We address the problem of verifying timed properties of Markovian models of
large populations of interacting agents, modelled as finite state automata. In
particular, we focus on time-bounded properties of (random) individual agents
specified by Deterministic Timed Automata (DTA) endowed with a single clock.
Exploiting ideas from fluid approximation, we estimate the satisfaction
probability of the DTA properties by reducing it to the computation of the
transient probability of a subclass of Time-Inhomogeneous Markov Renewal
Processes with exponentially and deterministically-timed transitions, and a
small state space. For this subclass of models, we show how to derive a set of
Delay Differential Equations (DDE), whose numerical solution provides a fast
and accurate estimate of the satisfaction probability. In the paper, we also
prove the asymptotic convergence of the approach, and exemplify the method on a
simple epidemic spreading model. Finally, we also show how to construct a
system of DDEs to efficiently approximate the average number of agents that
satisfy the DTA specification
