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<p><b>Abstract</b>—This paper addresses the problem of allocating (assigning and scheduling) periodic task modules to processing nodes in distributed real-time systems subject to task precedence and timing constraints. Using the branch-and-bound technique, a module allocation scheme is proposed to find an "optimal" allocation that maximizes the probability of meeting task deadlines.</p><p>The task system within a planning cycle is first modeled with a task flow graph which describes computation and communication modules, as well as the precedence constraints among them. To incorporate both timing and logical correctness into module allocation, the probability of meeting task deadlines is used as the objective function. The module allocation scheme is then applied to find an optimal allocation of task modules in a distributed system. The timing aspects embedded in the objective function drive the scheme not only to assign task modules to processing nodes, but also to use a module scheduling algorithm (with polynomial time complexity) for scheduling all modules assigned to each node, so that all tasks may be completed in time.</p><p>In order to speed up the branch-and-bound process and to reduce the computational complexity, a dominance relation is derived from the requirement of timely completion of tasks and use to eliminate the possibility of generating vertices in the state-space search tree, which never lead to an optimal solution, and an upper bound of the objective function is derived for every partial allocation with which the scheme determines whether or not to prune the corresponding intermediate vertex in the search tree. Several numerical examples are presented to demonstrate the effectiveness and practicality of the proposed scheme.</p>
Real-time systems, dynamic failure, task/module allocation, module scheduling, precedence and deadline constraints, task flow graph, branch-and-bound process.

K. G. Shin and C. Hou, "Allocation of Periodic Task Modules with Precedence and Deadline Constraints in Distributed Real-Time Systems," in IEEE Transactions on Computers, vol. 46, no. , pp. 1338-1356, 1997.
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