Fractional Brownian Motion with H < 1/2 as a Limit of Scheduled Traffic

Abstract

In this paper we show that fractional Brownian motion with H &lt; ½ can arise as a limit of a simple class of traffic processes that we call ‘scheduled traffic models’. To our knowledge, this paper provides the first simple traffic model leading to fractional Brownnian motion with H &lt; ½. We also discuss some immediate implications of this result for queues fed by scheduled traffic, including a heavy-traffic limit theorem.