Many real-life phenomena, such as computer systems, communication networks, manufacturing systems, supermarket checkout lines can be represented by means of queueing models. The queues with a controller may considerably improve the system performance by reducing queue lengths, or increasing the throughput, or diminishing the overhead. In this book, the essential work consists in designing controlled queueing systems with heterogeneous servers and investigation of their optimal control properties. This type of queues take into account many practical aspects in modelling real systems, e.g. network nodes with servers supplied by different types of processors as a consequence of system updates, nodes in telecommunication network with links of different capacities, etc, which should satisfy the demands for quality of service. For two types of optimization criterion (the model without penalties and with set-up costs) a class of controlled queues with Markov Arrival Process and heterogeneous Phase-Type service time distributions is defined. We derive some monotonicity relations for the dynamic programming value function and show that the optimal policy is of threshold type.

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