Mathematica Eterna
Open Access

Abstract

Matrix-Geometric Method for Queueing Model with Subject to Breakdown and N-Policy Vacations

M.ReniSagaya Raj and B.Chandrasekar

In this paper we present matrix-geometric method for analyzing the N-policy multiple vacation queueing model with server breakdown and repair studied in this paper. The service station, the server is subject to breakdown while in operation. Service resumes immediately after a repair process, and a vacation starts. Arrivals follows a Poisson process with rates depending upon the system rate, namely, vacation, service, or breakdown state. The repair times, time to breakdown follows a repair or vacation. Using quasi-birth death process and matrix-geometry model, we may gain the distribution of the steady-state queue system. Furthermore, we derive the formula of expected queue length and expected waiting period. Finally, numerical example are presented.