Mathematica Eterna
Open Access

Abstract

Matrix-Geometric Method for Queueing Model with State- Dependent Arrival of an Unreliable Server and PH Service

M.ReniSagaya Raj and B.Chandrasekar

In this paper, we consider a state-dependent queueing system in which the system is subject to random breakdowns. Customer arrive at the system randomly following a Poisson process with state-dependent rates. Service times follows PH distribution and repair times are exponentially distributed. The server may fail to service with probability depending on the number of customer completed since the last repair. The main result of this paper is the matrix-geometric solution of the steady-state queue length from which many performance measurements of this queueing system like the stationary queue length distribution, waiting time distribution and the distribution of regular busy period, system utilization are obtained. Numerical examples are presented for both cases.