We consider the M/M/K/S queue as a special but widely applicable finite queueing model. Although there exist formulas for various performance measures in the steady state almost nothing is known about first (monotony) and second-order properties (convexity/concavity) of these measures. In the paper we prove such properties. Then an optimisation problem is defined with parameters K and L = S − K as decision variables. Using the properties of the performance measures a simple algorithm to search for a solution of the optimisation problem is formulated. Numerical examples round off the investigations.
