Geodesic
On Ergodic Properties of Queues with Balking
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 112-120

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The queues with balking are considered as simple queues with the time of employment of a server by a given customer depending on the waiting time. A sufficient condition for the existence of a limit distribution for these queues is given. The proof of this fact is based on the technique developed for the simple queue. The case when the queue satisfies some additional condition of monotony is considered. In this case a necesswy and sufficient condition for ergodicity is found. The necessity of the condition is proved by constructing some majorizing simple queue. 
@article{TVP_1967_12_1_a9,
     author = {L. G. Afanas'eva and A. V. Martynov},
     title = {On {Ergodic} {Properties} of {Queues} with {Balking}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a9/}
}
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L. G. Afanas'eva; A. V. Martynov. On Ergodic Properties of Queues with Balking. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 112-120. http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a9/