On joint sequence design for feedback-based two-stage switch architecture

An N times N feedback-based two-stage switch is configured using a pre-determined and periodic joint sequence of N joint configurations. The joint sequence used is characterized by both in-order packet delivery and staggered symmetry properties. In this paper, we focus on designing optimal joint sequences. We first divide all possible joint sequences into four classes, with staggered symmetry property only, with in-order packet delivery property only, with both properties and with none of the properties. We then show that anchor output and ordered joint sequence are the necessary and sufficient conditions for packet inorder delivery. Since the staggered symmetry property is necessary for efficient feedback path implementation, we calculate that there are [(N-1)!]2 joint sequences with both inorder packet delivery and staggered symmetry properties. In order to find out the optimal joint sequence that can minimize the switch delay performance for a given traffic profile, we believe it can only be achieved by searching through the whole pool of [(N-1)!]2 joint sequences.