Rates of Convergence to Stationarity for Reflected Brownian Motion

Published Online:https://doi.org/10.1287/moor.2019.1006

References

  • [1] 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.LinkGoogle Scholar
  • [2] Blanchet J, Chen X (2015) Steady-state simulation of reflected Brownian motion and related stochastic networks. Ann. Appl. Probab. 25(6):3209–3250.CrossrefGoogle Scholar
  • [3] Blanchet J, Chen X (2019) Perfect sampling of generalized Jackson networks. Math. Oper. Res. 44(2):693–714.LinkGoogle Scholar
  • [4] Blanchet J, Chen X, Glynn P, Si N (2018) Efficient steady-state simulation of reflected Brownian motion. Working paper, Stanford University, Stanford, CA.Google Scholar
  • [5] Budhiraja A, Lee C (2007) Long time asymptotics for constrained diffusions in polyhedral domains. Stochastic Process. Appl. 117(8):1014–1036.CrossrefGoogle Scholar
  • [6] Budhiraja A, Lee C (2009) Stationary distribution convergence for generalized Jackson networks in heavy traffic. Math. Oper. Res. 34(1):45–56.LinkGoogle Scholar
  • [7] Chen H, Yao DD (2001) Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization (Springer, New York).CrossrefGoogle Scholar
  • [8] Creemers S, Lambrecht M (2010) Modeling a hospital queueing network. Boucherie R, van Dijk N, eds. Queueing Networks, International Series in Operations Research & Management Science, vol. 154 (Springer, Boston), 767–798.Google Scholar
  • [9] Feller W (1968) An Introduction to Probability Theory and Its Applications (John Wiley & Sons, New York).Google Scholar
  • [10] Gamarnik D, Zeevi A (2006) Validity of heavy traffic steady-state approximations in generalized Jackson networks. Ann. Appl. Probab. 16(1):56–90.CrossrefGoogle Scholar
  • [11] Harrison JM, Reiman MI (1981) Reflected Brownian motion on an orthant. Ann. Appl. Probab. 9(2):302–308.CrossrefGoogle Scholar
  • [12] Harrison JM, Williams RJ (1987) Brownian models of open queueing networks with homogeneous customer populations. Stochastics 22(2):77–115.CrossrefGoogle Scholar
  • [13] Harrison JM, Williams RJ (1992) Brownian models of feedforward queueing networks: Quasireversibilty and product form solutions. Ann. Appl. Probab. 2(2):263–293.CrossrefGoogle Scholar
  • [14] Kella O (1996) Stability and nonproduct form of stochastic fluid networks with Levy inputs. Ann. Appl. Probab. 6(1):186–199.CrossrefGoogle Scholar
  • [15] Kella O, Ramasubramanian S (2012) Asymptotic irrelevance of initial conditions for Skorokhod refection mapping on the nonnegative orthant. Math. Oper. Res. 37(2):301–312.LinkGoogle Scholar
  • [16] Kella O, Whitt W (1996) Stability and structural properties of stochastic storage networks. J. Appl. Probab. 33(4):1169–1180.CrossrefGoogle Scholar
  • [17] Sarantsev A (2017) Reflected Brownian motion in a convex polyhedral cone: Tail estimates for the stationary distribution. J. Theoret. Probab. 30(3):1200–1223.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.