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It has been shown by A.-L. Barabasi that the priority based scheduling rulesin single stage queuing systems (QS) generates fat tail behavior for the taskswaiting time distributions (WTD). Such fat tails are due to the waiting timesof very low priority tasks which stay unserved almost forever as the taskpriority indices (PI) are "frozen in time" (i.e. a task priority is assignedonce for all to each incoming task). Relaxing the "frozen in time" assumption,this paper studies the new dynamic behavior expected when the priority of eachincoming tasks is time-dependent (i.e. "aging mechanisms" are allowed). For twoclass of models, namely 1) a population type model with an age structure and 2)a QS with deadlines assigned to the incoming tasks which is operated under the"earliest-deadline-first" policy, we are able to analytically extract somerelevant characteristics of the the tasks waiting time distribution. As theaging mechanism ultimately assign high priority to any long waiting tasks, fattails in the WTD cannot find their origin in the scheduling rule alone thusshowing a fundamental difference between the present and the A.-L. Barabasi'sclass of models.Comment: 16 pages, 2 figure

Modeling human activity in the spirit of Barabasi’s queueing systems