Geodesic
Limiting distribution for the moment of first loss of a~customer in a~single-line service system with a~limited number of positions in the queue
Matematičeskie zametki, Tome 3 (1968) no. 5, pp. 541-546.

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We consider a single-line service system with a Palm arrival rate and exponential service time, with $n-1$ places in the queue. Let $\tau_n$ be the moment of first loss of a customer. It is assumed that $\alpha_0=\int_0^\infty e^{-t}dF(t)\to0$ , where $F(t)$ is the distribution function of the time interval between successive arrivals of customers. We shall study the class of limiting distributions of the quantity $\tau_n\delta(\alpha_0)$, where $\delta(\alpha_0)$ is some normalizing factor. We shall obtain conditions for which $P\{\tau_n/M\tau_n$. 
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     author = {O. P. Vinogradov},
     title = {Limiting distribution for the moment of first loss of a~customer in a~single-line service system with a~limited number of positions in the queue},
     journal = {Matemati\v{c}eskie zametki},
     pages = {541--546},
     publisher = {mathdoc},
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     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a6/}
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O. P. Vinogradov. Limiting distribution for the moment of first loss of a~customer in a~single-line service system with a~limited number of positions in the queue. Matematičeskie zametki, Tome 3 (1968) no. 5, pp. 541-546. http://geodesic.mathdoc.fr/item/MZM_1968_3_5_a6/