On service guarantees for input-buffered crossbar switches: a capacity decomposition approach by Birkhoff and von Neumann

Based on a decomposition result by Birkhoff (1946) and von Neumann (1953) 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(N^4.5) for an N×N switch. Once the algorithm is identified, its on-line computational complexity is O(logN) and its on-line memory complexity is O(N³logN). Neither framing nor internal speedup is required for our approach