Performance analysis of finite buffer discrete-time queue with bulk service

Discrete-time queues are extensively used in modelling the ATM environment at the cell level. In this paper, we model a single-server queue with finite buffer space in a discrete-time environment where the services are performed in batches of maximum size ‘b’ with a minimum threshold value ‘a’. The analytic analysis of the model is carried out for the both arrival first (AF) and departure first (DF) management policies and distributions of buffer content at various epochs have been obtained. The system performance measures such as average buffer content, average delay and probability of blocking are discussed. A comparative study of AF and DF management policies on certain performance measures is also presented.