Asymptotic Analysis of a Multiclass Queueing Control Problem Under Heavy Traffic with Model Uncertainty

Published Online:https://doi.org/10.1287/stsy.2019.0034

References

  • Atar R, Biswas A (2014) Control of the multiclass G/G/1 queue in the moderate deviation regime. Ann. Appl. Probab. 24(5):2033–2069.Google Scholar
  • Atar R, Cohen A (2016) A differential game for a multiclass queueing model in the moderate-deviation heavy-traffic regime. Math. Oper. Res. 41(4):1354–1380.LinkGoogle Scholar
  • Atar R, Cohen A (2017) Asymptotically optimal control for a multiclass queueing model in the moderate deviation heavy traffic regime. Ann. Appl. Probab. 27(5):2862–2906.Google Scholar
  • Atar R, Mendelson G (2016) On the non-Markovian multiclass queue under risk-sensitive cost. Queueing Systems 84(3-4):265–278.Google Scholar
  • Atar R, Saha S (2017) Optimality of the generalized cμ rule in the moderate deviation regime. Queueing Systems 87(1):113–130.Google Scholar
  • Atar R, Shifrin M (2014) An asymptotic optimality result for the multiclass queue with finite buffers in heavy traffic. Stochastic Systems 4(2):556–603.LinkGoogle Scholar
  • Bandi C, Bertsimas D, Youssef N (2015) Robust queueing theory. Oper. Res. 63(3):676–700.Google Scholar
  • Bassamboo A, Randhawa RS, Zeevi A (2010) Capacity sizing under parameter uncertainty: Safety staffing principles revisited. Management Sci. 56(10):1668–1686.LinkGoogle Scholar
  • Bayraktar E, Zhang Y (2015) Minimizing the probability of lifetime ruin under ambiguity aversion. SIAM J. Control Optim. 53(1):58–90.Google Scholar
  • Bell SL, Williams RJ (2001) 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.Google Scholar
  • Billingsley P (1999) Convergence of Probability Measures. Wiley Series in Probability and Statistics: Probability and Statistics, 2nd ed. (John Wiley & Sons Inc., New York).Google Scholar
  • Biswas A (2014) Risk-sensitive control for the multiclass many-server queues in the moderate deviation regime. Math. Oper. Res. 39(3):908–929.Google Scholar
  • Blanchet J, Murthy KR (2019) Quantifying distributional model risk via optimal transport. Math. Oper. Res. 44(2):565–600. Google Scholar
  • Blanchet J, Dolan C, Lam H (2014) Robust rare-event performance analysis with natural non-convex constraints. Tolk A, Yilmaz L, Diallo SY, Ryzhov IO, eds. Proc. 2014 Winter Simulation Conf. (IEEE Press, Piscataway, NJ), 595–603.Google Scholar
  • Budhiraja A, Ghosh AP (2006) Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function. Ann. Appl. Probab. 16(4):1962–2006.Google Scholar
  • Budhiraja A, Ghosh AP (2012) Controlled stochastic networks in heavy traffic: Convergence of value functions. Ann. Appl. Probab. 22(2):734–791.Google Scholar
  • Budhiraja A, Ross K (2006) Existence of optimal controls for singular control problems with state constraints. Ann. Appl. Probab. 16(4):2235–2255.Google Scholar
  • Budhiraja A, Ross K (2007) Convergent numerical scheme for singular stochastic control with state constraints in a portfolio selection problem. SIAM J. Control Optim. 45(6):2169–2206.Google Scholar
  • Cohen A (2017) Asymptotic analysis of a multiclass queueing control problem under heavy-traffic with model uncertainty. Preprint, submitted October 3, https://arxiv.org/abs/1710.00968.Google Scholar
  • Cohen A (2018) Brownian control problems for a multiclass M/M/1 queueing problem with model uncertainty. Math. Oper. Res. 44(2):739–766.Google Scholar
  • Dai JG, Williams RJ (1996) Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons. Theory Probab. Appl. 40(1):1–40.Google Scholar
  • Dellacherie C, Meyer PA (1978) Probabilities and Potential, North-Holland Mathematics Studies, vol. 29 (North-Holland Publishing Co., Amsterdam-New York).Google Scholar
  • Dupuis P (2003) Explicit solution to a robust queueing control problem. SIAM J. Control Optim. 42(5):1854–1875.Google Scholar
  • