Recensione dell'articolo: (Banik, A. D.; Chaudhry, M. L.; Gupta, U. C. - " On the finite buffer queue with renewal input and batch Markovian service process: GI/BMSP/1/N " - Methodol.Comput.Appl.Probab. 10 (2008), no.4, 559–575.)

In this paper the authors consider the batch Markovian service process (BMSP) which is a further generalization of a Markovian service process (MSP) and many other batch service processes. In particular they study a renewal input and BMSP which has a different service discipline than the general bulk service queue described in the literature. In fact their model considers service batch size as a random variable. So, customers are served by a single server in batches of random size. Moreover, in this service model a certain probability is assigned to the possible number of customers to be served. The paper carries out the analysis of the finite-buffer queue with renewal input and batch Markovian service process system: GI/BMSP/1/N. In this context the authors obtain the steady-state distribution at pre-arrival epochs using a combination of embedded Markov chain and supplementary variable methods. These results can be applied to solve several other queuing models which are a specific realization of this service system. Leonardo Pasini