The increase of HTTP-based video popularity causes that broadband and Internet service providers' links transmit mainly multimedia content. Network planning, traffic engineering or congestion control requires an understanding of the statistical properties of network traffic; therefore, it is desirable to investigate the characteristic of traffic traces generated by systems which employ adaptive bit-rate streaming. Our first contribution is an investigation of traffic originating from 120 client-server pairs, situated in an emulated content distribution network, and multiplexed onto a single network link. We show that the structure of the traffic is distinct from the structure generated by the first and second generation of HTTP video systems, and furthermore, not similar to the structure of general Internet traffic. The obtained traffic exhibits negative and positive correlations, anti-persistence, and its distribution function is skewed to the right. Our second contribution is an approximation of the traffic by ARIMA/FARIMA processes blue and artificial neural networks. As we show, the obtained traffic models are able to enhance the performance of an adaptive streaming algorithm.