Applied Probability Trust (1 April 2011) FRACTIONAL BROWNIAN MOTION WITH H < 1=2 AS A LIMIT OF SCHEDULED TRAFFIC

This paper shows that fractional Brownian motion with H < 1=2 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 < 1=2: We also discuss some immediate implications of this result for queues fed by scheduled traffic, including a heavy-traffic limit theorem. 1