Monte Carlo Simulation (MCS)

The explicit steady-state solutions (2.6)-(2.13) are simple and exact. However, there are no general explicit solution in the case when the call rate $\lambda$, and the service rate $\mu$ depend on time what often happens in the real service systems. The configuration and the operating rules of real service systems are to complicated for the exact solution, as usual. In such cases the Monte Carlo simulation (MCS) is needed. We start the discussion of MCS from the steady-state systems keeping all the assumptions described in the chapter 2.1.2. This way one can test the both the analytical and the Monte Carlo solutions by comparing the results. Later on we extend the MCS to more complicated and also to time-dependent cases when the call rate $\lambda=\lambda(t)$, and the service rate $\mu=\mu(t)$