Fluid Queues with Heavy-Tailed M/G/∞ Input
研究了由多个重尾会话长度的M/G/∞输入过程驱动的流体队列，推导出稳态工作负载分布的精确渐近行为，并得到瞬态分布的渐近结果，用于条件极限定理。
We consider a fluid queue fed by several heterogeneous M/G/∞ input processes with regularly varying session lengths. Under fairly mild assumptions, we derive the exact asymptotic behavior of the stationary workload distribution. In addition, we obtain several asymptotic results for the transient workload distribution, which are applied to obtain a conditional limit theorem for the most probable time to overflow. The results are strongly inspired by the large-deviations idea that overflow is typically due to some minimal combination of extremely long concurrent sessions causing positive drift. The typical configuration of long sessions is identified through a simple integer program, paving the way for the exact computation of the asymptotic workload behavior. The calculations provide crucial insight in the typical overflow scenario.