Recensione dell'articolo: (Chaudhry, Mohan L.; Yoon, Bong K.; Kim, Nam K. - " Analysis of a discrete-time finite-capacity single-server queue with Markovian- arrival process and random-bulk-service: D-MAP/GY /1/M " - Stoch.Anal.Appl. 28 (2010), no.6, 1061–1077)

This paper deals with the study of the queue model D-MAP/GY /1/M. This is a single server system which is modelled as a discrete time system and is characterised by the following assumptions. The arrival process of customers is modelled by a discrete- time Markovian arrival process (D-MAP). The service procedure is described by bulk service times with general distribution GY . Y is the random variable which determines bulk size for service at the starting instant of services. The authors assume that the model behaves as a late arrival system with delayed access (LAS-DA). The arrivals occur during a time slot, just prior to the end of the slot, and the services start at slot boundaries. So a customer which arrives to the queue can start its service no earlier than the beginning of the next time slot. This model has finite capacity; the number of waiting spaces in the queue is M. The authors discuss in this paper the distribution of the number of customers in the queue at various epochs and the performance measures, such as the average number of customers in the queue and the loss probability of customers. Leonardo Pasin