A controllable hybrid queueing system consists of a system controller and two nodes in tandem of the type M/M/ni. Customers arrive to the controller who allocates them between the nodes. After service completion at node 2 the controller can allocate the customer waiting at node 1 to node 2. With probability p after a service completion at node 1 a failure occurs. In this case the customer from node 1 joins node 2. With complement probability 1 − p the service completion at node 1 is successful. For the given cost structure we formulate an optimal allocation problem to minimize the longrun average cost per unit of time. Using dynamic-programming approach we show the existents of thresholds which divides the state-space into two contiguous regions where the optimal decision is to allocate the customers to node 1 or to node 2. Some monotonicity properties of the dynamic-programming value function are established.

В работе рассмотрен подход к моделированию управления системой с использованием среды схем радикалов. Приведено описания состояний системы в пространстве и времени. Обозначена проблема выбора оптимального способа решения задачи управления системой при учете пространства и времени.

While the problem of hierarchical menu design is very common in user interface design, existing approaches lack either semantic aspects or optimization techniques. We suggest a semantic-aware mathematical model of hierarchical menu optimization and algorithms developed on the basis of this theory. These algorithms are implemented in the ready-to use design tool. The approach is illustrated by optimization of a banking voice menu. Original Russian Text © A.I. Danilenko, M.V. Goubko, 2012, published in Problemy Upravleniya, 2012, No. 2, pp. 38–44. Первоначальный русский текст опубликован в журнале "Проблемы управления", № 2, 2012, С. 38-44 и доступен по адресу http://www.mtas.ru/search/search_results.php?publication_id=18742