Mean-field approximations for performance models with generally-timed transitions

Abstract

We show how the popular mean-field approach for analysing Markovian models of massively-parallel computer systems can be extended to incorporate generally-timed transitions. Specifically, in the context of a simple peer-to-peer software update model, we show how systems of delay differential equations can be formally derived from such models. Finally, we verify empirically that the approximation is accurate and converges under the usual mean-field scaling.