Video and LAN traffics can be modeled as self-similar processes and the Hurst parameter is a measure of the self-similarity of a process. The purpose of this work is to use this characteristic of Internet traffic allowing future Video on Demand Service Providers (VDSPs) to optimise their bandwidth utilization and consequently their communications cost. The work refers to one aspect of a global project that specifies intelligent agent architecture to manage the relationship among VDSP, Internet Service Providers (ISPs) and end-customers. In this paper, we also discuss the egress traffic aspect of the VDSP and propose a neural network approach to monitor and to estimate the nature of the future Value Added Service Provider (VASP) egress traffic using the Hurst parameter. This approach takes into account the real MPEG (Moving Picture Experts Group) streams in two scenarios: (i) with 13 individual MPEG streams; and (ii) with 6 mixed sequences.Full Text at Springer, may require registration or fee