Tomography is a popular technique to reconstruct the three-dimensional structure of an object from a series of two-dimensional projections. Tomography is resource-intensive and deployment of a parallel implementation onto Computational Grid platforms has been studied in previous work. In this work, we address on-line execution of the application where computation is performed as data is collected from an on-line instrument. The goal is to compute incremental 3-D reconstructions that provide quasi-real-time feedback to the user.We model on-line parallel tomography as a tunable application: trade-offs between resolution of the reconstruction and frequency of feedback can be used to accommodate various resource availabilities. We demonstrate that application scheduling/tuning can be framed as multiple constrained optimization problems and evaluate our methodology in simulation. Our results show that prediction of dynamic network performance is key to efficient scheduling and that tunability allows for production runs of on-line parallel tomography in Computational Grid environments.