Pii: S0166-5316(99)00054-1
نویسندگان
چکیده
The analytical evaluation of the completion time distribution of a general directed acyclic graph (DAG) is known to be an NP-complete problem. In this paper we present a new algorithm, named Tree Bound , for the evaluation of bounds on the completion time of stochastic graphs assuming ideal conditions for shared resources and independent random variables as task execution times. The Tree Bound method uses a hierarchical approach that first gives a tree-like representation of the graph, and then evaluates lower and upper bounds through a single visit of the tree. As lower bound the method takes the distribution of an embedded series–parallel graph which is evaluated by means of a simple recursion. The upper bound is based on a hierarchical application of other bounding techniques. In this paper, we use the Shogan algorithm because its determinism allows us to demonstrate some interesting properties of the Tree Bound method. Indeed, through stochastic ordering and stochastic comparison techniques, we demonstrate analytically that our approach provides tighter bounds than Shogan’s and Yazici-Pekergin’s bounds. On the other hand, we cannot compare formally the Tree Bound accuracy to that of other important methods, such as Kleinöder and Dodin, because of their non-determinism. Various empiric comparisons show that the Tree Bound algorithm provides analogous or superior results than heuristics derived from main non-deterministic methods. Moreover, the Tree Bound algorithm keeps linear complexity and avoids non-determinism. Finally, it represents a useful basis for the combination of different bounding techniques which seems the only way to achieve even tighter bounds on the completion time distribution of stochastic graphs. © 2000 Elsevier Science B.V. All rights reserved.
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تاریخ انتشار 1999