As one of the technologies for retrieval of desired contents over large scale networks, multi-agent systems receive much attention. Since there are too many contents on the network to search all the contents exhaustively, some applications on multi-agent systems have time constraint, that is, they have to obtain a result by the given deadline. In order to find a better result for such applications, it is important for the agents to complete their tasks on as many nodes as possible by the deadline. However, most existing agent systems using Processor Sharing as scheduling discipline do not take time constraint into account. Therefore, agents are likely to miss their deadlines on many nodes. In this paper, we propose an efficient agent dispatching method of time constraint applications. This method decides creation and migration of a clone agent according to the estimated value of the number of the agents that would have completed their tasks by the deadline. The results of the performance evaluation show the proposed method improves the number of agents that have completed their task.