Geodesic
One-channel system with unreliable server and different service times
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2013), pp. 12-17 
A. V. Tkachenko. One-channel system with unreliable server and different service times. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2013), pp. 12-17. http://geodesic.mathdoc.fr/item/VMUMM_2013_2_a2/
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     title = {One-channel system with unreliable server and different service times},
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Voir la notice de l'article provenant de la source Math-Net.Ru

An $M|GI|1|\infty$ queueing system is considered with an unreliable server and customer service times dependent on the system state. The ergodicity condition and generating function are found in the stationary mode.

[1] Gaver D.P.Jr., “A waiting line with interrupted service, including priorities”, J. Roy. Statist. Soc., B24 (1962), 73–90 | MR

[2] Maryanovich T.P., “Odnolineinaya sistema massovogo obsluzhivaniya s nenadezhnym priborom”, Ukr. matem. zhurn., 14:4 (1962), 417–422 | MR

[3] Gnedenko B.V., Kovalenko I.N., Vvedenie v teoriyu massovogo obsluzhivaniya, 5-e izd., URSS, M., 2007 | MR

[4] Ushakov I.A., Nadezhnost tekhnicheskikh sistem, Radio i svyaz, M., 1985

[5] Smith W.L., “Regenerative stochastic processes”, J. Roy. Statist. Soc., 232 (1955), 6–31 | MR

[6] Sevastyanov B.A., “Formula Erlanga v telefonii pri proizvolnom zakone raspredeleniya dlitelnosti razgovora”, 3-i Vsesoyuz. matem. s'ezd, AN SSSR, M., 1956, 58–70