Blood occlusions in the retinal microvasculature contribute to the pathology of many disease states within the eye. These events can cause haemorrhaging and retinal detachment, leading to a loss of vision in the affected patient. Here, we present a physical approach to characterising the collective cell dynamics leading to plug formation, through the use of a bespoke microfluidic device, and through the derivation of a probabilistic model. Our microfluidic device is based on a filtration design that can tune the particle volume fraction of a flowing suspension within a conduit, with sizes similar to arterioles. This allows us to control and reproduce an occlusive event. The formation of the occlusion can be examined through the extracted motion of particles within the channel, which enables the assessment of individual and collective particle dynamics in the time leading to the clogging event. In particular, we observe that at the onset of the occlusion, particles form an arch bridging the channel walls. The data presented here inform the development of our mathematical model, which captures the essential factors promoting occlusions, and notably highlights the central role of adhesion in these processes. Both the physical and probabilistic models rely on significant approximations, and future investigation will seek to assess these approximations, including the deformability and complex flow profiles of the blood constituents. However, we anticipate that the general mechanisms of occlusion may be elucidated from these simple models. As microvascular flows in the eye can now be measured in vivo and non-invasively with single cell resolution, our model will also be compared to the pathophysiological characteristics of the human microcirculation.