Title: On renewal input state dependent working vacations queue with impatient customers

Authors: Pikkala Vijaya Laxmi; Kanithi Jyothsna

Addresses: Department of Applied Mathematics, Andhra University, Visakhapatnam – 530 003, India ' Department of Applied Mathematics, Andhra University, Visakhapatnam – 530 003, India

Abstract: This paper studies the effect of balking and reneging in a finite buffer renewal input queue with multiple working vacations. Arriving customers balk with a probability and renege according to exponential distribution. As soon as the system becomes empty, the server leaves for a working vacation. During working vacations the server works at a different rate rather than completely stopping service. Service times during a service period, during a working vacation period and vacation times are assumed to be exponentially distributed with state dependent rates. Employing the supplementary variable and recursive techniques, the steady-state system length distributions at pre-arrival and arbitrary epochs have been derived. Some performance measures of the model and cost analysis through simulated annealing have been discussed. Finally, sensitivity analysis is carried out through some numerical experiments.

Keywords: renewal input queues; impatient customers; state dependent queues; multiple working vacations; MWVs; balking; reneging; simulated annealing; finite buffer.

DOI: 10.1504/IJMOR.2015.072276

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.6, pp.661 - 680

Received: 28 Dec 2013
Accepted: 28 May 2014
Published online: 08 Oct 2015 *

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