Performance evaluation of unreliable system with infinite number of servers

• Autorzy: Tikhonenko O. , Ziółkowski M.

Identyfikatory

DOI

10.24425/bpasts.2020.133107

• Języki publikacji: EN

Abstrakty

EN

In the paper, we investigate queueing system M/G/∞ with non-homogeneous customers. By non-homogeneity we mean that each customer is characterized by some arbitrarily distributed random volume. The arriving customers appear according to a stationary Poisson process. Service time of a customer is proportional to his its volume. The system is unreliable, which means that all its servers can break simultaneously and then the repair period goes on for random time having an arbitrary distribution. During this period, customers present in the system and arriving to it are not served. Their service continues immediately after repair period termination. Time intervals of the system in good repair mode have an exponential distribution. For such system, we determine steady-state sojourn time and total volume of customers present in it distributions. We also estimate the loss probability for the similar system with limited total volume. An analysis of some special cases and some numerical examples are attached as well.

Słowa kluczowe

EN

queueing systems with non-homogeneous customers; unreliable queueing systems; total volume; loss probability; Laplace–Stieltjes transform

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2020
• Tom: Vol. 68, nr 2
• Strony: 289--297
• Opis fizyczny: Bibliogr. 23 poz., tab.

Twórcy

autor

Tikhonenko O.

• Institute of Computer Science. Cardinal Stefan Wyszyński University in Warsaw, Poland

autor

Ziółkowski M.

• Institute of Information Technology. Warsaw University of Life Sciences – SGGW, Poland

Bibliografia

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• [18] O. Tikhonenko, M. Ziółkowski, and M. Kurkowski, “M/G/n/(0,V) Erlang queueing system with non-homogeneous customers, non-identical servers and limited memory space”, Bull. Pol. Ac.: Tech. 67 (3), 489–500 (2019).
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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).