Simple bounds and monotonicity results for finite multi-server exponential tandem queues

Simple and computationally attractive lower and upper bounds are presented for the call congestion such as those representing multi-server loss or delay stations. Numerical computations indicate a potential usefulness of the bounds for quick engineering purposes. The bounds correspond to product-form modifications and are intuitively appealing. A formal proof of the bounds and related mono tonicity results will be presented. The technique of this proof, which is based on Markov reward theory, is of interest in itself and seems promising for further application. The extension to the non-exponential case is discussed. For multi-server loss stations the bounds are argued to be insensitive. Keywords: Tandem queues, product form, call congestion, bounds, monotonicity results, Markov chains.