We consider a network of infinite-server queues where the input process is a Cox process of the following form: The arrival rate is a vector-valued linear transform of a multivariate generalized (i.e., being driven by a subordinator rather than a compound Poisson process) shot-noise process. We first derive some distributional properties of the multivariate generalized shot-noise process. Then these are exploited to obtain the joint transform of the numbers of customers, at various time epochs, in a single infinite-server queue fed by the above-mentioned Cox process. We also obtain transforms pertaining to the joint stationary arrival rate and queue length processes (thus facilitating the analysis of the corresponding departure process), as well as their means and covariance structure. Finally, we extend to the setting of a network of infinite-server queues.

中文翻译：

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具有 Coxian 到达的无限服务器系统

我们考虑一个无限服务器队列网络，其中输入过程是以下形式的 Cox 过程：到达率是多元广义的向量值线性变换（即，由下级驱动而不是复合泊松过程) 散粒噪声过程。我们首先推导出多元广义散粒噪声过程的一些分布特性。然后利用这些来获得由上述 Cox 过程提供的单个无限服务器队列中不同时间时期的客户数量的联合变换。我们还获得了与联合平稳到达率和队列长度过程有关的变换（从而有助于分析相应的出发过程），以及它们的均值和协方差结构。最后，