Resource-constrained systems are prevalent in communications. Such a system is composed of many components but only some of them can be allocated with resources such as time slots. According to the amount of information about the system, algorithms are employed to allocate resources and the overall system performance depends on the result of resource allocation. We do not always have complete information, and thus, the system performance may not be satisfactory. In this work, we propose a general model for the resource-constrained communication systems. We draw the relationship between system information and performance and derive the performance bounds for the optimal algorithm for the system. This gives the expected performance corresponding to the available information, and we can determine if we should put more efforts to collect more accurate information before actually constructing an algorithm for the system. Several examples of applications in communications to the model are also given.