caa a22 4500 60551965X CHVBK 20210128100731.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s11009-013-9391-2 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9391-2 Transient Behavior of Fractional Queues and Related Processes [Elektronische Daten] [Dexter Cahoy, Federico Polito, Vir Phoha] We propose a generalization of the classical M/M/1 queue process. The resulting model is derived by applying fractional derivative operators to a system of difference-differential equations. This generalization includes both non-Markovian and Markovian properties which naturally provide greater flexibility in modeling real queue systems than its classical counterpart. Algorithms to simulate M/M/1 queue process and the related linear birth-death process are provided. Closed-form expressions of the point and interval estimators of the parameters of the proposed fractional stochastic models are also presented. These methods are necessary to make these models usable in practice. The proposed fractional M/M/1 queue model and the statistical methods are illustrated using financial data. Springer Science+Business Media New York, 2013 Transient analysis nationallicence Fractional M/M/1 queue nationallicence Mittag-Leffler function nationallicence Fractional birth-death process nationallicence Parameter estimation nationallicence Simulation nationallicence Cahoy Dexter Department of Mathematics and Statistics, College of Engineering and Science, Louisiana Tech University, Ruston, LA, USA aut Polito Federico Department of Mathematics, University of Torino, Torino, Italy aut Phoha Vir Department of Computer Science, College of Engineering and Science, Louisiana Tech University, Ruston, LA, USA aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 739-759 1387-5841 17:3<739 2015 17 11009 https://doi.org/10.1007/s11009-013-9391-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9391-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cahoy Dexter Department of Mathematics and Statistics, College of Engineering and Science, Louisiana Tech University, Ruston, LA, USA aut NATIONALLICENCE 700 1- Polito Federico Department of Mathematics, University of Torino, Torino, Italy aut NATIONALLICENCE 700 1- Phoha Vir Department of Computer Science, College of Engineering and Science, Louisiana Tech University, Ruston, LA, USA aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 739-759 1387-5841 17:3<739 2015 17 11009