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Teoriya Veroyatnostei i ee Primeneniya, 1994, Volume 39, Issue 4, Pages 799–804
(Mi tvp3854)
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This article is cited in 4 scientific papers (total in 4 papers)
Short Communications
On certain asymptotic properties of waiting time in a multiserver queueing system with identical times
O. P. Vinogradov M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
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, tandem queues, waiting time, sojourn time, recurrence relation, limit theorem, regularly varying function, Tauberian theorem.
Received: 20.02.1991
Citation:
O. P. Vinogradov, “On certain asymptotic properties of waiting time in a multiserver queueing system with identical times”, Teor. Veroyatnost. i Primenen., 39:4 (1994), 799–804; Theory Probab. Appl., 39:4 (1994), 714–718
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https://www.mathnet.ru/eng/tvp3854 https://www.mathnet.ru/eng/tvp/v39/i4/p799
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Abstract page: | 140 | Full-text PDF : | 44 | First page: | 17 |
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