Title: Unreliable single server retrial queueing model with repeated vacation

Authors: J. Ebenesar Anna Bagyam; P. Suganthi; P. Visali

Addresses: Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore 641021, India; Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore 641043, Tamil Nadu, India ' R.M.K. Engineering College, Chennai, Tamil Nadu, 601206, India ' Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore 641043, Tamil Nadu, India

Abstract: The steady-state behaviour of a single server retrial queueing model with server breakdown and repeated vacation is analysed. If the server is accessible, the customer gets service immediately; otherwise, the customer waits for his turn. After each service, the server may take a vacation with a certain probability. However, if the system is empty, the server takes repeated vacations until the server finds at least one customer in the system. If the server is prone to breakdown, the repair of the server starts immediately. After the repair, the server continues the service to the same customer. The retrial, service, repair, and vacation times are assumed as arbitrary distributed. The steady-state solutions for various performance measures are determined using the supplementary variable method.

Keywords: retrial queue; repeated vacation; server breakdown; repair; unreliable server; performance measures; numerical analysis; call centre; multiple vacation; supplementary variable technique.

DOI: 10.1504/IJMOR.2023.134838

International Journal of Mathematics in Operational Research, 2023 Vol.26 No.3, pp.357 - 372

Received: 06 May 2022
Accepted: 10 Sep 2022
Published online: 14 Nov 2023 *

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