Analyzing Nonblocking Switching Networks using Linear Programming (Duality)

Abstract—The main task in analyzing a switching network design (including circuit-, multirate-, and photonic-switching) is to determine the minimum number of some switching components so that the design is non-blocking in some sense (e.g., strictor wide-sense). We show that, in many cases, this task can be accomplished with a simple two-step strategy: (1) formulate a linear program whose optimum value is a bound for the minimum number we are seeking, and (2) specify a solution to the dual program, whose objective value by weak duality immediately yields a sufficient condition for the design to be non-blocking. We illustrate this technique through a variety of examples, ranging from circuit to multirate to photonic switching, from unicast to f-cast and multicast, and from strict- to wide-sense non-blocking. The switching architectures in the examples are of Clos-type and Banyan-type, which are the two most popular architectural choices for designing non-blocking switching networks. T...

• Type: Journal
• Year: 2010
• Where: INFOCOM
• Authors: Hung Q. Ngo, Atri Rudra, Anh N. Le, Thanh-Nhan Nguyen
• Keywords: Communications, INFOCOM 2010, Minimum Number, Non-blocking Switching Networks, Switching Networks