Ciuiu, Daniel (2007): Gordon and Newell queueing networks and copulas. Published in: Yugoslav Journal of Operations Research , Vol. 19, No. 1 (July 2009): pp. 101112.

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Abstract
In this paper we have found an analytical formula for a copula that connects the numbers Ni of customers in the nodes of a Gordon and Newell queueing network. We have considered two cases: the first one is the case of the network with 2 nodes, and the second one is the case of the network with at least 3 nodes. The analytical formula for the second case has been found for the most general case (none of the constants from a list is equal to a given value), and the other particular cases have been obtained by limit.
Item Type:  MPRA Paper 

Original Title:  Gordon and Newell queueing networks and copulas 
Language:  English 
Keywords:  Gordon and Newell queueing networks, copulas. 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C65  Miscellaneous Mathematical Tools C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions; Specific Statistics 
Item ID:  15769 
Depositing User:  Daniel Ciuiu 
Date Deposited:  10. Aug 2009 09:37 
Last Modified:  13. Feb 2013 17:23 
References:  [1] Dall' Aglio, G., "Fréchet classes: the beginning", in: G., Dall' Aglio, S. Kotz, and G., Salinetti, (eds.), Advances in Probability Distributions with Given Marginals. Beyond the Copulas, Kluwer Academic Publishers, 1991, 112. [2] Buzen, J., "Computational algorithms for closed queueing networks with exponential servers", Communications of the ACM, 16 (9) (1973) 527531. [3] Ciuiu, D., "Simulation experiments on the service systems using arrivals and services depending through copulas", The Annals of Bucharest University, 1 (2005) 1730. [4] Garzia, M., Garzia, R., Kiemele, M., and Lockhart C., Network Modeling, Simulation and Analysis, Marcel Decker, New York, Bassel, 1990. [5] Gordon, W.J., and Newell, G.F., "Closed queueing systems with exponential servers", Operations Research, 15 (2) (1967) 254265. D. Ciuiu / Gordon and Newell Queueing Networks and Copulas 112 [6] Iosifescu, M., Finite Markov Chains and Applications, Technical Editure, Bucharest/, Romanian, 1977. [7] Kleinrock, L., Queueing Systems, John Wiley and Sons Inc., New York, Toronto, London, Sydney, 1975. [8] Nelsen, R., "Copulas and association", in: G., Dall' Aglio, S., Kotz, and G., Salinetti, (eds.) Advances in Probability Distributions with Given Marginals. Beyond the Copulas, Kluwer Academic Publishers, 1991, 5174. [9] Schweizer, B., "Thirty years of copulas", in: Advances in Probability Distributions with Given Marginals. Beyond the Copulas, (eds.) G., Dall' Aglio, S., Kotz, and G., Salinetti, Kluwer Academic Publishers, 1991, 1350. [10] Sungur, E., and Tuncer, Y., "The use of copulas to generate new multivariate distributions. The frontiers of statistical computation, simulation & modeling", Proceedings of the ICOSCOI Conference (The First International Conference on Statistical Computing, Çeşme, Izmir, Turkey), I (1987) 197222. [11] Văduva, I., Fast Algorithms for Computer Generation of Random Vectors used in Reliability and Applications, Preprint no. 1603, Jan. 1994, THDarmstadt. [12] Văduva, I., "Simulation of some Multivariate Distributions", The Annals of the Bucharest University, 1 (2003) 127140. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/15769 