In this article, we study machine repair problems (MRP) consisting of the finite number of operating machines with the provisioning of the finite number of warm standby machines under the care of a single unreliable server. For the machining system’s uninterrupted functioning, an operating machine is immediately replaced with the available warm standby machine in negligible switchover time whenever it fails. The concept of threshold vacation policy: N-policy is also considered. Under this vacation policy, the server starts to serve the failed machines on the accumulation of a pre-specified number of failed machines in the system. The server continues until the system is empty from the failed machines; after that, the server goes for vacation. The notion of an organizational delay, server breakdown, and repair in multiple phases is also conceptualized to build the studied model more realistic. The recursive matrix method is used to find steady-state queue size distribution, and subsequently, various system performance measures are also developed to validate the studied model. The optimal analysis has been performed to identify the critical design parameters for the governing model. The state-of-the-art of the present study is its mathematical modeling of the multi-machine stochastic problem with varied limitations and strategies. The methodology to obtain queue size distribution, optimal design parameters, is beneficial for dealing with other complex and sophisticated real-time machining problems in the service system, computer and communication system, manufacturing and production system, etc. The present problem is limited to fewer machines, which can be extended to more machines with different topologies with high computational facilities.
This paper is dedicated to the study of a machining system with standby provisioning, feedback and working vacation policy of the server. The failed machines are permitted by the server in the system according to the FCFS discipline. If no failed machines are found by server, it goes on vacation. But instead of stopping the service altogether, it still operates on a slow service and this process is said to be server's working vacation. When all the standby units are in use, failure of units occur in a degraded mode. The concept of feedback policy is also considered wherein customer (machine) getting service is unsatisfied with the services and wishes to rejoin the system as a feedback customer (machine) or leaves the system. Customer who wishes to provide feedback (unsatisfied customer) can join the queue at the back. The Markov process concept is utilized to present the differential-difference equations of the queuing model. The failure and repair rate of units in machining system is exponentially distributed. Various performance characteristics have been derived. Cost optimization function is evolved for getting the optimal operating conditions. The well-known meta-heuristic technique, particle swarm optimization (PSO) is implemented for obtaining the ideal operating conditions at minimum estimated cost including economic performance. Lastly, numerical results are described related to the studied model through tables and graphs.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.