N-policy And Multiple Working Vacations Discrete Time Queue

Working vacation is a semi-vacation policy:a server does not completely stop service but serves customers at a lower rate during a vacation.The essence of the working vacation policy is that,when the number of customers is less relatively, a " lower speed period " is established to economize the operational cost in the system.The analysis of the model with working vacations can provide the theory and analysis method to design the optimal lower speed period.Considering the exchange between the working period and vacation period,it will cost some fee.So, the successful exchange will bring more profit when the customer is enough.In this paper we consider a Geom/Geom/1 queue with working vacations and Npolicy. Using qusi-birth-and-death process and matrix-geometric solution method, we gain the steady-state distributions for queue length and conditional waiting time. Furthermore,we indicate the conditional stochastic decomposition structures of queue length and waiting time in the stationary state and obtain the distributions for additional queue length and additional delay.Finally,we study Geom/Geom/2 queue with N-policy and multi pleworkin gvacations.