Steady state analysis and transient solution of an M/M/2 queueing system with differentiated vacations and breakdown

Abstract

A heterogeneous two-server queueing system with differentiated vacations and server failures is examined in this paper. The matrix geometric method was applied to identify the system's stationary condition by analyzing the steady-state probability distribution of customer numbers, modeled as a quasi-birth-and-death (QBD) process. A few metrics regarding system performance are acquired. Graphs and tables illustrate how parameters affect performance metrics. Transient numerical analysis is given for the proposed model using RK method.