''Input-Queued Switches with Logarithmic Delay: Necessary Conditions and a Reconfigurable Scheduling Algorithm''

Krishnendu Roy

Ramachandran Vaidyanathan

Jerry L. Trahan

Proc. 4th ACM/IEEE Symposium on Architectures for Networking and Communications Systems (ANCS 2008), pp. 121-122.


Typically, a scheduling algorithm for an n x n packet switch with a crossbar as the data fabric divides time into slots, each of duration t_p sufficient to transmit a packet. If a scheduling round requires t_r > t_p time, then the switch can transmit multiple packets, up to s = floor(t_r / t_p), between each mapped input-output pair under the current mapping. If s = 1, there exists a frame-based scheduling algorithm with Theta(log n) delay. For uniform random traffic, we establish that the delay is Omega(n) for any s > 1, hence, s = 1 is the only case where a Theta(log n) delay is achievable. Given the importance of achieving a low s, it is imperative to develop extremely fast scheduling algorithms (that reduce t_r) on a mesh-based structure (corresponding to the cross- bar topology of the switch). We present results for a fast scheduling algorithm that runs on a mesh-of-trees topology that can be overlaid on the crossbar switching fabric.

This work was supported in part by the National Science Foundation under grant numbers CCR-0310916 and CCR-0073429.