An asymptotic method of differential inequalities for the investigation of periodic contrast structures: Existence, asymptotics, and stability

2000 ◽  
Vol 36 (2) ◽  
pp. 298-305 ◽  
Author(s):  
N. N. Nefedov
Keyword(s):  
Asymptotic Method ◽  
Differential Inequalities ◽  
Method Of Differential Inequalities ◽  
Contrast Structures

Asymptotic method of differential inequalities

Equadiff 99 ◽  
2000 ◽  
pp. 112-117
Author(s):  
Nikolay N. Nefedov
Keyword(s):  
Asymptotic Method ◽  
Differential Inequalities ◽  
Method Of Differential Inequalities

scholarly journals On the rate of convergence for a class of Markovian queues with group services

2020 ◽  
Vol 28 (3) ◽  
pp. 205-215
Author(s):  
Anastasia L. Kryukova
Keyword(s):  
Rate Of Convergence ◽  
Operator Function ◽  
Computer Network ◽  
Human Life ◽  
Queueing Models ◽  
Differential Inequalities ◽  
Queuing Systems ◽  
Stationary Model ◽  
Logarithmic Norm ◽  
Method Of Differential Inequalities

There are many queuing systems that accept single arrivals, accumulate them and service only as a group. Examples of such systems exist in various areas of human life, from traffic of transport to processing requests on a computer network. Therefore, our study is actual. In this paper some class of finite Markovian queueing models with single arrivals and group services are studied. We considered the forward Kolmogorov system for corresponding class of Markov chains. The method of obtaining bounds of convergence on the rate via the notion of the logarithmic norm of a linear operator function is not applicable here. This approach gives sharp bounds for the situation of essentially non-negative matrix of the corresponding system, but in our case it does not hold. Here we use the method of differential inequalities to obtaining bounds on the rate of convergence to the limiting characteristics for the class of finite Markovian queueing models. We obtain bounds on the rate of convergence and compute the limiting characteristics for a specific non-stationary model too. Note the results can be successfully applied for modeling complex biological systems with possible single births and deaths of a group of particles.

scholarly journals Bounds on the Rate of Convergence for MtX/MtX/1 Queueing Models

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1752
Author(s):  
Alexander Zeifman ◽  
Yacov Satin ◽  
Alexander Sipin
Keyword(s):  
Markov Chains ◽  
Rate Of Convergence ◽  
Continuous Time ◽  
Upper Bounds ◽  
Specific Class ◽  
Differential Inequalities ◽  
Method Of Differential Inequalities ◽  
Finite Markov Chains ◽  
Intensity Functions ◽  
Forward System

We apply the method of differential inequalities for the computation of upper bounds for the rate of convergence to the limiting regime for one specific class of (in)homogeneous continuous-time Markov chains. Such an approach seems very general; the corresponding description and bounds were considered earlier for finite Markov chains with analytical in time intensity functions. Now we generalize this method to locally integrable intensity functions. Special attention is paid to the situation of a countable Markov chain. To obtain these estimates, we investigate the corresponding forward system of Kolmogorov differential equations as a differential equation in the space of sequences l1.

The Method of Differential Inequalities

1991 ◽  
pp. 279-298 ◽  
Author(s):  
Anne Boutet de Monvel ◽  
Vladimir Georgescu
Keyword(s):  
Differential Inequalities ◽  
Method Of Differential Inequalities
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