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Many applications of existing grid systems are usually deployed on grid nodes in a static manner. Grid computing nodes with highly demanded applications deployed on are always busy; while the others are idle. If these applications could be dynamically deployed on idle nodes, the system performance would be greatly improved. However, the overhead (e.g., package download) caused by dynamic deployment in existing studies may be so much that the system performance is seriously degraded. It is because existing studies on dynamic deployment of applications do not exploit an application replacement strategy to deploy or undeploy applications. In this paper, we propose an application replacement strategy, the average latency ratio minimum (ALR-MIN) strategy. With this strategy, an application is either deployed or evicted, considering the minimum ALR of a node (NALR). A series of simulations have been performed and their results demonstrate that the ALR-MIN strategy results in 17% less relative delay-time of jobs than the well-known least recently used based (LRU-based) strategies with a typical setting.