Application of the Floyd algorithm to the asymptotic analysis of networks with unreliable ribs

The problem of finding parameters of asymptotic relations for the probability of operation of a graph with unreliable ribs is solved. These parameters are expressed through minimax functions of lengths of ribs. To compute them, an economical modification of the Floyd algorithm is constructed.     

Application of the finite difference method to the problem of pursuit in the distributed-parameter systems

The problem of pursuit in the controlled systems of parabolic type without mixed derivatives with variable coefficients was considered and solved using the finite difference method. Sufficient conditions for pursuit completion were established.     

Application of the method of extremal deviations to studying forced parametric bending vibrations of the pipeline

By means of a method of extremal deviations, dynamic stability of the pipeline and ensuring estimation of the amplitude of its bending vibrations and tensions caused by transported medium pressure pulsation are analyzed. The most dangerous pressure pulsations are synthesized. A criterion for dynamic stability and estimation of maximal possible amplitude of bending vibrations and tensions are obtained in analytic form.     

Analysis of the oral interface in the interactive servicing systems. II

A classification of the dialogue control algorithms at oral interaction of the client with the computer-aided servicing system was worked out. The most typical algorithms were described, analyzed, and compared in terms of duration using the formulas derived in the first part of the paper.     

Analysis of the oral interface in the interactive servicing systems. I

The oral technologies created a new type of the human-computer interaction. The oral servers and oral portals which implement a new model of human-computer communications may be studied using the methods of the queuing theory. Development of the analytical models to estimate some numerical characteristics of the human-computer one-channel dialogue such as the probability of successful dialogue, number of overinterrogations, and mean time of dialogue are the immediate subject matters of such studies. These characteristics may be used further to analyze operation of the entire queuing system that models the multichannel oral portal. The main parameters of the human-computer dialogue such as the probability of correct recognition of an element and the entire dialogue at overinterrogations and the time used for a dialogue element were considered. The parameters for estimation of the dialogue length were determined. A classification of the dialogue control algorithms at oral interaction of the client with the computer-aided information and servicing systems was developed. The algorithms were compared in terms of duration with regard for the desired reliability of recognition.     

Analysis of the problem of continuous-product inventory control under deterministic lead time

Consideration was given to the control of the continuous-product inventory in the storage system delivering to the end consumers. In the system, the product is replenished at a deterministic lead time of duration obeying the volume of order. The system behavior is described by a regenerative random or deterministic process. The general task of control lies in determining the optimal time to place the replenishment order. Functionals of the mean specific income and mean specific costs were constructed, and a theorem of solution existence and uniqueness was given. For several variants of the model, explicit solutions of the problem of control under different inter-parameters relations were obtained. A number of examples of particular economic systems obeying the model under study were discussed. A procedure for seeking numerical parameters of the optimal control was analyzed in detail.     

Comparison of the quantile and guaranteeing approaches to system analysis

The worst value of the quantile of the distribution of the linear loss function which depends on the uncertain stochastic parameters was compared with the maximum value of this function. The stochastic uncertainty is modelled by distributions from the Barmish class.     

Analysis of probability distribution of a random variable of an execution time of the program in the presence of random failures

The mathematical model of an estimation of an execution time of the program in the presence of random failures is studied. For decreasing of influence of failures on a program execution time the known method of checkpoints is considered. The main objective consists in reception of the formula for a distribution function of a random variable of an execution time of the program and an estimation of a quantile of the received distribution. Properties of a mean value of a random variable of an execution time of the program are studied.     

Operating ratio of the technical systems,subjected to failures

The original way of definition of operating ratio in view of reliability of the equipment of the control, time of the control over periodic checks and time of restoration is offered. The received results allow to define the best value of operating ratio of system both in view of, and without taking into account operational expenses.     

Application of Cayley-Klein parameters in the problem of strapdown navigation system stochastic state vector synthesis for a self-contained space vehicle

The state vector and observer equations are obtained for a strapdown (gimballess) navigation system with three accelerometers, three angular rate sensors, and a barometric altimeter. These equations are based on the nonlinear filtration methods that ensure required estimation accuracy under arbitrary space maneuver of a vehicle.     

Universal software packages to model the distributed-parameter systems

Consideration was given to the universal software packages for modeling objects and distributed-parameter systems obeying the partial differential equations. The packages may serve as important tools for industrial automation because the majority of industrial objects have distributed parameters. The review presented the results of comparing a number of commercial packages against a set of user-defined criteria. Its final part was devoted to some freeware packages. Conclusions were drawn, and recommendations for using the considered packages were given.     

