On the Emulation of Finite-Buffered Output Queued Switches Using Combined Input-Output Queuing

Abstract

We study the emulation of Output Queuing (OQ) using Combined Input-Output Queuing (CIOQ) switches in the setting where the emulated OQ switch and the CIOQ switch have buffer capacity B ≥ 1 packets at every output. We analyze the resource requirements of CIOQ policies in terms of the required fabric speedup and the additional buffer capacity needed at the CIOQ inputs.

For the family of work-conserving scheduling algorithms, we find that whereas every greedy CIOQ policy is valid for OQ emulation at speedup B, no CIOQ policy is valid at speedup $s < \sqrt[3]{B-2}$ when preemption is allowed. We also find that CCF in particular is not valid at any speedup s < B. We then introduce a CIOQ policy, CEH, that is valid at speedup $s \geq \sqrt{2(B-1)}$. Under CEH, the buffer occupancy at any input never exceeds $1+\lfloor\frac{B-1}{s-1}\rfloor$.

For non-preemptive scheduling algorithms, we characterize a trade-off between the CIOQ speedup and the input buffer occupancy. Specifically, we show that for any greedy policy that is valid at speedup s > 2, the input buffer occupancy cannot exceed $1+\lceil{\frac{B-1}{s-2}}\rceil$. We also show that at speedup 2, a greedy variant of the CCF policy requires input buffer capacity of only B packets for the emulation of non-preemptive OQ algorithms with PIFO service disciplines.