Construction of Asymptotically Optimal Control for Crisscross Network from a Free Boundary Problem

Published Online:https://doi.org/10.1287/15-SSY211

References

  • S. L. Bell and R. J. Williams. Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy. Ann. Appl. Probab., 11(3):608–649, 2001. MR1865018Google Scholar
  • S. L. Bell and R. J. Williams. Dynamic scheduling of a parallel server system in heavy traffic with complete resource pooling: Asymptotic optimality of a threshold policy. Electron. J. Probab., 10:1044–1115, 2005.Google Scholar
  • V. E. Beneš, L. A. Shepp, and H. S. Witsenhausen. Some solvable stochastic control problems. Stochastics, 4(1):39–83, 1980/81. MR0587428Google Scholar
  • A. Budhiraja and A. P. Ghosh. A large deviation approach to asymptotically optimal control of crisscross network in heavy traffic. The Annals of Applied Probability, 15(3):1887–1935, 2005.Google Scholar
  • A. Budhiraja and A. P. Ghosh. Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function. Ann. Appl Probab, 16(4):1962–2006, 2006. MR2288710Google Scholar
  • A. Budhiraja and K. Ross. Convergent numerical scheme for singular stochastic control with state constraints in a portfolio selection problem. SIAM J. Control Optim., 45(6):2169–2206, 2007. MR2285720Google Scholar
  • A. Budhiraja and K. Ross. Optimal stopping and free boundary characterizations for some brownian control problems. Ann Appl. Probab., 18:2367–2391, 2008. MR2474540Google Scholar
  • A. Budhiraja and A. P. Ghosh. Controlled stochastic networks in heavy traffic: convergence of value functions. Ann. Appl. Probab., 22(2):734–791, 2012. MR2953568Google Scholar
  • A. Budhiraja, A. P. Ghosh, and X. Liu, Scheduling control for Markov modulated single-server multiclass queueing systems in heavy traffic, Queueing Systems, 78(1), 57–97, 2014. MR3238008Google Scholar
  • H. Chen and A. Mandelbeaum. Leontief systems, RBV’s and RBM’s. In M. H. A. Davis and R. J. Elliott, editors, Applied Stochastic Analysis, pages 1–43. Gordon and Breach, 1991.Google Scholar
  • J. G. Dai and W. Lin. Asymptotic optimality of maximum pressure policies in stochastic processing networks. Ann. Appl. Probab., 18(6):2239–2299, 2008. MR2473656Google Scholar
  • S. N. Ethier and T. G. Kurtz, Markov processes: Characterization and convergence, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York 1986.Google Scholar
  • J. M. Harrison. Brownian models of queueing networks with heterogeneous customer population. In W. Fleming and F. L. Lion, editors, Stochastic Differential Systems, Stochastic Control Theory and Applications, pages 147–186. Springer, New York, 1988.Google Scholar
  • J. M. Harrison. Heavy traffic analysis of a system with parallel servers: Asymptotic optimality of discrete-review policies. Ann. Appl. Probab., 8(3):822–848, 1998.Google Scholar
  • J. M. Harrison and M. I. Taksar. Instantaneous control of Brownian motion. Math. Oper. Res., 8(3):439–453, 1983. MR0716123LinkGoogle Scholar
  • J. M. Harrison and J. A. Van Mieghem. Dynamic control of Brownian networks: state space collapse and equivalent workload formulations. Ann. Appl. Probab., 7(3):747–771, 1997. MR1459269Google Scholar
  • J. M. Harrison and L. M. Wein. Scheduling networks of queues: Heavy traffic analysis of a simple open network. Queueing Systems Theory Appl., 5(4):265–279, 1989.Google Scholar
  • Sunil Kumar. Two-server closed networks in heavy traffic: Diffusion limits and asymptotic optimality. Ann. Appl. Probab., 10(3):930–961, 2000.Google Scholar
  • Sunil Kumar and Kumar Muthuraman. A numerical method for solving singular stochastic control problems. Oper. Res., 52(4):563–582, 2004.LinkGoogle Scholar
  • H. J. Kushner and L. F. Martins. Numerical methods for stochastic singular control problems. SIAM J. Control Optim., 29:1443–1475, 1991.Google Scholar
  • H. J. Kushner and L. F. Martins. Heavy traffic analysis of a controlled multiclass queueing network via weak convergence methods. SIAM J. Control Optim., 34(5):1781–1797, 1996.Google Scholar
  • L. F. Martins, S. E. Shreve, and H. M. Soner. Heavy traffic convergence of a controlled, multiclass queueing system. SIAM J. Control Optim., 34:2133–2171, 1996.Google Scholar
  • Kumar Muthuraman and Sunil Kumar. Solving free-boundary problems with applications in finance. Found. Trends Stoch. Syst., 1(4):259–341, 2006. MR2438635Google Scholar
  • V. Pesic and R. J. Williams, Dynamic scheduling for parallel server systems in heavy traffic: Graphical structure, decoupled workload matrix and some sufficient conditions for solvability of the Brownian control problem, Preprint.Google Scholar
  • S. E. Shreve and H. M. Soner. A free boundary problem related to singular stochastic control. In Applied stochastic analysis (London, 1989), volume 5 of Stochastics Monogr., pages 265–301. Gordon and Breach, New York, 1991.Google Scholar
  • A. V. Skorohod. Stochastic equations for diffusions in a bounded region. Theory Probab. Appl., (6):264–274, 1961.Google Scholar
  • H. Mete Soner and S. E. Shreve. Regularity of the value function for a two-dimensional singular stochastic control problem. SIAM J. Control Optim., 27(4):876–907, 1989. MR1001925Google Scholar
  • P. Yang, H. Chen, and D. Yao. Control and scheduling in a two-station queueing network. Queueing Syst. Theory Appl., 18:301–332, 1994.Google 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.