A Single-Server Queueing System with Background Customers

A single-server queueing system with a Markov flow of primary customers and a flow of background customers from a bunker containing unbounded number of customers, i.e., the background customer flow is saturated, is studied. There is a buffer of finite capacity for primary customers. Service processes of primary as well as background customers are Markovian. Primary customers have a relative service priority over background customers, i.e., a background customer is taken for service only if the buffer is empty upon completion of service of a primary customer. A matrix algorithm for computing the stationary state probabilities of the system at arbitrary instants and at instants of arrival and completion of service of primary customers is obtained. Main stationary performance indexes of the system are derived. The Laplace—Stieltjes transform of the stationary waiting time distribution for primary customers is determined.__________Translated from Avtomatika i Telemekhanika, No. 6, 2005, pp. 74–88.Original Russian Text Copyright © 2005 by Bocharov, Shlumper.     

Analysis and Filtration of Special Discrete-Time Markov Processes. I. Martingale Representation

Part I is devoted to a class of discrete-time processes that are the generalization of Markov chains with a finite or denumerable number of states. Their transition probabilities, martingale representations in forward and backward time, the stochastic measures they generate are studied.__________Translated from Avtomatika i Telemekhanika, No. 6, 2005, pp. 114–125.Original Russian Text Copyright © 2005 by Borisov, Miller.This work was supported by INTAS, project no. YSF 04-83-3623.     

Optimization of Control of Doubly Stochastic Nonordinary Flows in Time-Sharing Systems

Control of conflicting flows in a class of time-sharing algorithms with regard for orientation and readjustment is studied. Probabilistic properties of flows are determined by the Markov environment. Conditions for the existence of a stationary operation mode of the system are determined and interpreted graphically. Optimization by the minimum of mean sojourn cost in a control cycle is studied. Imitation modeling is used to estimate the characteristics that cannot be found analytically.__________Translated from Avtomatika i Telemekhanika, No. 7, 2005, pp. 102–111.Original Russian Text Copyright © 2005 by Zorin, Fedotkin.     

Superposition of Markov Renewal Processes in Stationary Phase Integration

Heuristic principles of the phase integration of a superposition of Markov renewal process are substantiated. The limiting processes of phase integration in a series scheme for stationary integrated processes are proved to be the same as the limiting processes of phase integration for a superposition of Markov renewal processes. A stationary phase integration of a superposition of Markov renewal processes is constructed. The probability of failure of a two-lift system in a series scheme is calculated for the time to failure tending to zero. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 119–135, September–October 2005.     

A discrete-time on–off source queueing system with negative customers

This paper studies a discrete-time single-server infinite-capacity queueing system with correlated arrivals, geometrically distributed service times and negative customers. Positive customers are generated by a Bernoulli bursty source, with geometrically distributed lengths of the on-periods and off-periods. Negative customers arrive to the system according to a geometrical arrival process which is independent of the positive arrival process. A negative customer removes a positive customer in service if any, but has no effect on the system if it finds the system empty. We analyze the Markov chain underlying the queueing system and evaluate the performance of the system based on generating functions technique. Closed-form expressions of some performance measures of the system are obtained, such as stationary probability generating functions of queue length, unfinished work, sojourn time distribution and so on. Finally, the effect of several parameters on the system is shown numerically.     

Nonparametric system identification by kernel methods

A new nonparametric estimate for nonlinear discrete-time dynamic systems is considered. The new algorithm is weakly consistent under a specific condition on the transition probability operator of a stationary Markov process. The estimate is applicable when a parametric state model of the system is difficult to choose.     

Markov queueing system with finite buffer and negative customers affecting the queue end

A multiserver queueing system with finite buffer, Markov input flow, and Markov (general) service process of all customers on servers with the number of process states and intensities of inter-phase transitions depending on the number of customers in the system is considered. A Markov flow of negative customers arrives to the system; one negative customer “kills” one positive customer at the end of the queue. A recurrent algorithm for computing stationary probabilities of system states is obtained; and a method for calculating stationary distribution of waiting time before starting service of a positive customer is proposed.     

