Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Real-Time Systems Design and Analysis: An Engineer's Handbook
Real-Time Systems Design and Analysis: An Engineer's Handbook
Real-Time Systems
Hard Real-Time Systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation Techniques for Average Completion Time Scheduling
SIAM Journal on Computing
Utilization Bounds for Multiprocessor Rate-Monotonic Scheduling
Real-Time Systems
Minimum and Maximum Utilization Bounds for Multiprocessor Rate Monotonic Scheduling
IEEE Transactions on Parallel and Distributed Systems
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In this paper, we study the problem of scheduling a set of n periodic preemptive independent hard real-time tasks on the minimum number of processors. We assume that the partitioning strategy is used to allocate the tasks to the processors and the EDF method is used to schedule the tasks on each processor. It is known that this scenario is NPhard; thus, it is unlikely to find a polynomial time algorithm to schedule the tasks on the minimum number of processors. In this work, we derive a lower and an upper bound for the number of processors required to satisfy the constraints of our problem. We also compare a number of heuristic algorithms with each other and with the bounds derived in this paper. Numerical results demonstrate that our lower bound is very tight and it is very close to the optimal solution.