Bounds on the rate of convergence for Markovian queueing models with catastrophes

2021 ◽  
pp. 109150
Author(s):  
A. Zeifman
Keyword(s):  
Rate Of Convergence ◽  
Queueing Models

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.

On Sharp Bounds on the Rate of Convergence for Finite Continuous-Time Markovian Queueing Models

2018 ◽  
pp. 20-28 ◽  
Author(s):  
Alexander Zeifman ◽  
Alexander Sipin ◽  
Victor Korolev ◽  
Galina Shilova ◽  
Ksenia Kiseleva ◽  
...  
Keyword(s):  
Rate Of Convergence ◽  
Continuous Time ◽  
Queueing Models ◽  
Sharp Bounds

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

A Study of Multiple Finite-Source Queueing Models

1986 ◽  
Vol 37 (3) ◽  
pp. 275-283 ◽  
Author(s):  
M. Jeya Chandra
Keyword(s):  
Queueing Models ◽  
Finite Source

The rate of convergence for quadratic forms

1997 ◽  
Vol 37 (3) ◽  
pp. 191-206
Author(s):  
A. Basalykas
Keyword(s):  
Rate Of Convergence ◽  
Quadratic Forms
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