Performance Analysis of Machine Repair System with Balking, Reneging, Multiple Working Vacations and Two Removable Servers Operating under the Triadic (0,Q,N,M) Policy

Teketel Ketema

doi:10.7176/isde/11-4-03

Abstract

The main purpose of this paper is to investigate the performance analysis of machine repair problem with impatient customers. A population size of operating machines is considered and the failed machines are assumed to be repaired under the multiple working vacations and triadic policy. As soon as the system becomes empty, both servers leave for working vacations wherein only one of the two servers provide a service during the vacation. Steady state probabilities that describe the number of failed machines in system are derived and taken in closed form. Different performance measures of the system are developed and analysed with numerical illustrations to investigate the reliability of the model. Keywords: machine repair problem, multiple working vacations, triadic Policy, balking, reneging, steady state probability DOI: 10.7176/ISDE/11-4-03 Publication date: August 31 st 2020

Highlights

The interaction of human and machine with industrial plants and other dynamic technical systems is nowadays essential for the quality and efficiency of the performance
Impatient customers of a machine repair system with multiple working vacations and triadic (0, ) policy is considered for the first time
At a working vacation completion epoch, if the system size is or above, both servers will switch to a regular busy period and start working under the triadic(0, ) policy; otherwise, they will take another working vacations as often as necessary until the system size is or above at a vacation termination epoch

Summary

Introduction

The interaction of human and machine with industrial plants and other dynamic technical systems is nowadays essential for the quality and efficiency of the performance. Even if a customer does not balk and joins a queuing system, it is possible that the customer gets impatient and departs from the system without having completed the act of receiving service Such impatient behaviour is known as reneging. Wang et al (2015) studied a machine repair problem with balking and reneging with general inter-arrival and service time distribution. Impatient customers of a machine repair system with multiple working vacations and triadic (0, , , ) policy is considered for the first time. Only one of the two servers will be active and serve the arriving failed machines at a different rate, generally lower than the regular service rate. At a working vacation completion epoch, if the system size is or above, both servers will switch to a regular busy period and start working under the triadic(0, , , ) policy; otherwise, they will take another working vacations as often as necessary until the system size is or above at a vacation termination epoch

Description of the model

Analysis of the Model

Performance Measures of the Model

Conclusion