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Due to increasing numbers of real-time high-performance applications like control systems, autonomous robots, financial systems, scheduling these real-time applications on HPC resources has become an important problem. This paper presents a novel real-time multiprocessor scheduling algorithm, called Notional Approximation for Balancing Load Residues (NABLR), which heuristically selects tasks for execution by taking into account their residual loads and laxities. The NABLR schedule is created by considering a sequence of inter-arrival intervals (IAI) between two consecutive job arrivals of any task and using a heuristic to carefully plan task execution to fully utilize available resources in each of these intervals and avoid deadline misses as much as possible. Performance evaluation shows that NABLR outperforms previously known efficient algorithms (i.e. EDF and EDZL) in successfully scheduling sets of tasks in which total utilization of each task set equals available resource capacity, performing the closest to an optimal algorithm such as LLREF and Pfair. Out of 2500 randomly selected high-utilization task sets, NABLR can schedule up to 97.9% of the sets versus 63.2% by the best known efficient NABLR schedule are significantly smaller than those of optimal schedules (on average 80.57% fewer preemptions, migrations and 75.52% fewer scheduler invocations than those of LLREF) and comparably efficient suboptimal schedules (fewer or nearly the same number of invocations as EDZL and ASEDZL, but within only 0.12% more preemptions/migrations than ASEDZL). NABLR has the same O(NlogN) time complexity as other previously proposed efficient.