Series-Parallel Acyclic Directed Graphs

Abstract

In Chapter 2, we discussed models specialized for reliability and availability analysis. Now we turn to a kind of model typically used for performance modeling the task graph. Graph models are commonly used to study the behavior of programs or processes that contain concurrency and/or probabilistic branching. Many different kinds of graph models have been used, varying in aspects like degree of granularity of tasks, whether tasks have constant or random duration, what kinds of limitations (if any) are placed on the degree of concurrency, and whether cycles are allowed. Some graph models associate activities with the nodes of the graph and others associate activities with the edges. It is generally assumed that the completion times for individual tasks are statistically independent. Graph models are typically analyzed for measures such as mean completion time, completion time for the shortest path through the graph, and probability that a path is the shortest path. One well-known graph model is the PERT model and its various extensions [37, 43, 102].