GEOM/GEOM[a]/1/ queue with late arrival system with delayed access and delayed multiple working vacations

Abstract

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.

Keywords

• discrete time
• bulk-service
• working vacations
• queue
• waiting time distribution