Kim, Young B.Makowski, Armand M.Under most system assumptions, closed form solutions of performance measures for input queueing crossbar switches are not available. In this paper, we present expressions and bounds for the derivatives of cell loss probabilities with respect to the arrival rate evaluated at a zero arrival rate. These bounds are used to give an approximation by Taylor expansion, thereby providing an economical way to estimate cell loss probabilities in light traffic.en-USqueueing networksIntelligent Signal ProcessingCommunications SystemsTechnical Report