Tail asymptotics of heavy-tailed random sums and its applications to distributed server system

Byeongchan Lee, Jonghun Yoon, Yang Woo Shin, Ganguk Hwang

Abstract: The appearance of heavy-tailedness in users’ traffic significantly de- grades the performance of communication systems, and a distributed server system is considered as a good solution to this problem be- cause of its distributed service characteristic by multiple servers. So we tackle the question in this paper that a distributed server system can alleviate heavy-tailedness, so that users experience good QoS as if there were no heavy-tailedness. To this end, we first mathematically model a distributed server system and obtain a heavy-tailed random sum with the help of the theory of perturbed random walk. We then analyze the tail asymptotic of the heavy-tailed random walk to find a condition with which the distributed server system can alleviate heavy-tailedness.