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

Emulation of Output Queuing (OQ) switches using Combined Input-Output Queuing (CIOQ) switches has been studied extensively in the setting where the switch buffers have unlimited capacity. In this paper we study the general setting where the OQ switch and the CIOQ switch have finite 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: A CIOQ policy is said to be (s, b)-valid (for OQ emulation) if a CIOQ employing this policy can emulate an OQ switch using fabric speedup s ≥ 1, and without exceeding buffer occupancy b at any input port. For the family of work-conserving scheduling algorithms, we find that whereas every greedy CIOQ policy is valid at speedup B, no CIOQ policy is valid at speedup s < 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 ≥ p 2(B − 1). Under CEH, the buffer occupancy at any input never exceeds 1 + j B−1 s−1 k . Although the speedup required for the emulation of preemptive scheduling algorithms is not constant, it may be feasible in high-speed electronic or optical switches, which are expected to have limited buffering capacity. 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+ l B−1 s−2 m . We also show that a greedy variant of the CCF policy is (2, B)-valid for the emulation of non-preemptive OQ algorithms with PIFO service disciplines.