  Motivated by queueing systems with heterogeneous parallel servers, we
consider a class of structured multi-dimensional Markov processes whose state
space can be partitioned into two parts: a finite set of boundary states and a
structured multi-dimensional set of states, exactly one dimension of which is
infinite. Using separation of variables, we show that the equilibrium
distribution, typically of the queue length, can be represented as a linear
combination of product forms. For an important subclass of queueing systems, we
characterize explicitly the waiting time distribution in terms of mixtures of
exponentials.
