Ramirez-Velarde, RaulPareja Flores, CristóbalHernandez-Gress, NeilHervert-Escobar, Laura2026-02-112026-02-112025Ramirez-Velarde, R., Pareja-Flores, C., Hernandez-Gress, N., Hervert-Escobar, L. (2025). Modelling Extreme Uncertainty: Queues with Pareto Inter-arrival Times and Pareto Service Times. In: Paszynski, M., Barnard, A.S., Zhang, Y.J. (eds) Computational Science – ICCS 2025 Workshops. ICCS 2025. Lecture Notes in Computer Science, vol 15912. Springer, Cham. https://doi.org/10.1007/978-3-031-97573-8_1610.1007/978-3-031-97573-8_16https://hdl.handle.net/20.500.14352/132113When 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.engconference paperhttps://doi.org/10.1007/978-3-031-97573-8_16https://link.springer.com/chapter/10.1007/978-3-031-97573-8_16restricted access519.22-7519.21519.216Extreme uncertaintyPareto queuesLong-tailsEstadística aplicadaProbabilidades (Estadística)Procesos estocásticos1209 Estadística1208 Probabilidad1208.08 Procesos Estocásticos