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This paper presents two fast, best-effort real-time scheduling algorithms called MDASA and MLBESA. MDASA and MLBESA are novel in the way that they heuristically, yet accurately, mimic the behavior of the DASA and LBESA scheduling algorithms, but are faster with O\left( n \right) and O \left( n \lg \left( n \right) \right) worst-case complexities, respectively. Experimental results show that the performance of MDASA and MLBESA, in general, is close to that of DASA and LBESA, respectively, for a broad range of realistic workloads. However, for a highly bursty workload, MLBESA is found to perform worse than LBESA. Furthermore, the task response times under MDASA and MLBESA are very close to the values under their counterpart scheduling algorithms. Thus, MDASA and MLBESA can substitute for DASA and LBESA algorithms, respectively, in adaptive resource allocation techniques for asynchronous real-time distributed systems where DASA and LBESA have previously been serious bottlenecks on computational costs.