Buffered Cross-Bar Switches, Revisited: Design Steps, Proofs and Simulations Towards Optimal Rate and Minimum Buffer Memory

Regarding the packet-switching problem, we prove that the weighed max-min fair service rates comprise the unique Nash equilibrium point of a strategic game, specifically a throughput auction based on a ldquoleast-demanding first-servedrdquo principle. We prove that a buffered crossbar switch can converge to this equilibrium with no pre-computation or internal acceleration, with either randomized or deterministic schedulers, (the latter with a minimum buffering of a single
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packet per crosspoint). Finally, we present various simulation results that corroborate and extend our analysis.