Optimal real-time scheduling algorithms realize efficient systems theoretically. They achieve the schedulable utilization bound which is equal to the system capacity. T-R Plane Abstraction (TRPA) proposed in this paper is an abstraction technique of real-time scheduling on multiprocessors. This paper presents that NNLF (No Nodal Laxity First) based on TRPA is work-conserving and optimally solves the problem of scheduling periodic tasks on a multiprocessor system. TRPA can accommodate to dynamic environments due to its dynamic time reservation, while T-N Plane Abstraction (TNPA) and Extended-TNPA (E-TNPA) reserve processor time statically at every task release.