Convexity of Inverse Blocking Curves in Loss Systems

Abstract

Why Larger Service Systems Benefit More from Scale How much extra demand can a service system handle when capacity is increased while keeping the same target level of customer blocking? In the paper “Convexity of Inverse Blocking Curves in Loss Systems,” Benjamin Legros establishes an exact economies-of-scale result for loss systems. The paper proves that the maximum supportable demand is an increasing and globally convex function of the number of servers. In practical terms, as a system becomes larger, each additional server can support progressively more additional demand while maintaining the same blocking target. Equivalently, the extra capacity required to accommodate additional demand decreases as the system grows. The result provides a rigorous mathematical foundation for resource pooling in capacity-constrained services. It applies to the classical Erlang-B loss model and extends to systems with a finite waiting room, with potential relevance for telecommunications, healthcare, emergency response, and other service operations.