Fig. 6.

The sub-state diagram (cf. Fig. 3) for the scenario detailed in Example 5 after the application of Theorem 6 (extended LCT for dwell times given by competing Poisson processes). Here the X dwell time distribution is the minimum of two Erlang random variables $T_i\sim$Erlang($r_i,k_i$), $i=1,2$, which can be thought of as event time distribution under two homogeneous Poisson processes as detailed in the main text. We here assume that whichever of these occurs first determines whether particles leaving X transition to Y${}_1$ or Y${}_2$, respectively