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Extended T-N plane abstraction (E-TNPA) proposed in this paper realizes work-conserving and efficient optimal real-time scheduling on multiprocessors relative to the original T-N plane abstraction (TNPA). Additionally a scheduling algorithm named NVNLF (no virtual nodal laxity first) is presented for E-TNPA. E-TNPA and NVNLF relax the restrictions of TNPA and the traditional algorithm LNREF, respectively. Arbitrary tasks can be preferentially executed by both tie-breaking rules and time apportionment policies in accordance with various system requirements with several restrictions. Simulation results show that E-TNPA significantly reduces the number of task preemptions as compared to TNPA.