  This paper considers a network of infinite-server queues with the special
feature that, triggered by specific events, the network population vector may
undergo a linear transformation (a `multiplicative transition'). For this model
we characterize the joint probability generating function in terms of a system
of partial differential equations; this system enables the evaluation of
(transient as well as stationary) moments. We show that several relevant
systems fit in the framework developed, such as networks of retrial queues,
networks in which jobs can be rerouted when links fail, and storage systems.
Numerical examples illustrate how our results can be used to support design
problems.
