Analysis of Discrete-time queues with correlated arrivals, negative customers and server interruption

¹ Department of Mathematics, Dr.NGP Institute of Technology, 641048 Coimbatore, India.
asenthilvadivu@gmail.com
² Department of Mathematics, PSG College of Technology, 641004 Coimbatore, India.
ranpsgtech@yahoo.co.in
³ Department of Applied Mathematics & Computational Sciences, PSG College of Technology, 641004 Coimbatore, India.
mskumarin@yahoo.com

Received: 29 June 2013
Accepted: 17 April 2015

Abstract

This paper analysis a discrete time infinite capacity queueing system with correlated arrival and negative customers served by two state Markovian server. Positive customers are generated according to the first order Markovian arrival process with geometrically distributed lengths of On periods and Off periods. Further, the geometrically distributed arrival of negative customer removes the positive customers is any, and has no effect when the system is empty. The server state is a two state Markov chain which alternate between Good and Bad states with geometrically distributed service times. Closed-form expressions for mean queue length, unfinished work and sojourn time distributions are obtained. Numerical illustrations are also presented.