Sharing Resources at Nonuniform Access Rates

We introduce DPPr (for ``Dining Philosophers Problem with rates'') as a generalization of the heavy-load case of the Dining Philosophers Problem (DPP). In DPPr, processes are required to be scheduled to access shared resources with prespecified relative frequencies. DPPr is an abstraction of resource-sharing problems to which the synchronization of some distributed algorithms for neural-network models and the generation of timing signals in asynchronous digital circuits are related. Two fully distributed, synchronous solutions are given for DPPr in this paper. The first solution employs a reduction to heavy-load DPP and after that a distributed scheduling mechanism that has been used to solve this problem with optimal concurrency. The second solution tackles the DPPr instance directly by operating on a multigraph based on that instance. We conclude by indicating how the two synchronous solutions carry over to the asynchronous case.