International Journal of Stochastic Analysis
Volume 2014 (2014), Article ID 892867, 12 pages
Research Article

with Setup Time, Bernoulli Vacation, Break Down, and Delayed Repair

1Department of Mathematics, Pondicherry Engineering College, Pondicherry 605 014, India
2Department of Mathematics, Arunai Engineering College, Mathur, Thiruvannamalai, Tamil nadu 606 603, India

Received 17 September 2013; Revised 16 January 2014; Accepted 24 January 2014; Published 31 March 2014

Academic Editor: Enzo Orsingher

Copyright © 2014 G. Ayyappan and S. Shyamala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a single server in which customers arrive in batches and the server provides service one by one. The server provides two heterogeneous service stages such that service time of both stages is different and mandatory to all arriving customers in such a way that, after the completion of first stage, the second stage should also be provided to the customers. The server may subject to random breakdowns with brake down rate and, after break down, it should be repaired but it has to wait for being repaired and such waiting time is called delay time. Both the delay time and repair time follow exponential distribution. Upon the completion of the second stage service, the server will go for vacation with probability or stay back in the system probability , if any. The vacation time follows general (arbitrary) distribution. Before providing service to a new customer or a batch of customers that joins the system in the renewed busy period, the server enters into a random setup time process such that setup time follows exponential distribution. We discuss the transient behavior and the corresponding steady state results with the performance measures of the model.