Mathematrical model of packet routing problem

conference paper

English

Many current control systems for industrial control of manufacturing or production are build as distributed control system. There are used autonomous control systems like programmable logic controllers or other microprocessor based control systems, intelligent sensors, actors and logical inputs/outputs connected together by industrial serial fieldbuses. That control systems can be often connected to a high-level network, which can be accepted as network like Intranet, where are connected workstations, operator stations, database servers and etc. In near future a huge amount of new systems will be based on that scheme. Those systems are going to be larger and more complex, but more difficult and sensitive to faults. Very important problem is to achieve better safety, functionality and reliability. One of subparts to achieve fault-tolerance of a system is to create a mathematical model of packet’s routing in hierarchical decentralized control systems. The mathematical model has to be applicable for solving of optimal routing problem. There are several criterions which are corresponding with a miscellaneous configurations and requests. The formal specification used for mathematical model’s creation has to fill requests for easy and very fast solving of routing problem, because the routing problem is only one of many sub-problems like optimal program module mapping, resources administration, in-time tuning of system and etc., which are generating a huge and complex optimization problem. During last period of research at Department of Control and Instrumentation at Faculty of Electrical Engineering and Communication, Brno University of Technology a graphical models of both decentralized control systems and hierarchical decentralized control systems were developed. The graphical formal models are based on oriented weighted charts with respect to hierarchical structure of the decentralized control system. For solving of optimization problems like optimal routing problem, optimal mapping problem, resources administration, in-time tuning of system and etc. was developed a mathematical model. The mathematical model fully describes abilities of graphical model and is based on mathematical programming. For mathematical description of graphical model we use linear programming and mixed integer linear programming. Used mathematical formalisms are fully corresponding to requests of given problems to solve. Chosen mathematical model is relatively easy to solve and it is well know. Therefore, presented formal specification enables to make model of many decentralized systems.

optimal routing problem, hierarchical control system, balanced load, formal specification of decentralized system, mathematical model

BRADÁČ, Z., ZEZULKA, F.

2002

9. 6. 2002

University of Pardubice

Pardubice

80-7149-452-1

Proc. of the 5th International Scientific - Technical Conference, Process Control 2002

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95

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