Recensione dell'articolo: (Brandwajn, A.; Begin, T. - " A recurrent solution of PH/M/c/N-like and PH/M/c-like queues" - J. Appl. Probab. 49 (2012), no. 1, 84-99)

The authors are interested in queuing models where the request arrival process exhibits significant deviations from a simple Poisson process. They say that state dependent arrival rates may be useful, for instance, to represent congestion avoidance in IP networks. Moreover, since any distribution can be approximated arbitrarily closely by a finite number of exponential phases, a possible approach is to use a phase-type distribution for the time between request arrivals. In this context they study the queuing model and its corresponding version with finite buffer, . For this last case they consider two different assumptions regarding the arrival process when the buffer is full: "lost arrivals'' and "blocked arrivals''. The authors propose a semi-numerical approach to compute the steadystate probability distribution for the number of requests in the system both at arbitrary times and at instants of request arrivals.