Multiprocessor Synthesis for Periodic Hard Real-Time Tasks under a Given Energy Constraint

The energy-aware design for electronic systems has been an important issue in hardware and/or software implementations, especially for embedded systems. This paper targets a synthesis problem for heterogeneous multiprocessor systems to schedule a set of periodic real-time tasks under a given energy consumption constraint. Each task is required to execute on a processor without migration, where tasks might have different execution times on different processor types. Our objective is to minimize the processor cost of the entire system under the given timing and energy consumption constraints. The problem is first shown being NP-hard and having no polynomial-time algorithm with a constant approximation ratio unless NP = P. We propose polynomial-time approximation algorithms with (m + 2)-approximation ratios for this challenging problem, where m is the number of the available processor types. Experimental results show that the proposed algorithms could always derive solutions with system costs close to those of optimal solutions