Self-Similar Traffic and Buffer Overflow: A Bounded Buffer Allocation Approach

Long range dependence (LRD) in network traffic is known for sometime. Numerous efforts have been made to model and analyze effect of such traffic on user experience, resource management etc. Buffer management is one of the key element of such resource management. It has long been established that LRD traffic causes higher buffer overflow probability and number of studies confirms this. Although, many models have been proposed for predicting such overflow probability, less attempts have been made in utilizing such behaviour of network traffic for better management of buffer. In this paper we show that any process which can not look into the future and decide about its strategy, satisfies semimartingle property. Further, such a process behaves as a local martingle when they are considered within smaller time periods with bounded operating domain. On the other hand, fractional Brownian Motion (fBM) is known for its persistent self-similarity with ability to look into the future based on present performance. This immediately forces loss of semimartingle property and in turn allows one to devise an algorithm for buffer allocation. In this paper we propose one such algorithm where the buffer allocation strategy is allowed to review its decision depending on its performance during last period. We show that such strategy works well guaranteeing lower bound on free buffer availability provided the driving process is LRD.