Eye-movement control during scene viewing can be represented as a series of individual decisions about where and when to move the eyes. While substantial behavioral and computational research has been devoted to investigating the placement of fixations in scenes, relatively little is known about the mechanisms that control fixation durations. Here, we propose a computational model (CRISP) that accounts for saccade timing and programming and thus for variations in fixation durations in scene viewing. First, timing signals are modeled as continuous-time random walks. Second, difficulties at the level of visual and cognitive processing can inhibit and thus modulate saccade timing. Inhibition generates moment-by-moment changes in the random walk's transition rate and processing-related saccade cancellation. Third, saccade programming is completed in 2 stages: an initial, labile stage that is subject to cancellation and a subsequent, nonlabile stage. Several simulation studies tested the model's adequacy and generality. An initial simulation study explored the role of cognitive factors in scene viewing by examining how fixation durations differed under different viewing task instructions. Additional simulations investigated the degree to which fixation durations were under direct moment-to-moment control of the current visual scene. The present work further supports the conclusion that fixation durations, to a certain degree, reflect perceptual and cognitive activity in scene viewing. Computational model simulations contribute to an understanding of the underlying processes of gaze control. (Contains 7 footnotes, 4 tables, and 10 figures.)