Efficient and precise saccadic eye movements depend on the rapid integration of sensory and cognitive signals within a competitive neural environment. Here, we introduce a bio-inspired computational model of saccadic eye movement. The components of this model are named and behave like their biological counterparts. For example, it includes stochastic accumulator nodes on a two-dimensional retinotopic map, similar to those found in the intermediate superior colliculus (SCi). Each node receives input from the lateral intraparietal area (LIP) and cognitive influence from the frontal eye fields (FEF). These inputs compete with each other through lateral excitation and inhibition, driving a race-to-threshold process that leads to saccade generation. This model reproduces various oculomotor behaviours, such as pro-saccades, express saccades, memory-guided saccades, voluntary goal-directed movements, and saccade inhibition. It also produces the right-skewed distributions of saccadic reaction times observed in humans. We confirm the effectiveness of the model by simulating four experimental paradigms: baseline pro-saccade, high-contrast selection, low-contrast inhibition, and free-choice decision. These simulations demonstrate strong agreement between the predicted and actual reaction time distributions and error patterns. These findings highlight the biological relevance and predictive strength of the proposed model, offering a unified neural mechanism for rapid ocular decision-making processes. This approach could be useful in active vision systems and robotic platforms.