Title: A study on phases of service and multi-vacation policy in a non-Markovian queuing system

Authors: S. Maragathasundari; S. Kishore Eswar; R.S. Somasundaram

Addresses: Department of Mathematics, Kalasalingam Academy of Research and Education (Deemed to be University), Anand Nagar, Krishnankoil-626126, Tamilnadu, India ' Department of Mechanical Engineering, Kalasalingam academy of Research and Education (Deemed to be University), Anand Nagar, Krishnankoil-626126, Tamilnadu, India ' Department of Computer Applications, Coimbatore Institute of Technology, Coimbatore-641014, Tamilnadu, India

Abstract: This paper manages the queuing issue of various vacation policies. Clients showing up in clumps follow a Poisson distribution. Administration, on the other hand, follows a general distribution, rendered in two phases in which the second phase of administration is discretionary. Here, during the vacation period, the support work of the server is completed. Also 'get-away' is presented in two classifications, viz. compulsory vacation and broadened vacation, both following general conveyance. Expanded vacation is regarded to have two phases, in which the second phase of broadened get-away is of the server's decision. Set up time arrange is presented on the early stage of expanded vacation and with the idea of reneging occurring during the second phase of broadened vacation. The issue is solved by strengthening the variable technique and queue measures with the force parameter, mean inactive time, mean number of clients, and mean waiting time in the queue, determined in the system. The paper contains the numerical depiction and graphical appraisal that supports the model.

Keywords: multi vacation; composite materials; reneging; extended vacation; two stages of service.

DOI: 10.1504/IJMOR.2022.122809

International Journal of Mathematics in Operational Research, 2022 Vol.21 No.4, pp.444 - 465

Received: 28 Jul 2020
Accepted: 02 Feb 2021
Published online: 12 May 2022 *

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