In an in-home digital network (IHDN) it may be expected that several variable-bit-rate streams (audio, video) run simultaneously over a shared communication device, e.g. a bus. The data supply and demand of most of these streams will not be exactly known in advance, but only a coarse traffic characterization will be available. In this paper we assume that data streams are characterized by a concave function f, which gives a bound on the amount of data supplied for each length of a time window. We show how allocations of the bandwidth of a single bus and of buffers connected to the bus can be obtained for all streams, such that for each stream a feasible transmission strategy exists. For this, we show that a feasible solution for a data supply that exactly follows the function f is sufficient. This problem can then be solved by repeatedly solving single-stream problems for which we present efficient methods.