Queueing Systems 46, 389–407, 2004  2004 Kluwer Academic Publishers. Manufactured in The Netherlands. Optimal Control of Queueing Systems with Heterogeneous Servers ∗ V. RYKOV rykov@rykov.ins.ru; vrykov@kettering.edu Russian State University of Oil & Gas, Rusia, and Kettering University, Flint, USA D. EFROSININ efrosinin@info04.uni-trier.de Russian Peoples’ Friendship University, Moscow, Rusia, and Trier University, Trier, Germany Received 1 November 2002; Revised 10 March 2003 Abstract. An optimal policy to minimize the queue length in a multi-server controllable queueing system with heterogeneous servers has a threshold property, and it uses the fastest server if necessary (see [8] and [17]). This study gives a numerical description of optimal policies that minimize the operational cost for such a system. Keywords: controllable queueing systems, monotonicity of optimal policies, numerical analysis 1. Introduction This paper is an extended version of the talk given at the International Seminar on Ap- plied Stochastic Models and Information Processes in Karelia In Fall 2002 dedicated to the memory of Professor Vladimir V. Kalashnikov. Scientific interests of V. Kalashnikov were very diverse and included reliability theory, queueing theory, actuarial and finance mathematics, theory of simulation, etc. In his investigations he also used and devel- oped various methods such as Markov, semi-Markov, regenerative processes, coupling, geometric summation, simulation methods, etc. Along with his own investigations Vladimir devoted mach forces and time to is- sueing mathematical monographs in Russian. With his participation as translator or edditor many remarkable books were issued in Russian and among them the book of H. Mine and Sh. Osaki Markovian Decision Processes. Together with the previously translated first book on this topic, the monograph of R. Howard Dynamic Program- ming and Markov Processes this one essentially stimulated the investigation of Decision Markov Processes and its applications in Russia. The present paper was also influenced by these monographs. ∗ The paper was partially supported by the RFFI Grant No. 01-07-90259.