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In most of the machine repair queueing models, it is assumed that if any failed machine joins the queue, the server will be immediately activated for rendering the service.
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For the performance modeling and queueing analysis of the concerned machine repair problem, the investigation done is organized as follows.
In this investigation, we have developed a finite population queueing model of multi-component machine repair system wherein individual component failure and common-cause failure may occur.
The queue length in the machine repair problem refers the total number of failed machines waiting for repair in the queue including those which are in the process of repair with the server.
In order to examine the system's behavior, the quantitative assessment of the performance measures is the main objective and key component of the performance modeling of any queueing system including the machine repair system.
Jain et al. (2010) also published a survey article on various aspects of machine repair problems by emphasizing the practical importance of Markov queueing models.
The queueing and reliability indices of the machine repair systems with imperfect coverage and reboot have been studied by Jain et al. (2012), Jain (2013), Jain and Gupta (2013), Wang et al. (2013), and many more.
By including the F-policy Kumar and Jain (2013a) developed a queueing model for the performance prediction of the machine repair problems with standbys.
To overcome these problems, many queue theorists have paid attention towards the machine repair problems in different contexts.
Several papers have appeared in queueing and reliability literature which explored various aspects of machine repair problems with standby in different contexts.
In the context of machine repair system, the time-shared systems are the repair facility wherein the technical staff repairs the failed machines on time slicing basic, i.e., by dividing its unit time among all those failed machines which are presently waiting in the queue to be repaired by the repairman.
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