On The Renewal Input Batch-arrival Queue Under Single And Multiple Working Vacation Policy With Application To EPON

Abstract

This paper analyzes renewal input batch arrival queues with multiple and single working vacation policy. We obtain the steady state system-length distributions at pre-arrival and arbitrary epochs. The Laplace-Stieltjes transforms (LST) of the sojourn time distribution for the first customer and an arbitrary customer in an accepted batch have been derived. Also the probability density function of sojourn time distribution for the first customer in an accepted batch has been obtained. The proposed analysis is based on the roots of the characteristics equations formed using the probability generating functions (p.g.f.) of embedded pre-arrival epoch probabilities. Several performance measures such as the mean system-length and mean sojourn times of first and an arbitrary customer in an accepted batch are presented. The suggested queues have potential application in ethernet passive optical network (EPON).

Keywords:

• GI/M/I queue
• batch arrival
• multiple-
• single-working vacation
• sojourn time analysis
• roots

Acknowledgement

The second author acknowledges partial financial support from the Department of Science and Technology, New Delhi, India research grant SR/FTP/MS-003/2012. We are thankful to Dr. Barathram Ramkumar, School of Electrical Sciences, Indian Institute of Technology, Bhubaneswar, for his valuable comments.