Comparing some Monte Carlo methods through a single server queue subject to catastrophes with control and batch service under multiple vacations

This paper considers a single server queue subject to catastrophes with service lateness which consists on control and service, in batch of fixed-size. Catastrophes can occur when the server is on service, or on vacation. Whenever a catastrophe occurs, all customers present in the system are destroyed immediately and the server goes for multiple vacations until it finds at least a batch of K customers in the queue, at which point the control period of this batch begins in the service lateness. After completion of the control time, this batch enters the service immediately. This proposed model is solved by giving explicit formulas for the steady-state probabilities and some performance measures. Numerical results are sketched out to illustrate the effect of the system parameters on the main performance measures. In addition, a Monte Carlo simulation is performed using three sampling methods to manage the proposed model with large batches. We used the generators “rand”, “goLHS” and “goRDS” to sample the inputs for the simulation. The results have shown that RDS improves significantly the studied performance measures of the queue compared to the Monte Carlo method and LHS by considering the variance reduction and the relative error as comparison criteria.