Geodesic
A~virtual analog of Pollaczek-Khintchin transform equation
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2008), pp. 81-91.

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The virtual queue length distribution for the queueing system M|G|1 is obtained. It is shown that these results can be viewed as generalization of Pollaczek–Khintchin transform equation. 
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Gheorghe Mishkoy. A~virtual analog of Pollaczek-Khintchin transform equation. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2008), pp. 81-91. https://geodesic-test.mathdoc.fr/item/BASM_2008_2_a7/

[1] Allen A.O., Probability, Statistics and Queueing Theory with Computer Science Applications, Academic Press, New York, 1978 | MR | Zbl

[2] Kleinrock L., Queueing Systems. Volume 1: Theory, John Wiley and Sons, New York, 1975 | Zbl

[3] Cooper R.B., Introduction to Queueing Theory, Second edition, North-Holland Publishing Company, New York, 1981 | MR | Zbl

[4] Takagi H., Queueing Analysis. Volume 1: Vacation and Priority Systems, North-Hodland, Elsevier Science Publ., 1991 | MR | Zbl

[5] Gnedenko B.V. and Kovalenko I.N., Introduction to Queueing Theory, Moscow, 2005 | Zbl

[6] Pollaczek F., Theorie analytique des problemes stochastiques relatifs a un groupe de lignes telephoniques avec dispositif d'attente, Memorial de Sciences Mathematiques, Paris, 1961 | Zbl

[7] Khintchin A.Ya., Papers on Mathematical Queueing Theory, Fizmatgiz, Moscow, 1963 (in Russian)

[8] Gnedenko B.V. et all., Priority Queueing Systems, Moscow State University, 1973 (in Russian) | Zbl

[9] Klimov G.P. and Mishkoy G.K., Priority Queueing Systems with Orientation, Moscow State University, 1979 (in Russian)

[10] Asmusseu S., Applied Probability and Queues, John Wiley and Sons, New York, 1987 | MR

[11] Cohen J.W., The Single Server Queue, North-Holland Publishing Company, Amsterdam, 1982 | MR

[12] Kendall D.G., “Some problems in the theory of queues”, J. R. Stat. Soc. Ser B, 13:2 (1951), 151–185 | MR | Zbl

[13] Takacs L., Introduction to the Theory of Queues, Oxford University Press, New York, 1962 | MR | Zbl

[14] Mishkoy Gh., “Priority queueing systems with switchover time: Results and open problems”, Abstracts of Madrid Conference on Queueing Theory (Madrid, Spain, 2006), 43–44

[15] Mishkoy Gh., “Generalized Priority Systems in Queueing Analysis”, Congress of Romanian Mathematicians, Abstracts (Bucharest, Romania, 2007), 110

[16] Mishkoy Gh., “An analog of Kendall-Takacs equation for generalized queueing systems”, Proceedings of the 31th Annual Congress of the American Roumanian Academy of Arts and Sciences (Brasov, Romania, 2007), 483–486