A continuous model of human dynamics

Ideas and tools from statistical physics have recently been applied to the investigation of human dynamics. The timing   of human activities, in particular, has been studied both experimentally and analytically. Empirical data show that, in many different situations, the time interval separating two consecutive tasks executed by an individual follows a heavy-tailed probability distribution rather than Poisson statistics. To account for this data, human behaviour has been viewed as a decision-based queuing system where individuals select and execute tasks belonging to a finite list of items as an increasing function of a task priority parameter. It is then possible to obtain analytically the empirical result P(τ)∼1/τP(τ)∼1/τ, where P(τ)P(τ) is the waiting time probability distribution.Here a continuous model of human dynamics is introduced using instead an infinite   queuing list. In contrast with the results obtained by other models in the finite case we find a waiting time distribution explicitly depending on the priority distribution density function ρρ. The power-law scaling P(τ)∼1/τP(τ)∼1/τ is then recovered when ρρ is exponentially distributed.