Vacation policies in an M/G/1 type queueing system with finite capacity

This paper deals with a queueing system with finite capacity in which the server passes from the active state to the inactive state each time a service terminates withv customers left in the system. During the active (inactive) phases, the arrival process is Poisson with parameter (₀). Denoting byu_n the duration of thenth inactive phase and byx_n the number of customers present at the end of thenth inactive phase, we assume that the bivariate random vectors {(v_n,x_n),n 1} are i.i.d. withx_nv+l a.s. The stationary queue length distributions immediately after a departure and at an arbitrary instant are related to the corresponding distributions in the classical model.