The homeostatic regulation of sleep manifests as a relative constancy of its total daily amount, and the compensation of sleep loss by an increase in its subsequent duration and intensity. Theoretical descriptions of this phenomenon define “Process S”, a variable with dynamics dependent only on sleep-wake history and whose levels are reflected in EEG slow wave activity. While numerous hypotheses have been advanced regarding the substrate and role of Process S, such as synaptic or energy homeostasis, it remains unclear whether these dynamics are fundamentally driven by a need to homeostatically regulate specific variables, or by an unknown innate process which enforces that a certain daily sleep quota is obtained. Sleep is typically defined based on brain-derived criteria, such as behaviour or EEG power spectra, and variation in brain activity during wakefulness has been linked to variation in Process S accumulation. We therefore hypothesised that Process S dynamics might be related to the quantity and characteristics of spiking activity in cortical neurones. Specifically, we assumed that Process S changes as a function of the deviation of neuronal firing rate from a locally defined set point. To relate these dynamics explicitly to patterns of spiking activity, we incorporated the occurrence of network spiking off periods as both the defining measure of Process S and as the determinant of its rate of decay. This approach was able to describe the time course of Process S, crucially without explicit knowledge of the animal’s global sleep-wake state. This work provides a conceptual advance in our understanding of the substrate of sleep homeostasis and provides important links between local and global aspects of sleep regulation.