Solving nonlinear systems of equations and nonlinear systems of differential equations by the Monte Carlo method using queueing networks and games theory

Ciuiu, Daniel (2008): Solving nonlinear systems of equations and nonlinear systems of differential equations by the Monte Carlo method using queueing networks and games theory. Published in: Analele Universitatii Bucuresti, Seria Informatica. No. 1, 2008 (2010): pp. 111-125.

Abstract

In this paper we will solve some nonlinear systems of equations and nonlinear systems of differential equations by the Monte Carlo method using queueing networks and some results from games theory.

• Item Type: MPRA Paper
• Language: English
• Keywords: Monte Carlo, queueing networks, symmetric games.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

References

[1] Soren Asmussen, Applied Probabilities and Queues, John Wiley and Sons Inc., 1987.

[2] P. Bratley, L. B. Fox, L. E. Schrage, A Guide to Simulation, Springer Verlag, 1987.

[3] Jeffrey Buzen, “Computational Algorithms for Closed Queueing Networks with Exponential Servers”, Communications of the ACM, vol. 16, no 9, 1973, pg. 527-531.

[4] D. Ciuiu, “On Modeling of the Inventory Systems by Queueing Systems”, Proceedings of the Scientific Session of the Mathematics Department of TUCEB, 24 May 2003, pg. 14-16 (Romanian).

[5] D. Ciuiu, “Solving Linear Systems of Equations and Differential Equations with Partial Derivatives by the Monte Carlo Method using Service Systems”, the Annals of the Bucharest University, no 1, 2004, pg. 93-104.

[6] D. Ciuiu, “A Method to Solve Some Nonlinear Equations by the Monte Carlo Method Using Queueing Systems”, the Annals of the Bucharest University, no 1, 2006, pg. 21-30.

[7] D. Ciuiu, “Queueing Networks”, Ph.D. Thesis, supervisor prof. dr. Ion Văduva, Bucharest University, 2006 (Romanian).

[8] S. M. Ermakov, The Monte Carlo Method and Connected Problems, Technical Publishing House, Bucharest, 1976 (Romanian).

[9] S. M. Ermakov, N. Balakrishnan, V. B. Melas, Advances in Stochastic Simulation Models, Birkhäuser, Boston, Basel, Berlin, 2000.

[10] Mario Garzia, Ricardo Garzia, Mark Kiemele, Clayton Lockhart, Network Modeling, Simulation and Analysis, Ed. Marcel Decker, 1990.

[11] William J. Gordon, Gorden F. Newell, “Closed Queueing Systems with Exponential Servers”, Operations Research, vol. 15, no 2, 1967, pg. 254-265.

[12] William J. Gordon, Gorden F. Newell, “Cyclic Queueing Systems with Restricted Length Queues”, Operations Research, vol. 15, no 2, 1967, pg. 266-277.

[13] Marius Iosifescu, Finite Markov Chains and Applications, Technical Publishing House, Bucharest, 1977 (Romanian).

[14] Marius Iosifescu, Finite Markov Processes and Their Applications, John Wiley and Sons Inc. and Technical Publishing House, Bucharest, 1980.

[15] Leonard Kleinrock, Queueing Systems, John Wiley and Sons Inc., 1975.

[16] Anton Ştefanescu, Competitive Models in Game Theory and Economic Analysis, Bucharest University Publishing House, 2000.

[17] Anton Ştefanescu, Corneliu Zidaroiu, Operations Research, Didactical and Pedagogical Publishing House, Bucharest, 1981 (Romanian).

[18] I. Vaduva, “The Monte Carlo Method”, Thematic Collection for Mathematics-Mechanics, no 1, 1972, pg. 131-188 (Romanian).

[19] I. Vaduva, C. Dinescu, B. Savulescu, Mathematical Models for Organizing and Leading the Production, Didactical and Pedagogical Publishing House, Bucharest, 1974 (Romanian).

[20] I. Vaduva, Simulation Models using Computer, Technical Publishing House, Bucharest, 1977 (Romanian).

[21] I. Vaduva, Simulation Models, Bucharest University Publishing House, 2004 (Romanian).

[22] Jorgen Weibull, Evolutionary Game Theory, MIT Press, 1996.