9,526 research outputs found
Human activity modeling and Barabasi's queueing systems
It has been shown by A.-L. Barabasi that the priority based scheduling rules
in single stage queuing systems (QS) generates fat tail behavior for the tasks
waiting time distributions (WTD). Such fat tails are due to the waiting times
of very low priority tasks which stay unserved almost forever as the task
priority indices (PI) are "frozen in time" (i.e. a task priority is assigned
once for all to each incoming task). Relaxing the "frozen in time" assumption,
this paper studies the new dynamic behavior expected when the priority of each
incoming tasks is time-dependent (i.e. "aging mechanisms" are allowed). For two
class 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 some
relevant characteristics of the the tasks waiting time distribution. As the
aging mechanism ultimately assign high priority to any long waiting tasks, fat
tails in the WTD cannot find their origin in the scheduling rule alone thus
showing a fundamental difference between the present and the A.-L. Barabasi's
class of models.Comment: 16 pages, 2 figure
Simple bounds for queueing systems with breakdowns
Computationally attractive and intuitively obvious simple bounds are proposed for finite service systems which are subject to random breakdowns. The services are assumed to be exponential. The up and down periods are allowed to be generally distributed. The bounds are based on product-form modifications and depend only on means. A formal proof is presented. This proof is of interest in itself. Numerical support indicates a potential usefulness for quick engineering and performance evaluation purposes
About the cumulative idle time in multiphase queues
The paper is designated to the analysis of queueing systems, arising in the network theory and communications theory (called multiphase queueing systems, tandem queues or series of queueing systems). Also we note that multiphase queueing systems can be useful for modelling practical multi-stage service systems in a variety of disciplines, especially on manufacturing (assembly lines), computer networking (packet switch structures), and in telecommunications (e.g. cellular mobile networks), etc. This research presents heavy traffic limit theorems for the cumulative idle time in multiphase queues. In this work, functional limit theorems are proved for the values of important probability characteristics of the queueing system (a cumulative idle time of a customer)
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