Title: Performance of batch service queue model with second optional service, repairable breakdown and standby server

Authors: P. Vijaya Laxmi; Andwilile Abrahamu George; Hasan Abdulkader Qrewi

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

Abstract: In this paper, we investigate the performance of batch service queue model with second optional service, repairable breakdown and warm standby server. Both primary operating and warm standby servers provide First Essential Service (FES) and Second Optional Service (SOS) to customers, wherein FES is all arriving customers and only some of them may further request the SOS. The service times, failure times and repair times of both primary operating and warm standby server are assumed to follow exponential distributions. We use Runge-Kutta method to obtain the transient state probabilities and matrix-decomposition method to obtain the steady-state probabilities of the model. Also, a cost model is presented to determine the optimal service rates so that the expected cost is minimised. Finally, the effect of the model parameters on the system behaviour is demonstrated through numerical results and discussions.

Keywords: batch service queue model; first essential service; second optional service; repairable breakdown; standby server.

DOI: 10.1504/IJRS.2022.128611

International Journal of Reliability and Safety, 2022 Vol.16 No.1/2, pp.46 - 73

Received: 05 Mar 2022
Received in revised form: 23 Jun 2022
Accepted: 15 Aug 2022
Published online: 30 Jan 2023 *

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