Fluid limit analysis of FIFO and RR caching for independent reference models

We study the fluid limit analysis of random replacement (RR) caching for the independent reference model. Applying the limit theorem for the mean field interaction model, we derive the fluid limit of fault probability in the transient state as well as in the steady state. Since the stationary fault probability for the RR cache is identical to that for the first-in first-out (FIFO) cache, our results on the stationary fault probability are available for the FIFO caching. We see that the fluid limit of stationary fault probability that we obtain is coincident with the existing heuristic approximation of stationary fault probability. That is, our fluid limit analysis gives a rigorous theoretical foundation to the heuristic approximation.