On a system \(\text{GI/G}/\infty\) with a periodic input (Q2740452)

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.