On System-Wide Safety Staffing of Large-Scale Parallel Server Networks

Abstract

Large-scale stochastic networks are widely used for a variety of systems including telecommunications, patient flows, service and data centers, and so on. Because of their complexity, ensuring the stability of these networks by allocating the required resources needed by each customer class is quite challenging. When there are sufficient resources to serve each customer class, the existence of a policy that stabilizes the system is trivial. One can decouple the network and assign the required resources to each customer class. Conversely, one can anticipate that, when each class is resourceless, it is impossible to stabilize the system independent of the policy used. However, previous analyses did not tackle this question. In this work, we assume that some classes have excess resources, whereas others are deficient. We provide a full characterization of the stability of these networks by identifying a parameter that describes the overall excess or lack of resources in the network.