Discrete-time <Emphasis Type="Italic">MAP/G</Emphasis>/1/∞ system with inversive probabilistic servicing discipline

Consideration was given to the discrete-time MAP/G/1/∞ queuing system where the arriving customer is taken to the server with a certain probability depending only of the processed length of the customer in service and squeezes out its predecessor to the first place on the queue or, with the complementary probability, occupies the first place on the queue (inversive probabilistic servicing discipline). For this system, the main stationary operational characteristics were established.     

A BMAP/SM/1 Queueing System with Hybrid Operation Mechanism

A single-server queueing system BMAP/SM/1 is studied. It operates as a retrial queueing system under decentralized and centralized retrial strategies with and without loss of primary customers, as well as a system with waiting. The operation mechanism changes under the action of a random environment. The stationary state probability distributions at imbedded and arbitrary instants and main performance characteristics of the system are determined.__________Translated from Avtomatika i Telemekhanika, No. 5, 2005, pp. 111–124.Original Russian Text Copyright © 2005 by Klimenok.     

Studying the queue length in a single-server queuing system with unreliable server

The unreliable queuing system was studied in both the nonstationary and stationary modes. It was assumed that a Poisson flow of customers arrives to the system; the times of customer servicing and restoration of the server (servicing system) are random variables with arbitrary distributions; the flow of stable failures makes up the restoration process; the interfailure intervals are distributed hyperexponentially; and the waiting and sojourn times as well as the queue length are not limited.Translated from Avtomatika i Telemekhanika, No. 1, 2005, pp. 72–81.Original Russian Text Copyright © 2005 by Mikadze, Khocholava.This paper was recommended for publication by V.V. Rykov, a member of the Editorial Board     

A Two-Phase BMAP|G|1|N → PH|1|M – 1 System with Blocking

The stationary probability distribution of a two-phase queueing system with a finite or an infinite buffer for the first phase and a finite buffer for the second phase is derived. The input flow of the system is a batch Markov arrival process. Both phases have single-servers. The service time distribution is arbitrary for the first phase and of phase-type for the second phase. If the buffer of the second phase is full at the instant of completion of service at the first phase, the first server is blocked until the buffer is freed.     

Control design for a class of linear 0-controllable discrete systems with constraints

Formation of a feedback control for the class of 0-controllable linear stationary systems with constraints is studied.Translated from Avtomatika i Telemekhanika, No. 1, 2005, pp. 49–58.Original Russian Text Copyright © 2005 by Sirotin.This work was supported by the Russian Foundation for Basic Research, project no. 03-01-00050 and Russian Ministry of Education, project no. T02-14.0-681.This paper was recommended for publication by B.T. Polyak, a member of the Editorial Board     

Parametrization of the Input-Output Image of Nonlinear Dynamic Systems

For dynamic systems described by differential equations with smooth functions in the state space, the size of the parameter space is minimized such that the input-output image of the system is preserved by finding the complete set of algebraic invariants for a fixed structure of the equations of the system. A relationship between the constructs of the algebra of functions used in the problem and the mathematical constructs used in the differential geometric approach is established. A method for finding the algebraic invariants—the analogs of Markov parameters of linear systems—is described.__________Translated from Avtomatika i Telemekhanika, No. 8, 2005, pp. 173–183.Original Russian Text Copyright © 2005 by Shumskii.This work was supported by the Russian Foundation for Basic Research, project no. 03-01-00791.     

Control of Stochastically Perturbed Self-Oscillations

Control of the probabilistic distribution of the stochastic nonlinear self-oscillation cycle of a system to form a bundle of random trajectories with a given scatter about a deterministic limiting cycle is studied. A stochastic sensitivity function defining the Gaussian asymptote of the stationary distribution density is used a measure for the scatter. Complete controllability condition for a density cycle and optimal controller parameters are determined. The performance of designed methods is illustrated with an example on the design of controllers for a stochastically perturbed Brusselator.__________Translated from Avtomatika i Telemekhanika, No. 6, 2005, pp. 104–113.Original Russian Text Copyright © 2005 by Bashkirtseva, Ryashko.This work was supported in part by the Russian Foundation for Basic Research, project no. 04-01-96098ural.     

