Control of asymptotic variability in non-homogeneous Markov systems

1990 ◽  
Vol 27 (4) ◽  
pp. 756-766 ◽  
Author(s):  
P.-C. G. Vassiliou ◽  
A. C. Georgiou ◽  
N. Tsantas
Keyword(s):  
Markov Systems ◽  
Asymptotic Variability

In this paper we provide two basic results. First, we find the set of all the limiting vectors of expectations, variances and covariances in an NHMS which are possible provided that we control the limit vector of the sequence of vectors of input probabilities. Secondly, under certain conditions easily met in practice we find the distribution of the limiting vector of expectations, variances and covariances to be multinomial with probabilities the corresponding limiting expected populations in the various states of the NHMS.

Control of asymptotic variability in non-homogeneous Markov systems

1990 ◽  
Vol 27 (04) ◽  
pp. 756-766 ◽  
Author(s):  
P.-C. G. Vassiliou ◽  
A. C. Georgiou ◽  
N. Tsantas
Keyword(s):  
Markov Systems ◽  
Asymptotic Variability

In this paper we provide two basic results. First, we find the set of all the limiting vectors of expectations, variances and covariances in an NHMS which are possible provided that we control the limit vector of the sequence of vectors of input probabilities. Secondly, under certain conditions easily met in practice we find the distribution of the limiting vector of expectations, variances and covariances to be multinomial with probabilities the corresponding limiting expected populations in the various states of the NHMS.

Asymptotic variability of nonhomogeneous Markov systems under cyclic behaviour

1986 ◽  
Vol 27 (2) ◽  
pp. 215-228 ◽  
Author(s):  
P.-C.G. Vassiliou
Keyword(s):  
Markov Systems ◽  
Cyclic Behaviour ◽  
Asymptotic Variability

OPTIMIZATION OF MARKOV SYSTEMS OF QUEUEING WITH WAITING TIME IN THE MATLAB SYSTEM

2017 ◽  
pp. 39-47
Author(s):  
Viktor Afonin ◽  
Vladimir Valer'evich Nikulin
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Random Variable ◽  
Model Systems ◽  
Queuing Systems ◽  
Input Flow ◽  
Continuous Random Variable ◽  
Input Stream ◽  
Time Intervals ◽  
Markov Systems

The article focuses on attempt to optimize two well-known Markov systems of queueing: a multichannel queueing system with finite storage, and a multichannel queueing system with limited queue time. In the Markov queuing systems, the intensity of the input stream of requests (requirements, calls, customers, demands) is subject to the Poisson law of the probability distribution of the number of applications in the stream; the intensity of service, as well as the intensity of leaving the application queue is subject to exponential distribution. In a Poisson flow, the time intervals between requirements are subject to the exponential law of a continuous random variable. In the context of Markov queueing systems, there have been obtained significant results, which are expressed in the form of analytical dependencies. These dependencies are used for setting up and numerical solution of the problem stated. The probability of failure in service is taken as a task function; it should be minimized and depends on the intensity of input flow of requests, on the intensity of service, and on the intensity of requests leaving the queue. This, in turn, allows to calculate the maximum relative throughput of a given queuing system. The mentioned algorithm was realized in MATLAB system. The results obtained in the form of descriptive algorithms can be used for testing queueing model systems during peak (unchanged) loads.

scholarly journals Graph directed Markov systems on Hilbert spaces

2009 ◽  
Vol 147 (2) ◽  
pp. 455-488 ◽  
Author(s):  
R. D. MAULDIN ◽  
T. SZAREK ◽  
M. URBAŃSKI
Keyword(s):  
Hausdorff Measure ◽  
Iterated Function System ◽  
Sufficient Conditions ◽  
Topological Pressure ◽  
Limit Set ◽  
Covering Theorem ◽  
Limit Sets ◽  
Markov Systems ◽  
Polish Spaces ◽  
Iterated Function

AbstractWe deal with contracting finite and countably infinite iterated function systems acting on Polish spaces, and we introduce conformal Graph Directed Markov Systems on Polish spaces. Sufficient conditions are provided for the closure of limit sets to be compact, connected, or locally connected. Conformal measures, topological pressure, and Bowen's formula (determining the Hausdorff dimension of limit sets in dynamical terms) are introduced and established. We show that, unlike the Euclidean case, the Hausdorff measure of the limit set of a finite iterated function system may vanish. Investigating this issue in greater detail, we introduce the concept of geometrically perfect measures and provide sufficient conditions for geometric perfectness. Geometrical perfectness guarantees the Hausdorff measure of the limit set to be positive. As a by–product of the mainstream of our investigations we prove a 4r–covering theorem for all metric spaces. It enables us to establish appropriate co–Frostman type theorems.

H∞ control for nonlinear stochastic Markov systems with time-delay and multiplicative noise

2017 ◽  
Vol 30 (6) ◽  
pp. 1293-1315 ◽  
Author(s):  
Yuhong Wang ◽  
Zhiteng Pan ◽  
Yan Li ◽  
Weihai Zhang
Keyword(s):  
Time Delay ◽  
Multiplicative Noise ◽  
Markov Systems

On the construction of component importance measures for semi-Markov systems

2012 ◽  
Vol 77 (1) ◽  
pp. 15-32 ◽  
Author(s):  
Mario Hellmich ◽  
Heinz-Peter Berg
Keyword(s):  
Markov Systems ◽  
Component Importance

Recursive Markov Systems with Small Noise

2019 ◽  
pp. 79-117
Author(s):  
Amarjit Budhiraja ◽  
Paul Dupuis
Keyword(s):  
Small Noise ◽  
Markov Systems
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