相関をもつランダムウォークの極限分布の漸近的性質と待ち行列モデルへの応用

抄録

It is well known that, under fairly general conditions, the waiting time distribution of Markovian queueing systems decays exponentially fast. This property is used to estimate or approximate very small cell loss probability of high-speed information/communication networks. It has been reported, however, that the input traffic of the recent LAN and WAN are observed to have stronger correlation which can result in longer tail of a waiting time distribution. In this article, we describe how the correlation structure of the input traffic affect the tail behavior of the waiting time distributions. To unify the explanations, we investigate the correlated random walks that are frequently encountered in the analysis of queueing phenomena.