Method to determine an optimal control in the minimum of resource consumption for the nonlinear stationary systems

An iterative method to solve the nonlinear problems of minimization of resource consumption was proposed. It generalizes to a more general class of nonlinear systems the method of resource minimization for the nonlinear systems with the control-linear right-hand side separated in state and control.     

A note on application of the method of supplementary variables to the analysis of a processor sharing system

We present a new proof of Theorem of 1989 about non-stationary (transient) distribution of the number of jobs in the M/G/1 queue with egalitarian processor sharing. To get this goal, we use the well-known method of supplementary variables. The complete proof of that non-trivial Theorem of 1989 (see Theorem 2.1) was first given in the author’s monograph [12, §2.8] (1989) by means of essentially novel analytic method. Before appearing author’s work, this problem had been considered from analytic viewpoint as insoluble one. In essence, Theorem 2.2 almost repeats Theorem 2.1, but with other proof. In Section 3, Theorem 2.2 is extended to the case of an M/G/1-EPS queue with catastrophes which appear according to a Poisson process.     

Organization of the remote access to tomographic data through a slow communications link

Consideration is given to the problem of organization of the remote access to tomographic data obtained as a result of the investigation on the computerized tomograph through a slow communications link. The proposed access strategy together with the developed and realized method of tomographic data compression makes it possible to help users (physicians, scientists, and etc.) work with remote tomographic data, e.g., using the Internet. This, in its turn, opens up vast possibilities for using the data of tomographic investigations for conducting medical consultations “at a distance,” videoconferences, organizing network seminars for medical staff training, and etc.     

Adaptive algorithms to estimate parameters of the optimal policies of inventory control under limited stock-out

Consideration was given to the inventory control by the criterion for minimum of the cumulative mean costs over a sufficiently long planning horizon in conditions of uncertain demand characteristics. Adaptive algorithms to estimate the parameters of the optimal two-level control policies oriented to the supply systems with high level of customer servicing were constructed for the stationary mode of operation.     

Algorithms to construct suboptimal organization hierarchies

The problem of controlling an organization structure (hierarchy of organization control) was considered as that of discrete optimization, that is, minimization by selecting the permissible hierarchy of total costs of maintaining its managers. For the case of the so-called uniform functions of manager costs, the lower estimate of the costs of the optimal hierarchy was obtained allowing one, besides all other things, to determine approximately the main characteristics of the optimal hierarchy such as the number of managers, their norm of controllability, and so on. Quality of this lower estimate was studied, and effective algorithms to construct suboptimal hierarchies with costs slightly exceeding the optimal ones were proposed for some important cases.     

Design of modified PD algorithm to control angular motion of large space structure

Consideration was given to the design of an algorithm to control orientation of the large space structure (LSS) in the presence of infralow (less than 0.01Hz) frequencies of elastic oscillations exerting considerable influence on the quality of transients due to closeness of the LSS eigenfrequencies to the frequency of control of the object’s “rigid” motion. Procedure for designing a modified PD-algorithm for orientation of the LSS with infralow frequencies of elastic structural oscillations was described. Methods were proposed for calculation of the coefficients of additional components of the modified algorithm and determination of the LSS eigenfrequency boundary to the right of which the orientation control system is robust to the deviations of the object frequencies or inaccuracy of their definition. Some examples of mathematical modeling of the processes of the relay gyroforce control of LSS orientation using the proposed algorithm were given.     

On approximation of the subdifferential of the nonsmooth penalty functional in the problems of optimal control

For the problem of optimal program control with terminal equality constraints which is considered as an “elementary operation” within the framework of the algorithm to calculate the optimal positional control, a smooth approximation the Frechét-nondifferentiable penalty functional was proposed. Examples of numerical experiments were presented.     

Guaranteed approach with the farthest of the runaways

Games of the family {Λ _N } _N?2 are formulated and studied with the application of generalized Isaacs’s approach. The game Λ _N is a simplest model of the counteraction of one persecutor P and coalition N of E ^N runaways for the case when the payoff is the distance up to the coalition of E ^N equal to the Euclidean distance between P and the farthest from the runaways; P is in command of the termination moment. Moreover, an approach within the limits of which in games with a smooth terminal payoff are generated strategies prescribing players’ motions in the directions of local gradients of the payoff is described. The approach is used for constructing pursuit strategies in games in which smooth approximations of the maximum of Euclidean distances up to the runaways are in place of payoffs. Pursuit strategies prescribing the motion in the direction of the farthest of the runaways are studied. A numerical simulation of the development of the games Λ₂ and Λ₃ is conducted in using different strategies by the players.