Call packing bounds for overflow queues

Finite queueing loss systems are studied with overflow. For these systems there is no simple analytic expression for the loss probability or throughput. This paper aims to prove and promote easily computable bounds as based upon 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 which also leads to a secure lower bound. The call packing bound is also proven to be superior to the standard Erlang bound. Numerical results seem to indicate that the call packing bound is a substantial improvement over the Erlang bound and a quite reasonable first order and secure upper bound approximation. The results thus seem to support a practical usefulness as well as further extension.