An algorithmic analysis of the BMAP/MSP/1 generalized processor-sharing queue

This paper deals with the analysis of the BMAP/MSP/1 generalized processor-sharing queue. The analysis is based on RG-factorization technique applied to the Markov chain of the associated quasi-birth and death process. The stationary system-length distribution of the number of customers in the system and the Laplace-Stieltjes transform (LST) of the sojourn time distribution of a tagged customer in the system is obtained in this paper. The mean sojourn time of a tagged customer is derived using the previous LST. The corresponding finite-buffer queueing model is also analyzed and system-length distribution is derived using the same technique as stated above. Further, the blocking probabilities for customers with different positions, such as the first-, an arbitrary- and the last-customer of a batch are obtained. The detail computational procedure for these models is discussed. Various numerical results are presented to show the applicability of the results obtained in the study.