论文标题
在关键的GI/G/1队列和Bravo的繁忙时期
On Busy Periods of the Critical GI/G/1 Queue and BRAVO
论文作者
论文摘要
我们在有限的第二次假设下研究关键的GI/G/1队列。我们表明，繁忙的时期分布经常变化，索引一半。我们还回顾了先前已知的M/G/1/和M/M/1衍生物，得出了精确的渐近性以及GI/M/1的类似推导。繁忙的渐进时期决定了更新过程的矩矩计算繁忙周期的增长速度。我们进一步使用它来证明用于工作输出过程的Bravo现象（平衡降低了产出的渐近差异）（即繁忙时间）。这给出了对Bravo效应的新见解。 该论文的第二个贡献是解决先前关于GI/G/1和GI/G/S Bravo的猜想结果。以前，无限的缓冲液通常仅在第四阶假设下定居下来，以及关于繁忙周期的尾巴的假设。在当前论文中，我们通过简化为$ 2+ε$矩的假设来加强先前的结果。
We study critical GI/G/1 queues under finite second moment assumptions. We show that the busy period distribution is regularly varying with index half. We also review previously known M/G/1/ and M/M/1 derivations, yielding exact asymptotics as well as a similar derivation for GI/M/1. The busy period asymptotics determine the growth rate of moments of the renewal process counting busy cycles. We further use this to demonstrate a BRAVO phenomenon (Balancing Reduces Asymptotic Variance of Outputs) for the work-output process (namely the busy-time). This yields new insight on the BRAVO effect. A second contribution of the paper is in settling previous conjectured results about GI/G/1 and GI/G/s BRAVO. Previously, infinite buffer BRAVO was generally only settled under fourth-moment assumptions together with an assumption about the tail of the busy-period. In the current paper we strengthen the previous results by reducing to assumptions to existence of $2+ε$ moments.
