Geodesic
On certain asymptotic properties of waiting time in a multiserver queueing system with identical times
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 4, pp. 799-804

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A multiphase queueing system is considered. The service time of the nth arrival at the $i$th server is $T_{n,i} $ and $\mathbf{P}\{ T_{n,1} = \cdots = T_n \} = 1$, where $\{ T_n \} $ are independent identically distributed random variables with an arbitrary common distribution. Let $U_l (n)$ be the time spent by the $l$ arrival at the $l$th server. Some algebraic properties of the sequence $\{ U_l (n)\} (l \ge 2)$ are cleared up. In the case of Poisson input flow, the distributions of some characteristics of the system are obtained, as well as a number of limit theorems for the situation where the number of servers grows infinitely.
Keywords: multiphase queueing systems with identical service times, waiting time, sojourn time, recurrence relation, limit theorem, regularly varying function, Tauberian theorem.
Mots-clés : tandem queues 
@article{TVP_1994_39_4_a9,
     author = {O. P. Vinogradov},
     title = {On certain asymptotic properties of waiting time in a multiserver queueing system with identical times},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {799--804},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a9/}
}
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O. P. Vinogradov. On certain asymptotic properties of waiting time in a multiserver queueing system with identical times. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 4, pp. 799-804. http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a9/