On three methods for bounding the rate of convergence for some continuous-time Markov chains

• Autorzy: Zeifman Alexander , Satin Yacov , Kryukova Anastasia , Razumchik Rostislav , Kiseleva Ksenia , Shilova Galina

Identyfikatory

DOI

10.34768/amcs-2020-0020

• Języki publikacji: EN

Abstrakty

EN

Consideration is given to three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is particularly well suited to describe evolutions of the total number of customers in (in)homogeneous M/M/S queueing systems with possibly state-dependent arrival and service intensities, batch arrivals and services. One of the methods is based on the logarithmic norm of a linear operator function; the other two rely on Lyapunov functions and differential inequalities, respectively. Less restrictive conditions (compared with those known from the literature) under which the methods are applicable are being formulated. Two numerical examples are given. It is also shown that, for homogeneous birth-death Markov processes defined on a finite state space with all transition rates being positive, all methods yield the same sharp upper bound.

Słowa kluczowe

EN

inhomogeneous continuous time Markov chains; weak ergodicity; Lyapunov function; differential inequalities; forward Kolmogorov system

PL

łańcuchy Markowa z czasem ciągłym; funkcja Lapunowa; nierówność różniczkowa; system Kołmogorowa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2020
• Tom: Vol. 30, no. 2
• Strony: 251--266
• Opis fizyczny: Bibliogr. 36 poz., wykr.

Twórcy

autor

Zeifman Alexander

• Department of Applied Mathematics, Vologda State University, Lenina 15, Vologda, Russia; Vologda Research Center, Russian Academy of Sciences, 56A Gorky Street, Vologda, Russia; Institute of Informatics Problems, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Vavilova 44-2, 119333 Moscow, Russia

autor

Satin Yacov

• Department of Applied Mathematics, Vologda State University, Lenina 15, Vologda, Russia

autor

Kryukova Anastasia

• Department of Applied Mathematics, Vologda State University, Lenina 15, Vologda, Russia

autor

Razumchik Rostislav

• Institute of Informatics Problems, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Vavilova 44-2, 119333 Moscow, Russia

autor

Kiseleva Ksenia

• Department of Applied Mathematics, Vologda State University, Lenina 15, Vologda, Russia

autor

Shilova Galina

• Department of Applied Mathematics, Vologda State University, Lenina 15, Vologda, Russia

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).