Artificial Regeneration for a Two Input Flow G/M/1 Queue with Weibull Interarrivals

We study a G/M/1 queue fed by the superposition of two independent renewal arrival flows with Weibull interarrival times. Classical regeneration at arrivals to an empty system is not available in this model. We construct artificial regeneration by applying exponential splitting to one of the flows and estimate the mean number of customers via regenerative simulation. We provide optimal splitting parameters for the heavy-tailed case with Weibull shape parameter $\beta<1$ and show that no splitting with positive probability exists when $\beta>1$. Numerical experiments illustrate the regeneration frequency and the efficiency of the proposed estimation.