Title: MAP/PH(1), PH(2)/2 finite retrial inventory system with service facility, multiple vacations for servers

Authors: C. Suganya; B. Sivakumar

Addresses: Department of Mathematics, T.K.S. College of Arts and Science, Theni, Tamilnadu, India ' School of Mathematics, Madurai Kamaraj University, Madurai, Tamilnadu, India

Abstract: In this paper, we consider a retrial (s, S) inventory system with multiple server vacations for two heterogeneous servers. We have assumed that the customers arrive according to a Markovian arrival process and two parallel servers who provide heterogeneous phase type services to customers. The lead times for the orders are assumed to have independent and identical exponential distributions. The vacation times of both servers are assumed to be independent and identically distributed exponential random variables. The arriving customer who finds both servers are busy or both servers are on vacation, joins an orbit of finite size. These orbiting customers retry for their demand after a random time, which is assumed to be exponential distribution. Some important performance measures are obtained and the optimality of an expected total cost rate is shown through numerical illustration.

Keywords: service facility; heterogeneous servers; multiple vacations; retrial customers.

DOI: 10.1504/IJMOR.2019.102075

International Journal of Mathematics in Operational Research, 2019 Vol.15 No.3, pp.265 - 295

Accepted: 25 Mar 2018
Published online: 06 Sep 2019 *

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