Recently protocols have been introduced which enable us to integrate periodic traffic (voice or video) and aperiodic traffic (data) and to extend the size of local area networks without any loss in speed and capacity. One of these, the DRAMA protocol, is based on broadband technology and allows for dynamic allocation of bandwidth to clusters of nodes in the total network. In this paper we propose a distributed algorithm to allocate bandwidth in a fair manner, where we have defined fair to mean that every node in the network, regardless of its location, should have the same expected access delay to the net. We show by means of simulation that the algorithm is stable and within a few percentage points of the optimal solution. Stability is measured in terms of the time it takes the system to return to near optimal distribution of the bandwidth after strong disturbances. The algorithm is shown to handle total reallocation of the resources within O(100ms).