Analysis of a Splitting Estimator for Rare Event Probabilities in Jackson Networks

References

• 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.Google Scholar
• P. Arbenz and W. Gander. A survey of direct parallel algorithms for banded linear systems. Technical Report 221, Department Informatik, ETH Zurich, 1994.Google Scholar
• S. Asmussen and P. Glynn. Stochastic Simulation: Algorithms and Analysis. Springer-Verlag, New York, NY, USA, 2008. MR2331321Google Scholar
• J. Blanchet. Optimal sampling of overflow paths in Jackson networks. To Appear in Math. of O.R., 2011.Google Scholar
• 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. MR2434174Google Scholar
• J. Blanchet, K. Leder, and P. Glynn. Lyapunov functions and subsolutions for rare event simulation. Submitted, 2011.Google Scholar
• 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. MR2730763Google Scholar
• 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. MR2494004Google Scholar
• 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. MR1290716Google Scholar
• P. Dupuis, A. Sezer, and H. Wang. Dynamic importance sampling for queueing networks. Ann. Appl. Probab., 17:1306–1346, 2007. MR2344308Google Scholar
• P. Dupuis and H. Wang. Importance sampling, large deviations, and differential games. Stoch. and Stoch. Reports, 76:481–508, 2004. MR2100018Google Scholar
• P. Dupuis and H. Wang. Importance sampling for Jackson networks. Preprint, 2008.Google Scholar
• P. Glasserman, P. Heidelberger, P. Shahabuddin, and T. Zajic. Multilevel splitting for estimating rare event probabilities, 1999. MR1710951Google Scholar
• P. Glasserman and S. Kou. Analysis of an importance sampling estimator for tandem queues. ACM TOMACS, 5:22–42, 1995.Google Scholar
• I. Ignatiouk-Robert. Large deviations of Jackson networks. Annals of Applied Probability, 10:962–1001, 2000. MR1789985Google Scholar
• 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.Google Scholar
• 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.Google Scholar
• D. Kroese and V. Nicola. Efficient simulation of a tandem Jackson network. ACM Trans. Model. Comput. Simul., 12:119–141, 2002.Google Scholar
• K. Majewski and K. Ramanan. How large queues build up in a Jackson network. To Appear in Math. of O.R., 2008.Google Scholar
• 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.Google Scholar
• 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.Google Scholar
• S. Parekh and J. Walrand. Quick simulation of rare events in networks. IEEE Trans. Automat. Contr., 34:54–66, 1989. MR0970932Google Scholar
• P. Robert. Stochastic Networks and Queues. Springer-Verlag, Berlin, 2003. MR1996883Google Scholar
• 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.Google Scholar