Second order fluid models with general boundary behaviour
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A crucial property of second order fluid models is the behaviour of the fluid level at the boundaries. Two cases have been considered: the reflecting and the absorbing boundary. This paper presents an approach for the stationary analysis of second order fluid models with any combination of boundary behaviours. The proposed approach is based on the solution of a linear system whose coefficients are obtained from a matrix exponent. A practical example demonstrates the suitability of the technique in performance modeling.
- Agapie, M., & Sohraby, K. (2001). Algorithmic solution to second order fluid flow. In Proc. of IEEE infocom, Anchorage, Alaska, Usa, Apr. 2001.
- Ahn, S., & Ramaswami, V. (2003). Fluid flow models and queues—a connection by stochastic coupling. Communications in Statistics. Stochastic Models, 19(3), 325–348. CrossRef
- Ahn, S., & Ramaswami, V. (2004). Transient analysis of fluid flow models via stochastic coupling. Communications in Statistics. Stochastic Models, 20(1), 71–101. CrossRef
- Ang, E.-J., & Barria, J. (2000). The Markov modulated regulated Brownian motion: a second-order fluid flow model of a finite buffer. Queueing Systems, 35, 263–287. CrossRef
- Anick, D., Mitra, D., & Sondhi, M. M. (1982). Stochastic theory of a data-handling system with multiple sources. Bell System Technical Journal, 61(8), 1871–1894.
- Asmussen, S. (1995). Stationary distributions for fluid flow models with or without Brownian noise. Stochastic Models, 11, 1–20. CrossRef
- Bean, N. G., O’Reilly, M. M., & Taylor, P. G. (2005a). Algorithms for the first return probabilities for stochastic fluid flows. Stochastic Models, 21(1).
- Bean, N. G., O’Reilly, M. M., & Taylor, P. G. (2005b). Hitting probabilities and hitting times for stochastic fluid flows. Stochastic Processes and their Applications, 115, 1530–1556. CrossRef
- Chen, D.-Y., Hong, Y., & Trivedi, K. S. (2002). Second order stochastic fluid flow models with fluid dependent flow rates. Performance Evaluation, 49(1–4), 341–358. CrossRef
- Cox, D. R., & Miller, H. D. (1972). The theory of stochastic processes. London: Chapman & Hall.
- da Silva Soares, A., & Latouche, G. (2002). Further results on the similarity between fluid queues and QBDs. In G. Latouche & P. Taylor (Eds.), Proc. of the 4th int. conf. on matrix-analytic methods (pp. 89–106). Adelaide, 2002. Singapore: World Scientific.
- da Silva Soares, A., & Latouche, G. (2006). Matrix-analytic methods for fluid queues with finite buffers. Performance Evaluation, 63(4), 295–314. CrossRef
- German, R., Gribaudo, M., Horváth, G., & Telek, M. (2003). Stationary analysis of FSPNs with mutually dependent discrete and continuous parts. In International conference on petri net performance models—PNPM 2003 (pp. 30–39). Urbana, IL, USA, Sept. 2003. New York: IEEE CS Press. CrossRef
- Gribaudo, M., & German, R. (2001). Numerical solution of bounded fluid models using matrix exponentiation. In Proc. 11th GI/ITG conference on measuring, modelling and evaluation of computer and communication systems (MMB). Aachen, Germany, Sep. 2001. VDE Verlag.
- Horton, G., Kulkarni, V. G., Nicol, D. M., & Trivedi, K. S. (1998). Fluid stochastic Petri nets: theory, application, and solution techniques. European Journal of Operations Research, 105(1), 184–201. CrossRef
- Igelnik, B., Kogan, Y., Kriman, V., & Mitra, D. (1995). A new computational approach for stochastic fluid models of multiplexers with heterogeneous sources. Queueing Systems—Theory and Applications, 20, 85–116. CrossRef
- Karandikar, R. L., & Kulkarni, V. G. (1995). Second-order fluid flow models: reflected Brownian motion in a random environment. Operations Research, 43, 77–88. CrossRef
- Kobayashi, H., & Ren, Q. (1992). A mathematical theory for transient analysis of communication networks. IEICE Transactions Communications, E75-B(12), 1266–1276.
- Kosten, L. (1984). Stochastic theory of data-handling systems with groups of multiple sources. In Proceedings of the IFIP WG 7.3/TC 6 second international symposium on the performance of computer-communication systems (pp. 321–331). Zurich, Switzerland.
- Mitra, D. (1987). Stochastic fluid models. In Proceedings of performance’87 (pp. 39–51). Brussels, Belgium.
- Mitra, D. (1988). Stochastic theory of a fluid model of producers and consumers coupled by a buffer. Advances in Applied Probability, 20, 646–676. CrossRef
- Rabehasaina, L., & Sericola, B. (2003). Stability analysis of second order fluid flow models in a stationary ergodic environment. Annals of Applied Probability, 13(4).
- Ramaswami, V. (1996). Matrix analytic methods for stochastic fluid flows. In D. Smith & P. Hey (Eds.), Proc. ITC 16 (pp. 1019–1030). Edinburgh. Amsterdam: Elsevier.
- Ren, Q., & Kobayashi, H. (1995). Transient solutions for the buffer behavior in statistical multiplexing. Performance Evaluation, 23, 65–87. CrossRef
- Rogers, L. C. G. (1994). Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains. Annals of Applied Probability, 4(2), 390–413. CrossRef
- Rogers, L. C. G., & Shi, Z. (1994). Computing the invariant law of a fluid model. Journal of Applied Probability, 31(4), 885–896. CrossRef
- Sericola, B. (1998). Transient analysis of stochastic fluid models. Performance Evaluation, 32(4).
- Stern, T. E., & Elwalid, A. I. (1991). Analysis of separable Markov-modulated rate models for information-handling systems. Advances in Applied Probability, 23, 105–139. CrossRef
- Tanaka, T., Hashida, O., & Takahashi, Y. (1995). Transient analysis of fluid models for ATM statistical multiplexer. Performance Evaluation, 23, 145–162. CrossRef
- Wolter, K. (1997). Second order fluid stochastic petri nets: an extension of GSPNs for approximate and continuous modelling. In Proc. of world congress on system simulation (pp. 328–332). Singapore, Sep. 1997.
- Second order fluid models with general boundary behaviour
Annals of Operations Research
Volume 160, Issue 1 , pp 69-82
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