Title: Variant working vacation Markovian queue with second optional service, unreliable server and retention of reneged customers

Authors: Vijaya Laxmi Pikkala; Girija Bhavani Edadasari

Addresses: Department of Applied Mathematics, Andhra University, Visakhapatnam, India ' Department of Applied Mathematics, Andhra University, Visakhapatnam, India

Abstract: In this paper, a variant working vacation queueing system with second optional service, unreliable server, and retention of reneged customers is studied. This model has potential applications in tele-services, banks, manufacturing processes, etc. The expressions of the steady-state probabilities and the system sizes when the server is in different states are obtained using probability generating functions. This paper also discusses an optimisation problem under a given cost structure. Direct search method and quadratic fit search method (QFSM) are applied to obtain the optimum number of working vacations and optimum service rates during regular busy period and working vacation period, respectively.

Keywords: first essential service; FES; second optional service; SOS; working vacation; unreliable server; reneging; retention.

DOI: 10.1504/IJMOR.2021.115447

International Journal of Mathematics in Operational Research, 2021 Vol.19 No.1, pp.45 - 64

Received: 13 Dec 2019
Accepted: 01 Feb 2020
Published online: 02 Jun 2021 *

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