On Service Guarantees for Input Buffered Crossbar Switches: A Capacity Decomposition Approach by Birkhoff and von Neumann

Based on a decomposition result by Birkhoff and von Neumann for a doubly substochastic matrix, in this paper we propose a scheduling algorithm that is capable of providing service guarantees for input-buffered crossbar switches. Our service guarantees are uniformly good for all non-uniform traffic, and thus imply 100% throughput. The off-line computational complexity to identify the scheduling algorithm is O(N4:5) for an N N switch. Once the algorithm is identified, its on-line computational complexity is O(logN) and its on-line memory complexity isO(N3 logN). Neither framing nor internal speedup is required for our approach. Keywords— Input buffered switches, crossbar switches, service guarantees, scheduling, generalized processor sharing