  Queuing models provide insight into the temporal inhomogeneity of human
dynamics, characterized by the broad distribution of waiting times of
individuals performing tasks. We study the queuing model of an agent trying to
execute a task of interest, the priority of which may vary with time due to the
agent's "state of mind." However, its execution is disrupted by other tasks of
random priorities. By considering the priority of the task of interest either
decreasing or increasing algebraically in time, we analytically obtain and
numerically confirm the bimodal and unimodal waiting time distributions with
power-law decaying tails, respectively. These results are also compared to the
updating time distribution of papers in the arXiv.org and the processing time
distribution of papers in Physical Review journals. Our analysis helps to
understand human task execution in a more realistic scenario.
