Parallel fluid queues with constant inflows and simultaneous random reductions

We consider I fluid queues in parallel. Each fluid queue has a deterministi c inflow with a constant rate. At a random instant subject to a Poisson pro cess, random amounts of fluids are simultaneously reduced. The requested am ounts for the reduction are subject to a general I-dimensional distribution . The queues with inventories that are smaller than the requests are emptie d. Stochastic upper bounds are considered for the stationary distribution o f the joint buffer contents. Our major interest is in finding exponential p roduct-form bounds, which turn out to have the appropriate decay rates with respect to certain linear combinations of buffer contents.