Geom/Geom[A]/1/ Queue With Late Arrival System With Delayed Access and Delayed Multiple Working Vacations

Jiang Cheng, Yinghui Tang1, Miaomiao Yu

This paper considers a discrete-time bulk-service queue with infinite buffer space and delay multiple working vacations. Considering a late arrival system with delayed access (LAS-AD), it is assumed that the inter-arrival times, service times, vacation times are all geometrically distributed. The server does not take a vacation immediately at service complete epoch but keeps idle period. According to a bulk-service rule, at least one customer is needed to start a service with a maximum serving capacity 'a ' . Using probability analysis method and displacement operator method, the queue length and the probability generating function of waiting time at pre-arrival epochs are obtained. Furthermore, the outside observer’s observation epoch queue length distributions are given. Finally, computational examples with numerical results in the form of graphs and tables are discussed.