Title: Queue size dependent service in bulk arrival queueing system with server loss and vacation break-off
Authors: S.P. Niranjan; V.M. Chandrasekaran; K. Indhira
Addresses: Department of Mathematics, School of Advanced Sciences, VIT University, Vellore, India ' Department of Mathematics, School of Advanced Sciences, VIT University, Vellore, India ' Department of Mathematics, School of Advanced Sciences, VIT University, Vellore, India
Abstract: In this paper, server provides service in two service modes, as single or in bulk according to the queue length. The server provides single service, if the queue length reaches value 'a' and batch service, if the queue length reaches the value 'c' (c > a). After completing the service if the queue length is less than 'a' then the server leaves for vacation. During secondary job (vacation) if the queue length attains the value 'a' then the server breaks the vacation and provides primary service. In the service completion epoch if the server is not reliable then the server has undergone renovation of service station. For the proposed model probability generating function of queue size at an arbitrary time epoch is obtained. Various performance measures are derived with suitable numerical illustration. A cost model is also presented for the proposed model.
Keywords: bulk arrival; batch service; supplementary variable technique; dormant period; vacation break-off; cost optimisation.
International Journal of Knowledge Management in Tourism and Hospitality, 2017 Vol.1 No.2, pp.176 - 207
Received: 02 Feb 2017
Accepted: 27 Feb 2017
Published online: 15 Aug 2017 *