Reliability Analysis of M/G/1 Repairable Queueing System with Multiple Adaptive Vacations and p-Entering Discipline

Jiang Cheng,Yinghui Tang

doi:10.3390/mca19020105

Jiang Cheng, Yinghui Tang

Open Access

https://doi.org/10.3390/mca19020105

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Abstract

This paper considers the reliability of an M/G/1 queue with multiple adaptive vacations in which the arriving customers enter the system with probability p (0＜p≤1) during vacations. Through appropriate assumptions, the model is studied by the total probability decomposition technique and the tool of Laplace transform. Some reliability indices are studied. Moreover, we give some numerical examples to observe the effect of various parameters on the reliability indices.

Highlights

During the past three decades, queueing systems with server's vacations have been studied extensively and applied in many areas such as manufacturing systems, service and computer systems and communication network systems
Most works were concentrated on the study of models of multiple vacations and single vacation
Some researches on the discrete time multiple adaptive vacation queues can be found in Sun [8], Zhang [9], Ma [10], Tang [11] etc

Summary

1.INTRODUCTION

During the past three decades, queueing systems with server's vacations have been studied extensively and applied in many areas such as manufacturing systems, service and computer systems and communication network systems. Some researches on the discrete time multiple adaptive vacation queues can be found in Sun [8], Zhang [9], Ma [10], Tang [11] etc These literatures are mainly concentrated in the researches of the queue indices. Tang a single-server M / G /1queueing system subject to breakdowns—some reliability and queueing problems They didn’t study the case of server vacation. Yu et al [14] investigated some reliability indices in M X / G(M / G) /1 repairable queueing system with adaptive multistage delay vacation They only assumed that the arriving customers enter directly the system with probability 1. Liu and Tang [15] studied some reliability indices in M / G /1 repairable queueing system with p-entering discipline during server vacations, whereas they only considered the cases of vacations.

THE PROBABILITY DISTRIBUTION OF SYSTEM FIRST FAILURE TIME

THE PROBABILITY THAT THE SERVER FAILS AT TIME t

CONCLUSIONS