This work addresses the resource sharing problem in broadband communication networks that can guarantee some quality of service (QoS), and develops some results about data source and traffic modelling, especially in aspects of model testing and parameter estimation. The multiplexing of variable bit rate (VBR) sources poses a mathematical and statistical problem: the estimation of the resource requirements of a source or set of sources. The estimation method shall be simple enough to be practically implemented in the connection acceptance control (CAC) function. In this paper, the VBR video sources are taken as a typical case of variable rate, with real-time constraints. This association of requirements makes the case especially interesting. A Markov model is assumed for the VBR sources. The validity of such models is under research, they seem to be appropriate at least in certain time scales. The model is tested against real video traces. In order to estimate the resource allocation or channel occupation of each source, the concept of equivalent bandwidth proposed by Kelly [Notes on effective bandwidth, in: F.P. Kelly, S. Zachary, I.B. Ziedins (Eds.), Stochastic Networks: Theory and Applications, Oxford University Press, Oxford, 1996, pp. 141] is used, it is based on a consistent mathematical theory, and has proven to be robust and useful for technical applications. A calculation of the equivalent bandwidth of a Markov source, given its parameters, can be found in the literature [IEEE ACM Trans. Networking 1 (4) (1993) 424]. But in fact, one can only estimate model and parameters. In this work, an estimation of the equivalent bandwidth is given, which can be obtained from real data. The convergence and the consistency of the estimation are studied, and practical bounds are found. Illustrative calculations are performed from real video traces that were obtained using a software MPEG coder, developed by the authors. The mathematical and statistical results are valid for whatever phenomenon that can be modelled as a Markov process.