The Buffer-bandwidth Trade-off Curve Is Convex

To achieve a constant overflow probability, the two queueing resources, viz.,buffer and bandwidth, can be traded off. In this paper we prove that, under general circumstances, the corresponding trade -off curve is convex in the "many-sources scaling". This convexity enables optimal resource partitioning in a queueing system supporting heterogeneous traffic, with heterogeneous Quality-of-Service requirements.