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

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In this paper we show that fractional Brownian motion withH< 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 withH< ½. We also discuss some immediate implications of this result for queues fed by scheduled traffic, including a heavy-traffic limit theorem.