Recensione dell'articolo: (Yi, Xeung Won; Kim, Jin Dong; Choi, Dae Won; Chae, Kyung Chul - " The Geo/G/1 queue with disasters and multiple working vacations " - Stoch.Models 23 (2007), no.4, 537–549.

In this paper the authors study the discrete time queuing system model Geo/G/1 with disasters (DST). This system is denoted accordingly by the queue model Geo/G/1/DST. In this model, customers arrive at a single server queuing system according to a Bernoulli process and wait in the queue until being served. Queuing customers are ordered following a first-come first-served scheduling. Service times are independent and identically distributed discrete variables with a general probability mass function. The service times process and the arrival process are independent. The model includes disaster events that are generated by an independent Bernoulli process. Each time a disaster event occurs, all customers in the system are flushed out and the server fails. The authors present in this paper the queue-length distribution for the Geo/G/1/DST queue model at an arbitrary time in steady state. Moreover, in this paper, they study the same problem for the queuing system model Geo/G/1 with working vacation (WV). The queuing single server system Geo/G/1/WV behaviour can be described in the following manner. The server begins a working vacation at the instant that the system becomes empty. During the working vacation, customers are served at a reduced service rate. When a vacation period ends, if there are customers in the system, the server changes the reduced service rate to the nominal service rate. The services, interrupted at the end of a vacation period, restart from the beginning. The lengths of vacation periods are independent and identically geometrically distributed discrete variables. Leonardo Pasini