Oscillating ‎M[X]/G/1‎ Systems with Finite Capacity

We address the batch arrival‎ ‎M[X]/G/1 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.‎