Analysis of Heterogeneous Two Server Queueing System With Multiple Working Vacations and Server Breakdowns

Abstract

The steady state analysis and the time-dependent behaviour of a heterogeneous two-server multiple vacation queueing model is examined in this research work. The model also takes into account the possibility of a breakdown happening when server 1 is busy while server 2 is on working vacation and both servers are busy, with the restoration procedure starting right away. The stability condition is established through the use of matrix geometric technique, and the steady-state probability vector of the system’s number of customers has been evaluated as a quasi-birth and death (QBD) process. Some system performance measures are obtained. Numerical analysis for both steady-state and transient analysis are given to our proposed model.