Before revision: 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 , when stable, the network has a product-form stationary distribution. From a practical perspective, we propose an algorithm on this basis to allocate the resources of a computer cluster .
After revision: 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 . The service rate of a job at any given time is the sum of the service rates of all servers processing this job. We show that the corresponding queue is quasi-reversible and use this property to design a scheduling algorithm achieving balanced fair sharing of the service capacity .