Title: Mathematical modelling of breakdowns with soft failures and explicit analytical expressions of an M/M/1 queue's transient state probabilities

Authors: B. Janani

Addresses: Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India

Abstract: In the last decade, the increasing usage of digital electronics and software has given rise to a new form of failure occurrence known as soft failure. Soft failure is not the same as catastrophic failure. Catastrophic failure removes all waiting customers, including those receiving service, and the system enters the repair state, whereas soft failure does not require the removal of customers and instead requires the customer to wait for the server reactivation because repair can be accomplished by simply rebooting the system. A new approach for categorising and analysing these events is necessary to characterise and distinguish soft failures from hardware catastrophic failures. As a result, this paper considers a single server queueing model with soft failure. The system is prone to random breakdowns while providing service to the customer. When a system malfunctions, repair work begins right away. During the repair period, new customers are not permitted to join the system. For the first time, the transient state probabilities of an M/M/1 queue with soft failures are computed explicitly. Some performance metrics, such as availability and reliability, are derived. Numerical examples are also provided to demonstrate the effect of parameters.

Keywords: random breakdown; soft failure; hard failure; time dependent probabilities; Laplace transform; generating function.

DOI: 10.1504/IJMMNO.2023.127836

International Journal of Mathematical Modelling and Numerical Optimisation, 2023 Vol.13 No.1, pp.19 - 33

Received: 30 Dec 2021
Accepted: 02 May 2022
Published online: 19 Dec 2022 *

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