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This paper presents two proactive resource allocation algorithms, called RBA* and OBA, for asynchronous real-time distributed systems. The algorithms consider an application model where timeliness requirements are expressed using Jensen's benefit functions and propose adaptation functions to describe anticipated application workload during future time intervals. Furthermore, the algorithms consider an adaptation model, where application processes are dynamically replicated for sharing workload increases and a switched real-time Ethernet network as the underlying system model. Given such models, the objective of the algorithms is to maximize the aggregate application benefit and minimize the aggregate missed deadline ratio. Since determining the optimal allocation is computationally intractable, the algorithms heuristically compute near-optimal resource allocations in polynomial-time. While RBA* analyzes the process response times to determine resource allocation decisions, which is computationally expensive, OBA analyzes processor overloads to compute its decisions in a much faster way. RBA* incurs a quadratic amortized complexity in terms of process arrivals for its most computationally intensive component when DASA is used as the underlying scheduling algorithm, whereas OBA incurs a logarithmic amortized complexity for the corresponding component. Our benchmark-driven experimental studies reveal that RBA* produces a higher aggregate benefit and lower missed deadline ratio than OBA.