  We consider a multivariate L\'evy process where the first coordinate is a
L\'evy process with no negative jumps which is not a subordinator and the
others are nondecreasing. We determine the Laplace-Stieltjes transform of the
steady-state buffer content vector of an associated system of parallel queues.
The special structure of this transform allows us to rewrite it as a product of
joint Laplace-Stieltjes transforms. We are thus able to interpret the buffer
content vector as a sum of independent random vectors.
