Multi-Channel Bi-Level Heterogeneous Servers Bulk Arrival Queueing System with Erlangian Service Time

An easily applicable algorithm to solve problems involving bulk-arrival queues with a breakdown of one of the heterogeneous servers in case of steady state is introduced. A Monte Carlo study for numerically finding the limiting distribution of the number in the system for the bulk arrival, multi-server queueing model (M[x]/EK/C; C-1/FCFS) with heterogeneous servers is presented. The system consists of servers of varying efficiency. This paper presents multi-channel queue with Poisson arrivals, Erlangian service time distributions in which all servers have equal breakdown chance. Measures of system performance including mean queue length, mean waiting time, and blocking probability are reported. Numerical results are obtained by simulation of the entire system. Examples of extensive numerical results for certain measures of efficiency are presented in tabular and chart form. In all cases, the proposed method is computationally efficient, accurate and reliable for both high and low values of the model parameters.