We propose that human cognition consists of cascading cycles of recurring brain events. Each cognitive cycle senses the current situation, interprets it with reference to ongoing goals, and then selects an internal or external action in response. While most aspects of the cognitive cycle are unconscious, each cycle also yields a momentary "ignition" of conscious broadcasting. Neuroscientists have independently proposed ideas similar to the cognitive cycle, the fundamental hypothesis of the LIDA model of cognition. High-level cognition, such as deliberation, planning, etc., is typically enabled by multiple cognitive cycles. In this paper we describe a timing model LIDA's cognitive cycle. Based on empirical and simulation data we propose that an initial phase of perception (stimulus recognition) occurs 80-100 ms from stimulus onset under optimal conditions. It is followed by a conscious episode (broadcast) 200-280 ms after stimulus onset, and an action selection phase 60-110 ms from the start of the conscious phase. One cognitive cycle would therefore take 260-390 ms. The LIDA timing model is consistent with brain evidence indicating a fundamental role for a theta-gamma wave, spreading forward from sensory cortices to rostral corticothalamic regions. This posteriofrontal theta-gamma wave may be experienced as a conscious perceptual event starting at 200-280 ms post stimulus. The action selection component of the cycle is proposed to involve frontal, striatal and cerebellar regions. Thus the cycle is inherently recurrent, as the anatomy of the thalamocortical system suggests. The LIDA model fits a large body of cognitive and neuroscientific evidence. Finally, we describe two LIDA-based software agents: the LIDA Reaction Time agent that simulates human performance in a simple reaction time task, and the LIDA Allport agent which models phenomenal simultaneity within timeframes comparable to human subjects. While there are many models of reaction time performance, these results fall naturally out of a biologically and computationally plausible cognitive architecture.