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

V. F. Araman, and P. W. Glynn

Journal of Applied Probability, vol. 49, 710-718 (2012)

This paper shows that fractional Brownian motion with H<12 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<12. We also discuss some immediate implications of this result for queues fed by scheduled traffic, including a heavytraffic limit theorem.