A Continuous-Time Stochastic Model for a Single-Server System Susceptible to Random Failures and Repairs

Abstract

A continuous-time stochastic model of a single server queue subject to sudden breakdowns and repairs is proposed․ The system is modelled as a continuous-time Markov chain (CTMC) with two interdependent processes‚ one describing the service process and the other describing the transition process of the service state during breakdown and repair periods․ There are mathematical models for this theory‚ such as state equations‚ probability generating functions (PGF)‚ transient states‚ steady states‚ availability measures‚ failure rates‚ MTTF‚ MTTR‚ server performance‚ and queueing․ In addition‚ there are more advanced reliability parameters such as hazard rate‚ asymptotic failure rate‚ and sensitivity functions that can be acquired from the reliability models․ Data indicate how server failure signals can be used to limit network congestion‚ ensure reliability‚ and guarantee availability․