Application of Boolean Functions in Gateways Placement Task with Respect to the Minimum Average Group Response Time Criterion

The paper describes two-level networks of distributed control systems. For such systems group response time of nodes is critical. The average group response time of the nodes distributed across the second level nets was proposed then as an optimization criterion with the assumption that response time of the first level net is much greater than that of the second level nets. The basic task of integer optimization was formulated where variables are gateway coordinates in the second level nets. Each edge of the second level nets and each system task were associated with Boolean variables. The paper then defines constraints on the gateway coordinates and mapping rules of the Boolean variables. The Boolean functions were defined in form of DNFs. It was then shown that the basic task is equivalent to finding minimum weighted term in the obtained DNFs. Example usages of the algorithm were provided.