PATTERNS OF BUFFER OVERFLOW IN A CLASS OF QUEUES WITH LONG MEMORY IN THE INPUT STREAM
成果类型：
Article
署名作者：
Heath, David; Resnick, Sidney; Samorodnitsky, Gennady
署名单位：
Cornell University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1997
页码：
1021-1057
关键词：
摘要：
We study the time it takes until a fluid queue with a finite, but large, holding capacity reaches the overflow point. The queue is fed by an on/off process with a heavy tailed on distribution which is known to have long memory. It turns out that the expected time until overflow, as a function of capacity L, increases only polynomially fast; so overflows happen much more often than in the classical light tailed case, where the expected overflow time increases as an exponential function of L. Moreover, we show that in the heavy tailed case overflows are basically caused by single huge jobs. An implication is that the usual GI/G/1 queue with finite but large holding capacity and heavy tailed service times will overflow about equally often no matter how much we increase the service rate. We also study the time until overflow for queues fed by a superposition of k iid on/off processes with a heavy tailed on distribution, and we show the benefit of pooling the system resources as far as time until overflow is concerned.