Title: Analysis of batch arrival single server queue with random vacation policy and two types of general heterogeneous repeated service

Authors: Priyanka Kalita; Gautam Choudhury

Addresses: Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Guwahati-781035, Assam, India ' Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Guwahati-781035, Assam, India

Abstract: This article deals with batch arrival single server queue with random vacation policy and two types of general heterogeneous repeated service. We have obtained some explicit expressions for steady-state queue size distribution at service completion point and steady-state system size probabilities. Some significant measures such as mean system size, Laplace-Stieltjes transform of waiting time and its corresponding mean value have also obtained for the system. An optimal cost policy has been developed regarding the average cost function to determine the optimum mean service time of type 1 and type 2 services.

Keywords: M^X/G/1 queue; random vacation policy; RVP; optional repeated service; embedded Markov chain; Markov regenerative process; MRGP cost optimal policy.

DOI: 10.1504/IJOR.2021.118997

International Journal of Operational Research, 2021 Vol.42 No.2, pp.131 - 162

Received: 19 Apr 2018
Accepted: 09 May 2019
Published online: 16 Nov 2021 *

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