Network Decomposition: Theory and Practice

Abstract 

 
   In this paper we show that significant simplicities can arise in the analysis of a network when link capacities are large enough to carry many flows. We develop a network decomposition approach in which network analysis can be greatly simplified. We prove that the queue-length at the downstream queue converges to that of a single queue obtained by removing the upstream queue, as the capacity and the number of flows at the upstream queue increase. The precise modes of convergence vary depending on the type of input traffic, i.e., from regulated traffic arrivals to point process inputs. Our results thus help simplify network analysis by decomposing the original network into a simplified network in which all the nodes with large capacity have been eliminated. Through an extensive numerical investigation under various network scenarios, we demonstrate different aspects and implications of our network decomposition approach. Some of our findings are that our techniques perform well especially for the cases when (i) many flows are multiplexed and/or (ii) flows are routed to different nodes, i.e., no single flow dominates at any node.