number of vertices occupied by an agent during the processing of D. These measures, respectively, correspond to the maximum number of simultaneous connections interrupted and to the total number of interruptions during a routing reconfiguration in a WDM network.Previous works have studied the problem of independently minimizing each of these parameters. In particular, the corresponding minimization problems are APX-hard, and the first one is known not to be in APX. In this paper, we give several complexity results and study tradeoffs between these conflicting objectives. In particular, we show that minimizing one of these parameters while the other is constrained is NP-complete. Then, we prove that there exist some digraphs for which minimizing one of these objectives arbitrarily impairs the quality of the solution for the other one. We show that such bad tradeoffs may happen even for a basic class of digraphs. On the other hand, we exhibit classes of graphs for which good tradeoffs can be achieved. We finally detail the relationship between this game and the routing reconfiguration problem. In particular, we prove that any instance of the processing game, i.e. any digraph, corresponds to an instance of the routing reconfiguration problem.