In this work we address the problem of supporting the QoS requirements for applications while efficiently allocating the network resources. We analyse this problem at the source node where the traffic profile is negotiated with the network and the traffic is shaped according to the contract. We advocate VBR renegotiation as an efficient mechanism to accommodate traffic fluctuations over the burst time-scale. This is in line with the Integrated Service of the IETF with the Resource reSerVation Protocol (RSVP), where the negotiated contract may be modified periodically. In this thesis, we analyse the fundamental elements needed for solving the VBR renegotiation. A source periodically estimates the needs based on: (1) its future traffic, (2) cost objective, (3) information from the past. The issues of this estimation are twofold: future traffic prediction given a prediction, the optimal change. In the case of a CBR specification the optimisation problem is trivial. But with a VBR specification this problem is complex because of the multidimensionality of the VBR traffic descriptor and the non zero condition of the system at the times where the parameter set is changed. We, therefore, focus on the problem of finding the optimal change for sources with pre-recorded or classified traffic. The prediction of the future traffic is out of the scope of this thesis. Traditional existing models are not suitable for modelling this dynamic situation because they do not take into account the non-zero conditions at the transient moments. To address the shortfalls of the traditional approaches, a new class of shapers, the time varying leaky bucket shaper class, has been introduced and characterised by network calculus. To our knowledge, this is the first model that takes into account non-zero conditions at the transient time. This innovative result forms the basis of Renegotiable VBR Service (RVBR). The application of our RVBR mathematical model to the initial problem of supporting the applications' QoS requirements while efficiently allocating the network resources results in simple, efficient algorithms. Through simulation, we first compare RVBR service versus VBR service and versus renegotiable CBR service. We show that RVBR service provides significant advantages in terms of resource costs and resource utilisation. Then, we illustrate that when the service assumes zero conditions at the transient time, the source could potentially experience losses in the case of policing because of the mismatch between the assumed bucket and buffer level and the policed bucket and buffer level. As an example of RVBR service usage, we describe the simulation of RVBR service in a scenario where a sender transmits a MPEG2 video over a network using RSVP reservation protocol with Controlled-Load service. We also describe the implementation design of a Video on Demand application, which is the first example of an RVBR-enabled application. The simulation and experimentation results lead us to believe that RVBR service provides an adequate service (in terms of QoS guaranteed and of efficient resource allocation) to sources with pre-recorded or classified traffic.