Blocking in a completely shared resource environment with state dependent resource and residency requirements

The generalized Erlang blocking model has been used to analyze multiplexing, message storage, and communication network performance. The author modifies this model to permit blocked requests to retry, with reduced resource requirements and arbitrary mean residency requirements. Because the modification of the generalized Erlang model destroys the product-form structure and greatly increases the size of the state space, and exact solution is out of the question. The present approach modifies a well-known one-dimensional recursion developed for the generalized Erlang model in an intuitively satisfying manner, and results in an approximation scheme that is both efficient and quite accurate. This study arose in the context of high-speed networks in which high bandwidth but non-real-time messages may, upon being blocked, request service with smaller bandwidth and larger residency time, as long as the bandwidth-residency time product is the same as originally requested