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<p><b>Abstract</b>—We present an optimal solution to the problem of allocating communicating periodic tasks to heterogeneous processing nodes (PNs) in a distributed real-time system. The solution is optimal in the sense of minimizing the maximum normalized task response time, called the <it>system hazard</it>, subject to the precedence constraints resulting from intercommunication among the tasks to be allocated. Minimization of the system hazard ensures that the solution algorithm will allocate tasks so as to meet all task deadlines under an optimal schedule, whenever such an allocation exists. The task system is modeled with a task graph (TG), in which computation and communication modules, communication delays, and intertask precedence constraints are clearly described. Tasks described by this TG are assigned to PNs by using a branch-and-bound (B&B) search algorithm. The algorithm traverses a search tree whose <it>leaves</it> correspond to potential solutions to the task allocation problem. We use a bounding method that prunes, in polynomial time, nonleaf vertices that cannot lead to an optimal solution, while ensuring that the search path leading to an optimal solution will never be pruned. For each generated leaf vertex we compute the exact cost using the algorithm developed in [<ref rid="bibe07451" type="bib">1</ref>]. The lowest-cost leaf vertex (one with the least system hazard) represents an optimal task allocation. Computational experiences and examples are provided to demonstrate the concept, utility, and power of the proposed approach.</p>
Branch-and-bound (B&B) algorithm, computation and communication modules, intertask communication, precedence and timing constraints, task invocation and release times, lower-bound cost.

K. G. Shin, T. F. Abdelzaher and D. Peng, "Assignment and Scheduling Communicating Periodic Tasks in Distributed Real-Time Systems," in IEEE Transactions on Software Engineering, vol. 23, no. , pp. 745-758, 1997.
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