The Markov-modulated Erlang loss system

Furthermore, we consider a regime where, in a way that is common for this type of loss system, we scale the arrival rate and the number of servers, while also scaling the transition rates of the modulating Markov process. We establish convergence of the stationary distribution to a truncated Normal distribution, which leads to an approximation for the blocking probability. In this 'fast regime', the parameters of the limiting distribution critically depend on the precise scaling imposed. We also derive scaling results for a 'slow regime', in which the modulating Markov process is slow relative to the arrival process. Numerical experiments show that the resulting approximations are highly-accurate.