Robust Stabilization of Random-Structure Systems via Switchable Static Output Feedback

A class of jump control systems, whose structure changes in time according to the evolution of a homogeneous Markov chain, is studied. The control system in every fixed mode is described by a linear differential equation. The state vector of the system may also jump when the mode jumps. The number of modes is finite and mode jump process is observable. Necessary and sufficient conditions for the mean-square stabilization of the system via a static output feedback control, which is synchronously switched with mode changes, are formulated. These conditions are generalized to uncertain parameters of mode changes. Sufficient conditions under which a static-feedback control stabilizes the system under uncertainty of control parameters are derived. These results are generalized to the case of dynamic output feedback. Computational aspects of the problem related to the application of linear matrix inequalities are described.__________Translated from Avtomatika i Telemekhanika, No. 7, 2005, pp. 144–153.Original Russian Text Copyright © 2005 by Pakshin, Retinskii.This work was supported in part by the Russian Foundation for Basic Research, project no. 02-01-00220.     

Extremal principles and the limiting capabilities of open thermodynamic and economic macrosystems

General features of the macrosystems were considered, and for the stationary state of the active (controlling) subsystems of the open thermodynamic and microeconomic systems, which differs little from the equilibrium state, the stationary modes and optimal behavior were studied. Validity of the reciprocity conditions and the principle of minimum dissipation were demonstrated not only for the scalar flow in microeconomics, but for the vector flow as well. The ultimate capacity of the thermal separation systems was determined.Translated from Avtomatika i Telemekhanika, No. 3, 2005, pp. 121–138.Original Russian Text Copyright © 2005 by Tsirlin.This work was supported by the Russian Foundation for Basic Research, projects nos. 020680445, 010100020.This paper was recommended for publication by Yu.S. Popkov, a member of the Editorial Board     

Analysis and Filtration of Special Discrete-Time Markov Processes. II. Optimal Filtration

Mean-square optimal filtration of the states of a special Markov process, which is the generalization of Markov chains with a finite or denumerable number of states, is studied. By way of example, tracking of the state of a network connection under TCP is given.__________Translated from Avtomatika i Telemekhanika, No. 7, 2005, pp. 112–125.Original Russian Text Copyright © 2005 by Borisov, Miller.This work was supported by INTAS, project no. YSF 04-83-3623.     

The Stationary Characteristics of the <Emphasis Type="Italic">G</Emphasis>/<Emphasis Type="Italic">MSP</Emphasis>/1/<Emphasis Type="Italic">r</Emphasis> Queueing System

A single-server queueing system with recurrent input flow and Markov service process is considered. Both the cases of finite and infinite buffers are investigated. The analysis of this system is based on the method of embedded Markov chain. The main stationary characteristics of system performance are derived.     

Asymptotic properties of consensus-type algorithms for networked systems with regime-switching topologies

This paper is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a finite state space. The consensus control is achieved by using stochastic approximation methods. In the setup, the regime-switching process (the Markov chain) contains a rate parameter ε>0 in the transition probability matrix that characterizes how frequently the topology switches. On the other hand, the consensus control algorithm uses a stepsize μ that defines how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under suitable conditions, we show that when 0<ε=O(μ), a continuous-time interpolation of the iterates converges weakly to a system of randomly switching ordinary differential equations modulated by a continuous-time Markov chain. In this case a scaled sequence of tracking errors converges to a system of switching diffusion. When 0<ε?μ, the network topology is almost non-switching during consensus control transient intervals, and hence the limit dynamic system is simply an autonomous differential equation. When μ?ε, the Markov chain acts as a fast varying noise, and only its averaged network matrices are relevant, resulting in a limit differential equation that is an average with respect to the stationary measure of the Markov chain. Simulation results are presented to demonstrate these findings.     

A Queueing Network with Random-Delay Signals

A queueing network with an input flow of signals, along with a flow of ordinary (positive) customers, at its nodes is studied. A random time is required to activate a signal upon arrival at a node. The stationary state probability distribution for a network with single-server nodes and exponential service time distribution is derived in product form. A product-form solution for a symmetric network with Markov service at nodes is also derived.