School of Information Engineering Yangzhou University Yangzhou, China

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Abstract—Tasks scheduling is a key problem in multi-agent system, traditional tasks scheduling methods can’t be applied to new application areas of the MAS such as emergency system. In order to apply the Agent method to these new areas, a multi-agent system model is built in this paper, and corresponding task schedulable problem and maximum scheduling problem are defined based on this multi-agent system model. Task schedulable problem is modeled using flow network, and it is proved that maximum flow algorithm can be used to solve such problem, which means the problem can be solved in polynomial time. Furthermore, by analyzing the flow network model, a necessary and sufficient condition which can be used to determine whether tasks can be scheduled is gained and proved. Three approximation algorithms have been proposed to solve the maximum scheduling problem. The experiment results show that all above algorithms can get pretty solutions in solving maximum scheduling problem, and the approximation ratio for optimal solution of these approximation algorithms are all larger than or equal to 0.5 even though the resource ratio is very low.

Index Terms—task scheduling, task schedulable problem, maximum task scheduling problem, MAS, flow network, NP complete

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Cite: Bin Li, Xiaowei Zhang, Jun Wu, Junwu Zhu, "Task Schedulable Problem and Maximum Scheduling Problem in a Multi-agent System," Journal of Software vol. 6, no. 11, pp. 2225-2231, 2011.