%0 Conference Paper
%A Ramirez-Velarde, Raul
%A Pareja Flores, Cristóbal
%A Hernandez-Gress, Neil
%A Hervert-Escobar, Laura
%T Modelling extreme uncertainty: Queues with Pareto inter-arrival times and Pareto service times
%D 2025
%U https://hdl.handle.net/20.500.14352/132113
%X When an operational parameter presents extremely high variability, uncertainty becomes extreme. Long-tail probability distributions can be used to model such uncertainty. We present a queuing system in which extreme uncertainty is modelled using long-tail probability distributions. There have been many queuing analyses for a single server queue fed by an M/G/traffic process, in which G is a Pareto distribution, that focus on certain limiting conditions. In this paper, we present a mathematical model to solve an infinite queuing system with one server where the inter-arrival time between jobs follows a Pareto probability distribution with shape parameter α and a scale parameter A. The system service time is also a Pareto probability distribution with shape parameter β and scale parameter B. We call this the P/P/1 queuing model.
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