Title: Analysis of an M^[X]/G(a, b)/1 queueing model with multiple vacation controllable arrival during multiple vacation and two phases of repair with delay

Authors: G. Ayyappan; T. Deepa

Addresses: Department of Mathematics, Pondicherry Engineering College, Pillaichavady, Puducherry - 605 014, India ' Department of Mathematics, Pondicherry Engineering College, Pillaichavady, Puducherry - 605 014, India

Abstract: The objective of this paper is to analyse an M^[X]/G(a, b)/1 queueing model with multiple vacation, controllable arrival during multiple vacation and two phases of repair with delay. Whenever the queue size is less than 'a', the server resumes multiple vacation and continues this until at least 'a' customers are waiting in the queue. After finishing a batch of service, if the server is breakdown with probability γ, the server will be sent for repair after a short interval of time called delay time. After this delay, two consecutive phases of repair (first phase repair, second phase repair) are considered. After the second phase of repair or when there is no breakdown with probability 1-γ, the server starts a vacation if the queue length is less than 'a'. Otherwise, the server starts a service under the general bulk service rule. Using supplementary variable technique, the probability generating function of the queue size at an arbitrary time is obtained for the steady-state case. Also some performance measures and cost model are derived. Numerical illustrations are presented to visualise the effect of various system parameters.

Keywords: bulk queue; controllable arrival; multiple vacation; two phases of repair; delay time to repair.

DOI: 10.1504/IJISE.2020.105738

International Journal of Industrial and Systems Engineering, 2020 Vol.34 No.3, pp.409 - 431

Received: 24 Apr 2018
Accepted: 12 Jul 2018
Published online: 11 Mar 2020 *

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