The variance of departure processes: puzzling behavior and open problems

We consider the variability of queueing departure processes. Previous results have shown the so-called BRAVO effect occurring in M/M/1/K and GI/G/1 queues: Balancing Reduces Asymptotic Variance of Outputs. A factor of (1 ¡ 2=¼) appears in GI/G/1 and a factor of 1=3 appears in M/M/1/K, for large K. A missing piece in the puzzle is the GI/G/1/K queue: is there a BRAVO effect? If so, what is the variability? Does 1=3 play a role? This open problem paper addresses these questions by means of numeric and simulation results. We conjecture that at least for the case of light tailed distributions, the variability parameter is 1=3 multiplied by the sum of the squared coe±cients of variations of the inter-arrival and service times