As one of the technologies for the retrieval of desired contents over large-scale networks, multi-agent systems are receiving much attention. Since there are too many contents on the network to search them all exhaustively, some applications on multi-agent systems have time constraints, that is, they must obtain a result by a given deadline. To find better results 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 round robin scheduling disciplines do not take time constraints into account. Therefore, agents are likely to miss their deadlines on many nodes. In this paper, we propose an efficient agent-dispatching method for time-constrained applications. This method decides creation and migration of a clone agent according to the estimated value of the number of agents that would have completed their tasks by the deadline. The results of our performance evaluation show that the proposed method increases the number of agents that complete their tasks.