Fluid Approximation of CTMC with Deterministic Delays

We compare population models in terms of Continuous Time Markov Chains with embedded deterministic delays (delayed CTMC), in which an exponential timed transition can only update the state of the system after a deterministicdelay, and delay differential equations (DDE). We prove a fluid approximation theorem, showing that, when the size of the population goes to infinity, the delayed CTMC converges to a solution of the DDE.