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

• Published in: Computers & operations research Vol. 79; pp. 1 - 11
• Main Authors: Ghosh, Souvik, Banik, A.D.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.03.2017; Pergamon Press Inc
• Subjects: Algorithms; Batch Markovian arrival process (BMAP); Generalized processor-sharing (GPS) queue; Internet Protocol; Markov analysis; Markovian service process (MSP); Queuing; RG-factorization; Studies; Markovian service process (MSP); Generalized processor-sharing (GPS) queue; RG-factorization; Batch Markovian arrival process (BMAP)
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2016.10.001

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. •An infinite-buffer single server queue with batch Markovian arrival is considered.•The service process is non-renewal as well under generalized processor sharing.•Stationary system-length distribution is obtained using RG-factorization approach.•The mean sojourn time of a tagged customer is analyzed in detail.•Performance indices and blocking probability for finite-buffer are also obtained.