Did something like that: An organization with some boats, quite a lot of boats, some that might be involved in global nuclear war, maybe limited to sea, wanted to know how long some of the boats might survive. The ocean had Red and Blue boats and airplanes, and the Reds and Blues were looking for each other and trying to kill each other.
So, the state of the system was the remaining Red/Blue inventories.
Some work by Koopmans showed that the encounter rates were a Poisson process. So, the time to the next encounter had exponential distribution, depending on the current state.
At an encounter, depending on the types, could have the Red die, the Blue die, both die, or neither die. Then after the encounter, the state of the system changed. So, the state of the system was a continuous time, discrete state space Markov process subordinated to a Poisson process. That is, in part, a Markov chain.
Yes, there is a closed form solution, but the combinatorial explosion of the discrete state space size meant that a direct attack via the closed form solution was not reasonable.
But it was easy enough to do Monte-Carlo, that is, generate a few hundred sample paths and average those, get confidence intervals, etc. While in grad school working on operations research I did that. While the state space was enormous, the Monte-Carlo was really fast. On any computer of today, the code would run before could get finger off the mouse button or the Enter key. And running off 1 million sample paths would be feasible. For the random numbers I looked in Knuth's appropriate volume of The Art ... and used
X(n + 1) = X(n) * 5^15 + 1 mod 2^47
programmed in assembler.
Work passed review by famous applied probabilist J. Keilson.
Apparently the work was sold to some intelligence agency. I could guess which one, but then I'd have to ...!