An Analysis of Queueing Model with a Multiple System Governed by a Quasi-Birth Death Process and PH Service and PH Repair

M. Reni Sagaya Raj, B. Chandrasekar

Abstract: In this paper we study the multiple systems of repair problem and present N-system with one working and the other systems are in repair, in standby or waiting repair. When the working system can fails it goes to repair and instantaneously a standby system becomes the working one. Standby system stands to system when the original system is on under repair. The systems are repair following the arrival order. We let the time between service and repair times have phase-type distribution. The working system has a life time governed by a phase-type distribution. We show the process that governs the system is a quasi-birth and death process, we perform steady state analysis of this model. A numerical example is presented and the expressions calculated through the paper are computationally implemented using the Matlab programme

Keywords: Repairman problem, Phase-type distribution, Quasi-Birth and death process, Matrix Geometric Method, Conditional probability of failure, Stationary distribution