Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)
On a single-server queueing system with refusal
I. K. Matsak
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Abstract: A single-server queueing system is considered with refusal of a general type. Stationary probabilities are found and the central limit theorem is established for the sojourn time.
Keywords: Queueing systems, stationary probabilities, central limit theorem
Bibliography: 1. B. V. Gnedenko and I. N. Kovalenko, Introduction to Queueing Theory, Nauka'', Moscow, 1966; English transl., Birkhäser Boston, Inc., Boston, MA, 1989. (translated from the second Russian edition by Samuel Kotz)
2. T. L. Saaty, Elements of Queueing Theory, with Applications, McGraw-Hill, New York, 1961.
3. J. Riordan, Stochastic Service Systems, Wiley, New York, 1962.
4. A. A. Borovkov, Stochastic Processes in Queueing Theory, ''Nauka'', Moscow, 1972; English transl., Springer-Verlag, New York-Berlin, 1976.
5. L. Takács, Some probability questions in the theory of telephone traffic, Magyar Tud. Akad. Mat. Fiz. Oszt. Közl. 8 (1958), 151-210. (Hungarian)
6. L. Takács, Introduction to the Theory of Queues, Oxford University Press, New York, 1962.
7. I. N. Kovalenko, Studies on the Analysis of Reliability of Compound Systems, ''Naukova Dumka'', Kiev, 1975. (Russian)
8. V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and their Applications, ''Naukova Dumka'', Kiev, 1976. (Russian)
9. V. V. Anisimov, Asymptotic Methods of Analysis of Stochastic Systems, Metsniereba, Tbilisi, 1984. (Russian)
10. K. Yu. Zhernovyĭ, An investigation of an M^θ/G/1/m queueing system with service mode switching, Teor. Imovirnost. Matem. Statyst. 86 (2012), 56-68; English transl. in Theor. Probab. Math. Statist. 86 (2013), 65-78.
11. Ya. V. Goncharenko, M. V. Prats'ovytyĭ, and G. M. Torbin, Topological, metric and fractal properties of the set of incomplete sums of a positive series and distributions defined on it, Naukovi Zap. Nat. Pedagogical Dragomanov Univ. Ser. Phys. Mat. (2005), no. 6, 210-224. (Ukrainian)
12. D. R. Cox, Renewal Theory, Methuen, London, 1962.
13. W. L. Smith, Renewal theory and its ramifications, J. Roy. Statist. Soc. Ser. B 20 (1958), 243-302.
14. B. V. Gnedenko, Yu. K. Belyaev, and A. D. Solov'yev, Mathematical Methods in Reliability Theory, ''Nauka'', Moscow, 1965. (Russian)
15. A. A. Borovkov, Probability Theory, ''Nauka'', Moscow, 1976; English transl. Springer, London, 2013. (translated from the 2009 Russian fifth edition)
