  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
shot noise. A shot-noise rate emerges as a natural model, if the arrival rate
tends to display 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 for analysis. In
particular, we perform transient analysis on the number of customers in the
queue jointly with the value of the driving shot-noise process. Additionally,
we derive heavy-traffic asymptotics for the number of customers 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.
