Abstract:

A discretetime Geom／Geom／1 queue with generalized random working vacation policy is studied. By using the quasi birth and death chain and matrixgeometric solution approaches, the generating functions and the expectations of the steady state queue length and sojourn time are derived. In addition, the generating functions and the means of the regular busy period, busy cycle and vacation period are obtained. Finally, two special cases of the model are given.

Key words:  discrete-time queue; generalized random working vacation; matrix-geometric solution; sojourn time