Markov model of a digital stochastic generator

A stochastic process generator based on a chain of modulo-two adders with asynchronous feedback loops is investigated. The generator dynamics is described by the Erlang equations. A mathematical model of the generated stochastic process is proposed. The implementation of the generator using modern electronic devices is considered.     

Successive identification of the random-parameter linear dynamic system

For the case of unknown parameters that are subject to noise, a successive algorithm for identification of the discrete-time linear stochastic system was proposed. Special selection of a random instant of observation abortion in the least-squares method enabled determination of the theoretical boundary of the root-mean-square precision of the vector estimator which is inversely proportional to the procedure parameter defining its duration. The results of numerical modeling were presented.     

Multidimensional analogs of the kendall equation for priority queueing systems: computational aspects

An analogy between celebrated Kendall equation for busy periods in the system M|GI|1 and analytical results for busy periods in the priority systemsM _r |GI _r |1 is drawn. These results can be viewed as generalizations of the functional Kendall equation. The methodology and algorithms of numerical solution of recurrent functional equations which appear in the analysis of such queueing systems are developed. The efficiency of the algorithms is achieved by acceleration of the numerical procedure of solving the classical Kendall equation. An algorithm of calculation of the system workload coefficient calculation is given.     

Performance analysis of the broadband wireless network with decentralized control and hidden terminals

A new method of analytical modeling of the broadband wireless networks with hidden terminals operating under the IEEE 802.11 protocol was proposed. It was assumed that the network stations operate in saturation and access the wireless channel using both the basic and alternative RTS/CTS methods. Results of analytical modeling and simulation were presented.     

Modeling document movement in corporate systems document circulation

Developed were a model and software complex for calculation of the characteristics required to design the architecture of a computerized document circulation system in a largescale organization with hierarchical control. The open stochastic network was used as a model adequately describing the main functions of the designed document circulation system.     

On analysis of periodic polling systems

New alternative approach to the analysis of polling systems is developed. It is based on the theory of decomposable semi-regenerative processes.     

To the optimal identification of multivariate systems under perturbations of unknown covariances

We consider the problem of parameter and covariance estimation for multivariate stochastic systems described by regression models with special structure perturbations of unknown covariance. Sufficient conditions of uniformly optimal estimations are obtained for system parameters and covariances. The observation vector distribution family is factorized, and the full sufficient statistics is found under those conditions. Equations for uniformely optimal unbiased estimates of covariance parameters are obtained.     

The <Emphasis Type="Italic">MAP</Emphasis> + <Emphasis Type="Italic">MAP/PH</Emphasis>/1/<Emphasis Type="Italic">N</Emphasis> queuing system with single and batch arrivals of customers

The single-server queuing system with finite buffer was considered. The customers may arrive one-by-one or in batches. Arrivals of single customers and their batches obey the Markov input processes. The customers from a batch taken for servicing come one at a time at the exponentially distributed time intervals. The numbers of customers in batches are distributed geometrically. The time of customer servicing has a phase-type distribution. The numbers of batches and single customers that may be simultaneously accepted by the system are controllable parameters. The joint distribution of the number of batches and the number of customers in system, loss probabilities, distribution of the time of batch sojourn, and problems of optimization were analyzed.     

Signal restoration in linear systems with trends

For the unique solution of the problem of calculation of the inputs and outputs of a linear system from observations comprising additive quasipolynomial additives (trends) with unknown parameters, the existence conditions were established. Formulas to calculate the system signals and trends from the observations of the total signal were presented.     

A stochastic estimation problem at aeromagnetometer deviation compensation

A formulation of the problem of magnitometer deviation compensation occurring at aeromagnetic survey is considered in the form of a standard stochastic estimation problem. A specific feature of this approach is the introduction of the model of a geomagnetic field anomaly. The parameters of the stochastic model are selected basing on spectral and variance analysis of the aeromagnetic survey data. Normalization of the problem parameters is made; this makes it possible to estimate the accuracy of compensation and conduct a necessary decomposition. The posed stochastic estimation problem is solved by the method of Kalman filtering.     

Signal restoration in linear systems with trends. II

Consideration was given to calculation of the inputs and outputs of a linear system from the observations involving quasipolynomial additive extra terms (trends) with unknown parameters. Formulas to calculate the system signals and trends from the observations of the total perturbed signal were derived. Under the assumption that the signal measurements include additive independent identically distributed random perturbations, the solution corresponds to the maximum likelihood method.     

Compensation of unknown sinusoidal disturbances in linear plants of arbitrary relative degree

A new algorithm is proposed for compensating parametrically uncertain harmonic disturbances. In contrast to the known results, the compensation is carried out in the situation where only the output variable and the control signal are measured, and the relative degree of the plant is arbitrary.     

Stabilization of linear autonomous systems of differential equations with distributed delay

Consideration is given to the problem of optimal stabilization of differential equation systems with distributed delay. The optimal stabilizing control is formed according to the principle of feedback. The formulation of the problem in the functional space of states is used. It was shown that coefficients of the optimal stabilizing control are defined by algebraic and functional-differential Riccati equations. To find solutions to Riccati equations, the method of successive approximations is used. The problem for this control law and performance criterion is to find coefficients of a differential equation system with distributed delay, for which the chosen control is a control of optimal stabilization. A class of control laws for which the posed problem admits an analytic solution is described.     

Power distribution analysis in the international monetary fund

In this paper we propose a model for taking into account International Monetary Fund (IMF) mebers’ preferences to coalesce based on joint membership in political end economic organizations beyond the IMF and on regional proximity. The analysis of members’ effective power is carried out on the base of developed power indices for three variations of decision making thresholds implemented in the Fund.     

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.     

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.     

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.     

Estimating parameters of the synchronous twofold-stochastic flow of events

Consideration was given to estimation of the parameters of the synchronous twofold-stochastic flow of events which makes up a mathematical model of the information flow of demands circulating in the queuing systems and networks. Two variants were studied. For the first variant, the problem of optimal estimation of the parameters of a synchronous flow of events with a finite arbitrary number of states was solved. The second variant differs in that the event flow operates in the environment where part of events is lost during the so-called dead time. Consideration was given to a synchronous flow with two states. The problem of estimating the length of the dead time in the conditions of continued dead time was solved. The results of numerical estimation based on the simulation model of the synchronous flow were presented for both variants.     

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.