Controlled Arrival Machine Repair Problem with Working Vacation and Reattempts

Amita Bhagat,Rachita Sethi,Deepika Garg

doi:10.33889/ijmems.2021.6.1.018

Amita Bhagat, Rachita Sethi + Show 1 more

Open Access

https://doi.org/10.33889/ijmems.2021.6.1.018

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Abstract

This paper addresses machine repair problem (MRP) with M identical operating machines and control arrival policy. The server is unreliable, and can break down during service which is further repaired soon so as to avoid interruption with the service process. The server may go for working vacation in case all the customers are served. The transient analysis of machine repair problem has been done using numerical technique. Various performance measures have been derived. With the help of tables and graphs the numerical results have been shown. The present investigation find applications in various industrial and workshop situations like Automobile repair shop (ARS).

Highlights

Machining system is of great importance for human beings
The state transition diagram for concerned machine repair model is given by Figure 1, which readily explains the functioning of the model and various policies
Machine repair problem holds a significant place with variety of realistic applications associated to their modelling and so their investigations

Summary

Introduction

Machining system is of great importance for human beings. The failure of machining system is quite common and has impact on productivity of the system. Many researchers have analysed queueing models with working vacation owing to its significance in machining environment, computer networks etc. According to this control policy, the arrival of the machines requiring services is stopped if total capacity has been achieved This arrival is again initiated only if the number of machines in the queue have been reduced to threshold value, say F after being served. The service rates basically follow exponential distribution with rates as b and V during busy period and working vacation state respectively. The repair process follows exponential distribution with rates and 1 corresponding to the rupture of system during the normal busy period and working vacation period respectively. The state transition diagram for concerned machine repair model is given by Figure 1, which readily explains the functioning of the model and various policies

Application to Automobile Repair Shop (ARS)

Model Formulation

Reliability and Queueing Measures

State Probabilities

Conclusions