Algorithms for Computing Limit distributions of Oscillating Systems with Finite Capacity

We address the batch arrival  systems with finite capacity under partial batch acceptance strategy where service times or rates oscillate between two forms according to the evolution of the number of customers in the system. Applying the theory of Markov regenerative processes and resorting to Markov chain embedding, we present a new algorithm for computing limit distributions of the number customers in the system. The numerical results are given in the paper for a clearer expression of the proposed computational methodologies.