Call packing bound for overflow loss systems

Finite loss queues with overflow naturally arise in a variety of communications structures. For these systems, there is no simple analytic expression for the loss probability. This paper proves and promotes easily computable bounds based on the so-called call packing principle. Under call packing, a standard product form expression is available. It is proven that call packing leads to a guaranteed upper bound for the loss probability. In addition, an analytic error bound for the accuracy is derived. This also leads to a secure lower bound. The call packing bound is also proven to be superior to the standard loss bound. Numerical results seem to indicate that the call packing bound is a substantial improvement over the standard loss bound and a quite reasonable upper bound approximation. The results seem to support a practical usefulness. Keywords: Overflow; Call packing; Finite loss queues; Product-form model