Blocking in a Shared Resource Environment

In recent years, considerable effort has focused on evaluating the blocking experienced by "customers" in contending for a commonly shared "resource." The customers and resource in question have typically been messages and storage space in message storage applications or data streams and bandwidth in data multiplexing applications. The model employed in these studies, a multidimensional generalization of the classical Erlang loss model, has been limited to exponentially distributed storage (or data transmission) times, questions concerning efficient computational schemes have largely been ignored, and the class of resource sharing policies considered has been unnecessarily restricted. The contribution of this paper is threefold. We first show that the state distribution (obtained by previous authors) is valid for the large class of residency time distributions which have rational Laplace transforms. Second, we show that, for the important and commonly implemented policy of complete sharing, a simple one-dimensional recursion can be developed which eliminates all difficulty in computing quantities of interest-regardless of both the size and dimensionality of the underlying model. Third, we show that the state distribution holds for completely arbitrary resource sharing policies.