Author : K . Sikdar 1
Date of Publication :8th June 2017
Abstract: Discrete-time queueing models have gained prominence in recent years due to its wide applications. These have received much interest due to the emerging broadband integrated services digital network(B-ISDN) which provides the transfer of messages in the form of video, voice and data through high speed local area networks (LAN). The asynchronous transfer mode (ATM) is adopted as the network transport technique in the implementation of B-ISDN. In this paper, we deliberate a finite buffer discrete-time Geo/G/1 queue where the server takes finite number of at most L (≥0) vacations. The server takes vacations whenever the system is empty. After the vacation, the server checks out the system whether to resume the service or to go for another vacation or to be dormant. In this system, jobs arrive according to Bernoulli process and service, vacation times are arbitrarily distributed. We adopt the supplementary variable method and the imbedded Markov chain techniques to attain the queue length distributions at the service completion, vacation termination and arbitrary epochs. The analysis of actual waiting time under the First-Come-First-Served (FCFS) queueing discipline is also carried out. The objective of this paper is to create awareness and better utilization of the queueing theories involved in the analysis of a discrete-time model with at most L vacations
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