Authors: Rakesh Kumar
Addresses: School of Mathematics, Shri Mata Vaishno Devi University, Katra (J&K) 182320, India
Abstract: In this paper, a correlated input queuing model with catastrophic and restorative effects and customer impatience has been studied. When the system is down due to catastrophe and undergoes a restoration/repair process, each waiting customer becomes impatient and abandons the system as soon as his actual waiting time exceeds his individual (random) waiting time threshold. The customers become impatient only when the system is not working and they have no information on the time when it will become operative again. The transient solution of the stochastic queuing model has been obtained. The probability generating function of the system size has been obtained in the Laplace transform form. The expressions for expected number of customers in the system have also been obtained. At the end, some queuing models have been obtained as particular cases of this model.
Keywords: correlated input; restoration; impatient customers; catastrophes; transient solution; queuing models; stochastic modelling.
International Journal of Agile Systems and Management, 2012 Vol.5 No.2, pp.122 - 131
Received: 15 Apr 2011
Accepted: 28 Aug 2011
Published online: 13 May 2012 *