Networks of ·/G/∞ queues with shot-noise-driven arrival intensities

We study infinite‐server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by a shot‐noise process. A shot‐noise rate emerges naturally in cases where the arrival rate tends to exhibit sudden increases (or shots) at random epochs, after which the rate is inclined to revert to lower values. Exponential decay of the shot noise is assumed, so that the queueing systems are amenable to analysis. In particular, we perform transient analysis on the number of jobs in the queue jointly with the value of the driving shot‐noise process. Additionally, we derive heavy‐traffic asymptotics for the number of jobs in the system by using a linear scaling of the shot intensity. First we focus on a one‐dimensional setting in which there is a single infinite‐server queue, which we then extend to a network setting.