Single-server queueing system with external and internal customers

• Autorzy: Tikhonenko O. , Ziółkowski M.

Identyfikatory

DOI

10.24425/124270

• Języki publikacji: EN

Abstrakty

EN

In the paper, we investigate a single-server queueing system with unlimited memory space and non-homogeneous customers (calls) of the two following types: 1) external customers that are served by the system under consideration, 2) internal customers that arrive and interrupt the service process only when an external customer is being served. The external customers appear according to a stationary Poisson process. Customers of each of the above-mentioned types are characterized by some random volume. The customer service time depends arbitrarily on its volume. Two schemes of customer service organization are analyzed. The non-stationary and stationary distributions of the total volume of customers present in the system are determined in terms of Laplace and Laplace-Stieltjes transforms. The stationary first and second moments of total customers volume are also calculated. The obtained results are used to approximate loss characteristics in analogous systems with limited buffer space. Numerical examples illustrating theoretical results are attached as well.

Słowa kluczowe

EN

single-server queueing system with non-homogeneous customers; random volume customers; loss probability; total volume distribution; Laplace transform; Laplace-Stieltjes transform; RAM memory space

PL

prawdopodobieństwo straty; transformacja Laplace'a; transformata Laplace'a-Stieltjesa; pamięć RAM

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2018
• Tom: Vol. 66, nr 4
• Strony: 539--551
• Opis fizyczny: Bibliogr. 15 poz., wykr., tab.

Twórcy

autor

Tikhonenko O.

• Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyński University in Warsaw, Poland

autor

Ziółkowski M.

• Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences, Poland

Bibliografia

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• [3] M. Schwartz, Telecommunication Networks: Protocols, Modeling and Analysis, Addison-Wesley Publishing Company, 1987.
• [4] N.B. Zeliger, O.S. Chougreev, and G.G. Yanovsky, Design of Networks and Systems of Discrete Messages Transmission, Radio i Svyaz, Moscow, 1984 (in Russian).
• [5] O.M. Tikhonenko, Queueing Models in Information Systems, Universitetskoe, Minsk, 1990 (in Russian).
• [6] O. Tikhonenko, Probability Methods of Information Systems Analysis, Akademicka Oficyna Wydawnicza EXIT, Warszawa, 2006 (in Polish).
• [7] A.M. Aleksandrov and B.A. Kaz, “Non-homogeneous demands arrival servicing”, Izv. AN SSSR. Tekhnicheskaya Kibernetika N 2, 47–53 (1973) (in Russian).
• [8] B. Sengupta, “The spatial requirement of M/G/1 queue or: how to design for buffer space”, Lect. Notes Contr. Inf. Sci. 60, 547–562 (1984).
• [9] O. Tikhonenko, “Determination of loss characteristics in queueing systems with demands of random space requirement”, Communications in Comp. and Inf. Sci. 564, 209–215 (2015).
• [10] O. M. Tikhonenko, “The problem of determination of the summarized messages volume in queueing systems and its applications”, J. Inf. Process. Cybern. EIK 23(7), 339–352 (1987).
• [11] V.B. Iversen, Teletraffic Engineering Handbook, Geneva, 2005.
• [12] G.P. Klimov, Stochastic Service Systems, Nauka, Moscow, 1966 (in Russian).
• [13] P.P. Bocharov, C. D’Apice, A.V. Pechinkin, and S. Salerno, Queueing Theory, VSP, Utrecht-Boston, 2004.
• [14] Y.L. Luke, Mathematical Functions and their Approximations, Academic Press Inc. New York, 1975.
• [15] M.L. Abell and J.P. Braselton, The Mathematica Handbook, Elsevier, 1992.

Uwagi

PL

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