M/G→ /n/0 Erlang queueing system with heterogeneous servers and non-homogeneous customers

• Autorzy: Ziółkowski M.

Identyfikatory

DOI

10.24425/119059

• Języki publikacji: EN

Abstrakty

EN

In the present paper, we investigate a multi-server queueing system with heterogeneous servers, unlimited memory space, and non-homogeneous customers. The arriving customers appear according to a stationary Poisson process. Service time distribution functions may be different for every server. Customers are additionally characterized by some random volume. On every server, the service time of the customer depends on their volume. The number of customers distribution function is obtained in the classical model of the system. In the model with non-homogeneous customers, the stationary total volume distribution function is determined in the term of Laplace–Stieltjes transform. The stationary first and second moments of a total customers volume are calculated. An analysis of some special cases of the model and some numerical examples are also included.

Słowa kluczowe

EN

multi-server queueing systems; queueing systems with non-homogeneous customers; queueing systems with heterogeneous servers; total volume distribution; Laplace–Stieltjes transform

PL

system kolejkowania; transformata Laplace'a-Stieltjesa; dystrybucja

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2018
• Tom: Vol. 66, nr 1
• Strony: 59--66
• Opis fizyczny: Bibliogr. 12 poz., tab.

Twórcy

autor

Ziółkowski M.

• Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences, 159 Nowoursynowska St., 02–787 Warsaw, Poland

Bibliografia

• [1] M.L. Abell, J.P. Braselton, The Mathematica Handbook, Elsevier, 1992.
• [2] P.P. Bocharov, C.D’Apice, A.V. Pechinkin, S. Salerno, Queueing Theory, VSP, Utrecht-Boston, 2004.
• [3] A. Erlang, “The theory of probabilities and telephone conversations”, Nyt Tidsskrift for Matematik B 20, (1909).
• [4] A. Erlang, “Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges”, The Post Office Electrical Engineers’ Journal 10, (1918).
• [5] D. Fakinos, “The generalized M/G/k blocking system with heterogeneous servers”, The Journal of the Operational Research Society 33 (9), (1982).
• [6] H. Gumbel, “Waiting lines with heterogeneous servers”, Operations Research 8 (4), (1960).
• [7] V.P. Singh, “Two-server Markovian queues with balking: Heterogeneous vs. homogeneous servers”, Operation Research 18 (1), (1970).
• [8] V.P. Singh, “Markovian queues with three heterogeneous servers”, AIIE Transactions 3 (1), 1971.
• [9] J. Sztrik, “On the n/G/M/1 queue and Erlang’s loss formulas”, Serdica 12 (1986).
• [10] J. Sztrik, Basic Queueing Theory, University of Debrecen, Faculty of Informatics, 2012.
• [11] O. Tikhonenko, Probability Methods of Information Systems Analysis, Akademicka Oficyna Wydawnicza EXIT, Warszawa, 2006 (in Polish).
• [12] M. Ziółkowski, M/M/n/m Queueing Systems with Non-Homogeneous Servers, Jan Długosz University in Częstochowa, Scientific Issues, Mathematics XVI, 2011.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).