Geodesic
Service Systems in Heavy Traffic
Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 3, pp. 327-330

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Let $\eta _n$ be the waiting time of the $n$ customer arriving at a service line. It is proved that under certain conditions the distribution of $\delta\eta _n$ tends to a negative exponential distribution as $\delta\to0$, and $n\delta^2\to\infty$, where $\delta={{({\mathbf M}\tau-{\mathbf M}\chi)}/{\mathbf M\tau;}}$ ${\mathbf M}\tau$ and ${\mathbf M}\chi$ are the mean inter-arrival time and the service time, respectively. 
@article{TVP_1963_8_3_a9,
     author = {\`E. G. Samandarov},
     title = {Service {Systems} in {Heavy} {Traffic}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {327--330},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {1963},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a9/}
}
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È. G. Samandarov. Service Systems in Heavy Traffic. Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 3, pp. 327-330. http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a9/