  Human activity patterns display a bursty dynamics, with interevent times
following a heavy tailed distribution. This behavior has been recently shown to
be rooted in the fact that humans assign their active tasks different
priorities, a process that can be modeled as a priority queueing system [A.-L.
Barabasi, Nature 435, 207 (2005)]. In this work we obtain exact results for the
Barabasi model with two tasks, calculating the priority and waiting time
distribution of active tasks. We demonstrate that the model has a singular
behavior in the extremal dynamics limit, when the highest priority task is
selected first. We find that independently of the selection protocol, the
average waiting time is smaller or equal to the number of active tasks, and
discuss the asymptotic behavior of the waiting time distribution. These results
have important implications for understanding complex systems with extremal
dynamics.
