Title: An M^x/G/1 retrial queue with two phase service under active server breakdowns, two types of repair and multiple vacations with N-policy

Authors: V. Jailaxmi; R. Arumuganathan; A. Rathinasamy

Addresses: Department of Mathematics, PSG College of Technology, Coimbatore 641 004, Tamil Nadu, India ' Department of Mathematics, PSG College of Technology, Coimbatore 641 004, Tamil Nadu, India ' Department of Mathematics, PSG College of Technology, Coimbatore 641 004, Tamil Nadu, India

Abstract: This paper analyses a single server batch arrival retrial queue with active breakdowns, two types of repair, a second optional service and multiple vacations with N-policy. The server may breakdown while providing first essential service. When the server fails, it is repaired immediately. On successful completion of first essential service, the customer may opt for second optional service with probability α. At a service completion epoch, without any request for re-service and the orbit size being zero, the server does a secondary job (vacation) repeatedly until the number of customers in the orbit reaches the threshold value N. At a secondary job completion epoch, if the orbit size in at least N, then the server remains in the system to render service for customers from main pool or from retrial group. The steady state queue size distribution of number of customers in the orbit and expected number of customers in the retrial group are obtained. Some particular cases and reliability measures are discussed. Also, some performance measures are obtained. Numerical illustrations are also provided.

Keywords: retrial queues; impatient customers; multiple vacations; server breakdowns; repair; reliability measures; performance measures.

DOI: 10.1504/IJOR.2013.055532

International Journal of Operational Research, 2013 Vol.18 No.1, pp.35 - 61

Received: 21 Jan 2012
Accepted: 29 Jun 2012
Published online: 29 Jul 2014 *

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