|We consider a network of multi-server queues wherein each job can be processed in parallel by any subset of servers within a pre-defined set that depends on its class. Each server is allocated in FCFS order at each queue. Jobs arrive according to Poisson processes, have independent exponential service requirements and are routed independently at random. We prove that the network state has a product-form stationary distribution, in the open, closed and mixed cases. From a practical perspective, we propose an algorithm on this basis to allocate the resources of a computer cluster.