Blocking with retrials in a completely shared resource environment.

*(English)*Zbl 0762.90026Summary: The classical Erlang blocking model has been generalized by many workers to permit multiple customer types, each with its own resource and mean residency requirements, and this generalized model has been extensively used to analyze multiplexing, message store and communication network performance, to name only three of its many applications. In this paper, we modify this important model to permit blocked requests to retry, with reduced resource requirements and arbitrary mean residency requirements. Our motivation for studying this model 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 or originally requested.

Because this modification of the generalized Erlang model destroys the product-form structure, and greatly increases the size of the state space, an exact solution is out of the question. Our 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. Moreover, the basic framework can be easily modified to handle a number of important variants including multiple retries and state dependent resource and residency requirements.

Because this modification of the generalized Erlang model destroys the product-form structure, and greatly increases the size of the state space, an exact solution is out of the question. Our 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. Moreover, the basic framework can be easily modified to handle a number of important variants including multiple retries and state dependent resource and residency requirements.

##### MSC:

90B18 | Communication networks in operations research |