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 ETNPA significantly reduces the number of task preemptions as compared to TNPA.