Analytical models for parallel programs have been successful at providing simple qualitative insights and bounds on scalability, but have been less successful in practice for predicting detailed, quantitative information about program performance. We develop a conceptually simple model that provides detailed performance prediction for parallel programs with arbitrary task graphs, a wide variety of task scheduling policies, shared-memory communication, and significant resource contention. Unlike many previous models, our model assumes deterministic task execution times which permits detailed analysis of synchronization, task scheduling, the order of task execution as well as mean values of communication costs. The assumption of deterministic task times is supported by a recent study of the influence of non-deterministic delays in parallel programs. We show that the deterministic task graph model is accurate and efficient for five shared-memory programs, including programs with large and/or complex task graphs, sophisticated task scheduling, highly non-uniform task times, and significant communication and resource contention. We also use three example programs to illustrate the predictive capabilities of the model. In two cases, broad insights and detailed metrics from the model are used to suggest improvements in load-balancing and the model quickly and accurately predicts the impact of these changes. In the third case, further novel metrics are used to obtain insight into the impact of program design changes that improve communication locality as well as load-balancing. Finally, we briefly present results of a comparison between our model and representative models based on stochastic task execution times.