Geodesic
On existence of a~limit distribution in queueing systems with bounded sojourn time
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 570-578

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A necessary and sufficient condition for the existence of a limit distribution in queueing systems with bounded sojourn time is given. The proof of sufficiency is carried out with the help of the technique developed by Kiefer and Wolfowitz [5]. The necessity of the condition is proved by constructing some majorizing system with a simple queue. 
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     author = {L. G. Afanas'eva},
     title = {On existence of a~limit distribution in queueing systems with bounded sojourn time},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {570--578},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1965},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a20/}
}
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L. G. Afanas'eva. On existence of a~limit distribution in queueing systems with bounded sojourn time. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 570-578. http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a20/