Efficient Steady-State Simulation of High-Dimensional Stochastic Networks

References

• Armony M, Israelit S, Mandelbaum A, Marmor YN, Tseytlin Y, Yom-Tov GB (2015) On patient flow in hospitals: A data-based queueing-science perspective. Stochastic Systems 5(1):146–194.Link, Google Scholar
• Banerjee S, Budhiraja A (2020) Parameter and dimension dependence of convergence rates to stationarity for reflecting Brownian motions. Ann. Appl. Probab. 30(5):2005–2029.Google Scholar
• Blanchet J, Chen X (2015) Steady-state simulation of reflected Brownian motion and related stochastic networks. Ann. Appl. Probab. 25(6):3209–3250.Google Scholar
• Blanchet J, Chen X (2020) Rates of convergence to stationarity for reflected Brownian motion. Math. Oper. Res. 45(2):660–681.Link, Google Scholar
• Cottle RW, Pang JS, Stone RE (2009) The Linear Complementarity Problem (Society for Industrial and Applied Mathematics, Philadelphia, PA).Google Scholar
• Dai JG, Harrison JM (1992) Reflected Brownian motion in an orthant: Numerical methods for steady-state analysis. Ann. Appl. Probab. 2:65–86.Google Scholar
• Giles MB (2008) Multilevel Monte Carlo path simulation. Oper. Res. 56(3):607–617.Link, Google Scholar
• Giles MB (2015) Multilevel Monte Carlo methods. Acta Numerica 24:259–328.Google Scholar
• Giles MB, Majka M, Szpruch L, Vollmer S, Zygalakis K (2020) Multi-level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations. Statistics and Computing 30:507–524.Google Scholar
• Glynn PW, Rhee CH (2014) Exact estimation for Markov chain equilibrium expectations. J. Appl. Probab. 51A:377–389.Google Scholar
• Harrison JM (1985) Brownian Motion and Stochastic Flow Systems (Wiley, New York).Google Scholar
• Harrison JM, Reiman MI (1981) Reflected Brownian motion on an orthant. Ann. Appl. Probab. 9(2):302–308.Google Scholar
• Harrison JM, Williams RJ (1987) Brownian models of open queueing networks with homogeneous customer populations. Stochastics 22(2):77–115.Google Scholar
• Karlin S, Taylor HE (1981) A Second Course in Stochastic Processes (Academic Press, New York).Google Scholar
• Kella O, Ramasubramanian S (2012) Asymptotic irrelevance of initial conditions for Skorokhod reflection mapping on the nonnegative orthant. Math. Oper. Res. 37(2):301–312.Link, Google Scholar
• Kushner H (2013) Heavy Traffic Analysis of Controlled Queueing and Communication Networks, vol. 47 (Springer-Verlag, New York).Google Scholar
• Lipshutz D, Ramanan K (2021) Sensitivity analysis for the stationary distribution of reflected Brownian motion in a convex polyhedral cone. Math. Oper. Res. Forthcoming.Google Scholar
• Maguluri ST, Srikant R, Ying L (2012) Stochastic models of load balancing and scheduling in cloud computing clusters. Proc. IEEE INFOCOM (IEEE), 702–710.Google Scholar
• Mandelbaum A, Ramanan K (2010) Directional derivatives of oblique reflection maps. Math. Oper. Res. 35(3):527–558.Link, Google Scholar
• Rhee CH, Glynn PW (2015) Unbiased estimation with square root convergence for SDE models. Oper. Res. 63(5):1026–1043.Link, Google Scholar
• Shen X, Chen H, Dai J, Dai W (2002) The finite element method for computing the stationary distribution of an SRBM in a hypercube with applications to finite buffer queueing networks. Queueing Systems 42(1):33–62.Google Scholar