The variance of departure processes: puzzling behavior and open problems

作者：Nazarathy Yoni^*

来源：Queueing Systems, 2011, 68(3-4): 385-394.

DOI：10.1007/s11134-011-9249-7

• Queueing theory
• Loss systems
• Asymptotic variance rate
• BRAVO

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/pi) 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 coefficients of variations of the inter-arrival and service times.

• 出版日期2011-8