Fig. 1.

Example diagram where state X has an Erlang(r, k) distributed dwell time, represented either as a a single state and corresponding integral equation, or b as a set of k sub-states each with exponential dwell time distributions whose mean field equations can be represented as either integral equations or a system of ODEs (see Theorem 1). Rate $\mathcal{I}(t)$ is an integrable non-negative function describing the mean field influx rate into state X