On Multiplexing Models for Independent Traffic Flows in Single- and Multi-Node Networks

In packet switched networks, statistical multiplexing of independent variable bit rate flows achieves significant resource savings, i.e., N flows require considerably less than N times the resources needed for one flow. In this work, we explore statistical multiplexing using methods from the current stochastic network calculus, where we compare the accuracy of different analytical approaches. While these approaches are known to provide identical results for a single flow, we find significant differences if several independent flows are multiplexed. Recent results on the concatenation of nodes along a network path allow us to investigate both single- as well as multi-node networks with cross traffic. The analysis enables us to distinguish different independence assumptions between traffic flows at a single node as well as between cross traffic flows at consecutive nodes of a network path. We contribute insights into the scaling of end-to-end delay bounds in the number of nodes n of a network path under statistical independence. Our work is complemented by numerical applications, e.g., on access multiplexer dimensioning and traffic trunk management.