In wireless cyber-physical systems (CPS), with a growing number of sensors being deployed, more and more data will be transmitted over wireless links. This essentially requires that wireless network protocols should be further studied and amended to improve their transmission efficiency. The delayed channel access (DCA) protocol is of great practical importance in improving channel utilization. DCA is an improved version of IEEE 802.11 distributed coordination function (DCF). In DCA, a node first waits for an extra delay before it enters the normal DCF procedure, so that more packets can be aggregated and transmitted upon each transmission opportunity. However, how the extra delay affects the performance of DCA has never been theoretically investigated. In this paper, we first propose a theoretical model to characterize the impact of a deterministic extra delay on collision probability, throughput, and medium access control (MAC) delay. With this model, we perform asymptotic analysis to calculate the optimal deterministic delay that can maximize the system throughput. We find that the system performance is significantly affected by the relationship between the deterministic delay and the number of nodes; and therefore, carefully choosing a suitable deterministic delay is crucial in improving channel utilization. The extensive ns2 simulations verify that our model is very accurate, and the theoretical optimal deterministic delay can make the system achieve the maximum system throughput. This study is very useful for better designing and implementing the packet aggregation technology that has been adopted by IEEE wireless networking standards including 802.11n and the latest 802.11ac.