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On a system \(\text{GI/G}/\infty\) with a periodic input. (English. Ukrainian original) Zbl 0986.60090

Theory Probab. Math. Stat. 61, 101-108 (2000); translation from Teor. Jmovirn. Mat. Stat. 61, 97-104 (2000).
Let us consider a queueing system with periodical recurrent input. If \(t_{n}, n=1,2,\dots\), are moments of \(n\)th claim to the system, then \(\tau_{n}=t_{n}-t_{n-1}, n=1,2,\dots\), are independent random variables, provided \(\tau_{mr+k}, k=1,2,\dots,r,\) for \(m=1,2,\dots\) are identically distributed with distribution function \(G_{k}(t), k=1,2,\dots,r.\) There is an infinite number of one-typed devices in the system for queueing. The main aim of this paper is to study conditions of existence of a stationary regime for the process of queueing of claims of the above-described model and to construct the explicit formula for characteristics of stationary distribution over parameters of the system.

MSC:

60K25 Queueing theory (aspects of probability theory)
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
60F17 Functional limit theorems; invariance principles
90B22 Queues and service in operations research
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