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## References[1] V. Anantharam, P. Heidelberger, and P. Tsoucas. Analysis of rare events in continuous time marked chains via time reversal and fluid approximation. IBM Research Report, REC 16280, 1990. [2] P. Arbenz and W. Gander. A survey of direct parallel algorithms for banded linear systems. Technical Report 221, Department Informatik,ETH Zurich, 1994. [3] S. Asmussen and P. Glynn. Stochastic Simulation: Algorithms and Analysis. Springer-Verlag, New York, NY, USA, 2008. MR2331321 [4] J. Blanchet. Optimal sampling of overflow paths in Jackson networks. To Appear in Math. of O.R., 2011. [5] J. Blanchet and P. Glynn. Efficient rare-event simulation for the maximum of a heavy-tailed random walk. Ann. of Appl. Probab., 18:1351–1378, 2008. MR2434174 [6] J. Blanchet, K. Leder, and P. Glynn. Lyapunov functions and subsolutions for rare event simulation. Submitted, 2011. [7] J. Blanchet and M. Mandjes. Rare event simulation for queues. In G. Rubino and B. Tuffin, editors, Rare Event Simulation Using Monte Carlo Methods, pages 87–124. Wiley, West Sussex, United Kingdom, 2009. Chapter 5. MR2730763 [8] T. Dean and P. Dupuis. Splitting for rare event simulation: A large deviation approach to design and analysis. Stochastic Processes and Its Applications, (119):562–587. MR2494004 [9] P. Dupuis and R. S. Ellis. The large deviation principle for a general class of queueing systems I. Trans. of the American Mathematical Society, 347:2689–2751, 1995. MR1290716 [10] P. Dupuis, A. Sezer, and H. Wang. Dynamic importance sampling for queueing networks. Ann. Appl. Probab., 17:1306–1346, 2007. MR2344308 [11] P. Dupuis and H. Wang. Importance sampling, large deviations, and differential games. Stoch. and Stoch. Reports, 76:481–508, 2004. MR2100018 [12] P. Dupuis and H. Wang. Importance sampling for Jackson networks. Preprint, 2008. [13] P. Glasserman, P. Heidelberger, P. Shahabuddin, and T. Zajic. Multilevel splitting for estimating rare event probabilities, 1999. MR1710951 [14] P. Glasserman and S. Kou. Analysis of an importance sampling estimator for tandem queues. ACM TOMACS, 5:22–42, 1995. [15] I. Ignatiouk-Robert. Large deviations of Jackson networks. Annals of Applied Probability, 10:962–1001, 2000. MR1789985 [16] S. Juneja and V. Nicola. Efficient simulation of buffer overflow probabilities in Jackson networks with feedback. ACM Trans. Model. Comput. Simul., 15(4):281–315, 2005. [17] S. Juneja and P. Shahabuddin. Rare event simulation techniques: An introduction and recent advances. In S. G. Henderson and B. L. Nelson, editors, Simulation, Handbooks in Operations Research and Management Science, pages 291–350. Elsevier, Amsterdam, The Netherlands, 2006. [18] D. Kroese and V. Nicola. Efficient simulation of a tandem Jackson network. ACM Trans. Model. Comput. Simul., 12:119–141, 2002. [19] K. Majewski and K. Ramanan. How large queues build up in a Jackson network. To Appear in Math. of O.R., 2008. [20] M.Villen-Altamirano and J. Villen-Altamirano. Restart: A method for accelerating rare even simulations. In J.W. Colhen and C.D. Pack, editors, Proceedings of the 13th International Teletraffic Congress. In Queueing, performance and control in ATM, pages 71–76. Elsevier Science Publishers, 1993. [21] V. Nicola and T. Zaburnenko. Efficient importance sampling heuristics for the simulation of population overflow in Jackson networks. ACM Trans. Model. Comput. Simul., 17(2), 2007. [22] S. Parekh and J. Walrand. Quick simulation of rare events in networks. IEEE Trans. Automat. Contr., 34:54–66, 1989. MR0970932 [23] P. Robert. Stochastic Networks and Queues. Springer-Verlag, Berlin, 2003. MR1996883 [24] M. Villén-Altamirano and J. Villén-Altamirano. Restart: a straightforward method for fast simulation of rare events. In Winter Simulation Conference, pages 282–289, 1994. | |||||

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