A Note on the Determination of the Processing Capacity in a Multiserver Job System as a Model of Cloud Datacenters

Systems with multiserver jobs, inspired by modern datacenters, present a challenge in terms of the analysis of their performance and, in particular, the determination of their processing capacity as some servers may remain idle even though there are jobs queued for service. We consider a generalization of the multiserver jobs model to a resource of not necessarily integer quantity and jobs of different classes requiring arbitrary fractions of that resource. We present a simple approach to the analysis of such a system in steady state. Our approach relies on a suitably chosen state description and the use of conditional probabilities. The limiting values of these conditional probabilities allow us to determine the asymptotic maximum job processing capacity without having to obtain the full solution for the system.