The number of rearrangements for Clos networks xe2x80x93 new results Abstract   Rearrangeable Clos networks have been studied for a long time due to their many applications, as well as their theoretical interest. In a rearrangeable Clos network, a newly requested connection may be blocked by existing connections. However, this blocking is eliminated by adequately rearranging some other existing connections. In this operation, an interesting topic is the sufficient number of rearrangements required to eliminate the blocking. Despite previous studies, the sufficient number of rearrangements has only been found for limited cases and has not been completely determined for generic parameter values. This paper analyses the number of rearrangements using the connection chain concept, which clearly and efficiently represents a sequence of connections to be rearranged. The analysis assumes the employment of a rearrangement algorithm, which eliminates the blocking using the shortest connection chain. The usage of the shortest connection chain results in the minimum number of rearrangements. As a result, this paper determines a new bound on the number of rearrangements for a parameter range that has not been considered in any previous studies. In addition, this paper examines the condition for which the system is unblocked via one rearrangement.

G2: A Network Optimization Framework for HighPrecision Analysis of Bottleneck and Flow Performance Congestion control algorithms for data networks have been the subject of intense research for the last three decades. While most of the work has focused around the characterization of a flowu0027s bottleneck link, understanding the interactions amongst links and the ripple effects that perturbations in a link can cause on the rest of the network has remained much less understood. The Theory of Bottleneck Ordering is a recently developed mathematical framework that reveals the bottleneck structure of a network and provides a model to understand such effects. In this paper we present G2, the first operational network optimization framework that utilizes this new theoretical framework to characterize with highprecision the performance of bottlenecks and flows. G2 generates an interactive graph structure that describes how perturbations in links and flows propagate, providing operators new optimization insights and traffic engineering recommendations to help improve network performance. We provide a description of the G2 implementation and a set of experiments using production TCPIP code to demonstrate its operational efficacy.