4 research outputs found
Two approaches to the construction of perturbation bounds for continuous-time Markov chains
The paper is largely of a review nature. It considers two main methods used
to study stability and obtain appropriate quantitative estimates of
perturbations of (inhomogeneous) Markov chains with continuous time and a
finite or countable state space. An approach is described to the construction
of perturbation estimates for the main five classes of such chains associated
with queuing models. Several specific models are considered for which the limit
characteristics and perturbation bounds for admissible "perturbed" processes
are calculated
Bounds for markovian queues with possible catastrophes
We consider a general Markovian queueing model with possible catastrophes and obtain new and sharp bounds on the rate of convergence. Some special classes of such models are studied in details, namely, (a) the queueing system with S servers, batch arrivals and possible catastrophes and (b) the queueing model with "attracted" customers and possible catastrophes. A numerical example illustrates the calculations. Our approach can be used in modeling information flows related to high-performance computing. © ECMS Zita Zoltay Paprika, Péter Horák, Kata Váradi,Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics (Editors)
Bounds for markovian queues with possible catastrophes
We consider a general Markovian queueing model with possible catastrophes and obtain new and sharp bounds on the rate of convergence. Some special classes of such models are studied in details, namely, (a) the queueing system with S servers, batch arrivals and possible catastrophes and (b) the queueing model with "attracted" customers and possible catastrophes. A numerical example illustrates the calculations. Our approach can be used in modeling information flows related to high-performance computing. © ECMS Zita Zoltay Paprika, Péter Horák, Kata Váradi,Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics (Editors)