Rate of Convergence to Stationary Distribution for Unreliable Jackson-Type Queueing Network with Dynamic Routing

2016 ◽  
pp. 253-265 ◽  
Author(s):  
Elmira Yu. Kalimulina
Keyword(s):  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Queueing Network ◽  
Dynamic Routing ◽  
Jackson Type

Approximations by multivariate perturbed neural network operators

2017 ◽  
Vol 15 (03) ◽  
pp. 413-432 ◽  
Author(s):  
George A. Anastassiou
Keyword(s):  
Neural Network ◽  
Rate Of Convergence ◽  
Activation Function ◽  
Jackson Type ◽  
Partial Derivatives ◽  
Right Hand ◽  
Hidden Layer ◽  
The Right ◽  
Derivatives Of

This article deals with the determination of the rate of convergence to the unit of each of three newly introduced here multivariate perturbed normalized neural network operators of one hidden layer. These are given through the multivariate modulus of continuity of the involved multivariate function or its high-order partial derivatives and that appears in the right-hand side of the associated multivariate Jackson type inequalities. The multivariate activation function is very general, especially it can derive from any multivariate sigmoid or multivariate bell-shaped function. The right-hand sides of our convergence inequalities do not depend on the activation function. The sample functionals are of multivariate Stancu, Kantorovich and quadrature types. We give applications for the first partial derivatives of the involved function.

Overall station balance and decomposability for non-Markovian queueing networks

1998 ◽  
Vol 30 (03) ◽  
pp. 870-887 ◽  
Author(s):  
D. Fakinos ◽  
A. Economou
Keyword(s):  
Queueing Networks ◽  
Sufficient Conditions ◽  
Queueing Network ◽  
Necessary And Sufficient Conditions ◽  
Jackson Type ◽  
Necessary And Sufficient ◽  
Markovian Queueing Networks

Introducing the concept of overall station balance which extends the notion of station balance to non-Markovian queueing networks, several necessary and sufficient conditions are given for overall station balance to hold. Next the concept of decomposability is introduced and it is related to overall station balance. A particular case corresponding to a Jackson-type queueing network is considered in some more detail.

Stability and exponential convergence of continuous-time Markov chains

2003 ◽  
Vol 40 (04) ◽  
pp. 970-979 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Continuous Time ◽  
Exponential Convergence ◽  
Perturbation Bounds ◽  
Continuous Time Markov Chains ◽  
The Relationship

For finite, homogeneous, continuous-time Markov chains having a unique stationary distribution, we derive perturbation bounds which demonstrate the connection between the sensitivity to perturbations and the rate of exponential convergence to stationarity. Our perturbation bounds substantially improve upon the known results. We also discuss convergence bounds for chains with diagonalizable generators and investigate the relationship between the rate of convergence and the sensitivity of the eigenvalues of the generator; special attention is given to reversible chains.

Overall station balance and decomposability for non-Markovian queueing networks

1998 ◽  
Vol 30 (3) ◽  
pp. 870-887 ◽  
Author(s):  
D. Fakinos ◽  
A. Economou
Keyword(s):  
Queueing Networks ◽  
Sufficient Conditions ◽  
Queueing Network ◽  
Necessary And Sufficient Conditions ◽  
Jackson Type ◽  
Necessary And Sufficient ◽  
Markovian Queueing Networks

Introducing the concept of overall station balance which extends the notion of station balance to non-Markovian queueing networks, several necessary and sufficient conditions are given for overall station balance to hold. Next the concept of decomposability is introduced and it is related to overall station balance. A particular case corresponding to a Jackson-type queueing network is considered in some more detail.

Local contractivity of the process of a player rating variation in the Elo model with one adversary

2015 ◽  
Vol 25 (5) ◽  
Author(s):  
Vadim A. Avdeev
Keyword(s):  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Infinite Series ◽  
Limit Distribution ◽  
Rating Model ◽  
Upper Estimate

AbstractWe study the process of variation of a player rating in an infinite series of games with the same adversary in the Elo rating model. This process is shown to have a stationary distribution, an upper estimate of the rate of convergence to which is established. In a previous paper by the author, the existence of a limit distribution was proved under more stringent assumptions on the parameters of a rating model.

Rate of convergence of the fluid approximation for generalized Jackson networks

1996 ◽  
Vol 33 (3) ◽  
pp. 804-814 ◽  
Author(s):  
Hong Chen
Keyword(s):  
Rate Of Convergence ◽  
Queue Length ◽  
Queueing Network ◽  
Exponential Rate ◽  
Fluid Level ◽  
Fluid Approximation ◽  
Uniform Topology ◽  
Jackson Networks ◽  
Fluid Network ◽  
Level Process

It is known that a generalized open Jackson queueing network after appropriate scaling (in both time and space) converges almost surely to a fluid network under the uniform topology. Under the same topology, we show that the distance between the scaled queue length process of the queueing network and the fluid level process of the corresponding fluid network converges to zero in probability at an exponential rate.

scholarly journals Random walks in a queueing network environment

2016 ◽  
Vol 53 (2) ◽  
pp. 448-462 ◽  
Author(s):  
M. Gannon ◽  
E. Pechersky ◽  
Y. Suhov ◽  
A. Yambartsev
Keyword(s):  
Random Walks ◽  
Stationary Distribution ◽  
Detailed Balance ◽  
Queueing Network ◽  
Main Tool ◽  
Product Formula ◽  
Network Environment ◽  
Strong Correlations ◽  
Balance Equations ◽  
The Difference

Abstract We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The environment is cast in terms of a Jackson/Gordon–Newell network although alternative interpretations are possible. The main tool is the detailed balance equations. The difference compared to earlier works is that the position of the random walk influences the transition intensities of the network environment and vice versa, creating strong correlations. The form of the stationary distribution is closely related to the well-known product formula.

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