Title: Bi-level threshold policy of MX/(G1,G2)/1 queue with early setup and single vacation

Authors: K. Julia Rose Mary, M.I. Afthab Begum, M. Jemila Parveen

Addresses: Department of Mathematics, Nirmala College for Women, Coimbatore 641018, Tamil Nadu, India. ' Department of Mathematics, Avinashilingam University for Women, Coimbatore 641043, Tamil Nadu, India. ' Avinashilingam University for Women, Coimbatore 641043, Tamil Nadu, India

Abstract: In this paper, we analyse a queueing system with a second optional service channel under bi-level control policy and server|s single vacation. There is a single server who provides the first essential service to all arriving customers. As soon as the first service of a customer is complete, then with probability r, the customer may opt for the second service in which case the second service will immediately commence, or else with probability (1 − r) he may opt to leave the system, so that another customer at the head of the queue (if any) is taken up for his first essential service. The server operates an (m, N) policy with an early setup and takes a single vacation whenever the system becomes empty. For this model, the stationary probability generating function of the queue length distribution is obtained through supplementary variable technique and a decomposition property is discussed. The expected length of the cycle, various performance measures and the optimal values of thresholds m and N which minimise the total expected operating cost are also calculated.

Keywords: bi-level threshold policy; first essential service; second optional service; early setup; single vacation policy; queueing systems.

DOI: 10.1504/IJOR.2011.039714

International Journal of Operational Research, 2011 Vol.10 No.4, pp.469 - 493

Published online: 14 Feb 2015 *

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