Investigation of G-network with bypasses of queueing systems by positive customers at a non-stationary regime

• Autorzy: Naumenko Victor , Kopats Dmitry , Matalytski Mikhail , Pankov Andrey

Identyfikatory

DOI

10.17512/jamcm.2020.3.07

• Języki publikacji: EN

Abstrakty

EN

An open queuing network (QN) with single-line queuing systems (QS) is considered. QS are characterized by the presence of bypasses and the possibility of coming of negative customers. The network receives two independent elementary streams. The first stream is formed from the ordinary (positive) customers, while the second is composed of negative customers. Arriving of each negative customer to the system destroys exactly one positive customer in the queue, if those are contained. Negative customers do not require maintenance as the service of positive customers in the network systems is carried out in accordance with the FIFO discipline. Positive customers with a probability depending on the state of the node when they are sent to it are added to the queue, and with an additional probability, they immediately bypass it and behave in the future as served. The service in the systems is exponential, the routing of positive customers in the network is Markov, taking into account the possibility of turning the customer into a negative one after sending it to another system.

Słowa kluczowe

EN

queuing network; non-stationary regime; negative customers; bypass

PL

sieć kolejkowa; bypass; negatywny klient; pozytywny klient

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2020
• Tom: Vol. 19, nr 3
• Strony: 85--97
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Naumenko Victor

• Faculty of Mathematics and Computer Science, Yanka Kupala State University of Grodno Grodno, Belarus

autor

Kopats Dmitry

• Faculty of Mathematics and Computer Science, Yanka Kupala State University of Grodno Grodno, Belarus

autor

Matalytski Mikhail

• Department of Mathematics, Czestochowa University of Technology Czestochowa, Poland

autor

Pankov Andrey

• Faculty of Mathematics and Computer Science, Yanka Kupala State University of Grodno Grodno, Belarus

Bibliografia

• [1] Gelenbe, E. (1991). Product-form queueing networks with negative and positive customers. Journal of Applied Probability, 28, 656-663.
• [2] Gelenbe, E., & Schassberger, R. (1992). Stability of product-form G-networks. Probability in Engineering and Informational Science, 6, 271-276.
• [3] Naumenko, V., & Matalytski, M. (2013). Analysis networks with positive and negative customers in transition mode. Tomsk State University Journal. Management, Computer Engineering and Informatics, 4(25), 61-70.
• [4] Malinkovski, V. (1991). Queuing networks with bypasses Nodes. Automation and Remote Control, 2, 102-110.
• [5] Matalytski, M., & Naumenko, V. (2013). Network analysis with bypasses of queueing systems by multiple claims. Grodno State University Journal, 2(1), 152-159.
• [6] Malinkovski, Y., & Nikitenko, O. (2000). Stationary distribution of network states with bypasses and negative claims. Automation and Remote Control, 8, 79-85.
• [7] Dovzhenok, T. (2002). Invariance of the stationary distribution of networks with bypasses and “negative” claims. Automation and Remote Control, 9, 97-110.
• [8] Kopats, D., & Matalytski, M. (2019). Finding the expected revenues in the G-network with bypasses. Information Technologies and Mathematical Modeling: Proc. of the XVI Int. Conf., Tomsk, June 26-30, 2019, 189-195.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).