Abstract. We consider a finite capacity queue in which arrivals occur according to a batch Markovian process. Services are offered to groups of varying size and the service times are assumed to be of phase type. When the buffer size exceeds $N$, the service rate is increased by a factor $\theta > 1$, $L \le N < K$ and the service is brought back to its normal rate upon completion of the current service. For this queuing model the steady state analysis is performed. The duration in normal as well as fast periods are shown to be of phase type. Efficient algorithms for computing system performance measures, based on regular splittings, are presented. A comparison of this algorithm to (block) Gauss-Seidel method is provided. Some numerical examples are discussed.

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