Upper bounds on the rate of convergence for constant retrial rate queueing model with two servers

2018 ◽  
Vol 59 (4) ◽  
pp. 1271-1282
Author(s):  
Yacov Satin ◽  
Evsey Morozov ◽  
Ruslana Nekrasova ◽  
Alexander Zeifman ◽  
Ksenia Kiseleva ◽  
...  
Keyword(s):  
Rate Of Convergence ◽  
Upper Bounds ◽  
Queueing Model ◽  
Constant Retrial Rate

Mixing rates for Brownian motion in a convex polyhedron

1990 ◽  
Vol 27 (2) ◽  
pp. 259-268 ◽  
Author(s):  
Peter Matthews
Keyword(s):  
Brownian Motion ◽  
Rate Of Convergence ◽  
Convex Polyhedron ◽  
Upper Bounds ◽  
Convergence In Distribution ◽  
Convex Polyhedral ◽  
Variation Distance ◽  
Mixing Rates

For Brownian motion on a convex polyhedral subset of a sphere or torus, the rate of convergence in distribution to uniformity is studied. The main result is a method to take a Markov coupling on the full sphere or torus and create a faster coupling on the convex polyhedral subset. Upper bounds on variation distance are computed, and applications are discussed.

scholarly journals On the Rate of Convergence and Limiting Characteristics for a Nonstationary Queueing Model

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 678 ◽  
Author(s):  
Yacov Satin ◽  
Alexander Zeifman ◽  
Anastasia Kryukova
Keyword(s):  
Rate Of Convergence ◽  
Queue Length ◽  
Arrival Rate ◽  
Service Rate ◽  
Queueing Model ◽  
Simple Method ◽  
Numerical Example

Consideration is given to the nonstationary analogue of M / M / 1 queueing model in which the service happens only in batches of size 2, with the arrival rate λ ( t ) and the service rate μ ( t ) . One proposes a new and simple method for the study of the queue-length process. The main probability characteristics of the queue-length process are computed. A numerical example is provided.

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.

Mixing rates for Brownian motion in a convex polyhedron

1990 ◽  
Vol 27 (02) ◽  
pp. 259-268
Author(s):  
Peter Matthews
Keyword(s):  
Brownian Motion ◽  
Rate Of Convergence ◽  
Convex Polyhedron ◽  
Upper Bounds ◽  
Convergence In Distribution ◽  
Convex Polyhedral ◽  
Variation Distance ◽  
Mixing Rates

For Brownian motion on a convex polyhedral subset of a sphere or torus, the rate of convergence in distribution to uniformity is studied. The main result is a method to take a Markov coupling on the full sphere or torus and create a faster coupling on the convex polyhedral subset. Upper bounds on variation distance are computed, and applications are discussed.

scholarly journals Uniform decomposition of probability measures: quantization, clustering and rate of convergence

2018 ◽  
Vol 55 (4) ◽  
pp. 1037-1045 ◽  
Author(s):  
Julien Chevallier
Keyword(s):  
Rate Of Convergence ◽  
Uniform Approximation ◽  
Approximation Error ◽  
Upper Bounds ◽  
Probability Measures ◽  
Finite Approximations ◽  
Elementary Construction

AbstractThe study of finite approximations of probability measures has a long history. In Xu and Berger (2017), the authors focused on constrained finite approximations and, in particular, uniform ones in dimensiond=1. In the present paper we give an elementary construction of a uniform decomposition of probability measures in dimensiond≥1. We then use this decomposition to obtain upper bounds on the rate of convergence of the optimal uniform approximation error. These bounds appear to be the generalization of the ones obtained by Xu and Berger (2017) and to be sharp for generic probability measures.

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.

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