On propagation of self-similar traffic through an energy-conserving wireless gateway

It has been well established by now that high-speed wireline traffic exhibits self-similar behavior. Several studies in the past have hypothesized that wireless traffic is also self-similar but without adequate justification. In this paper we study the propagation of self-similarity as self-similar wireline traffic feeds to a gateway that interconnects a wireline to a wireless network. We model the wireline traffic as an on/off process. We propose models for buffering and repacking performed at the gateway. Based on those models and also statistical models for the wireless channel, we study the statistics of the outgoing on/off traffic. We show that when the on and off state durations of the input traffic are both heavy-tail distributed, such as is the case in LAN traffic, the outgoing traffic is self-similar. On the other hand, if the on state durations are heavy-tail distributed but the off state durations have finite variance, such as in variable-bit-rate video traffic, the self-similarity may disappear if the gateway has a buffer much larger than the maximum channel capacity and it operates under an energy conserving protocol.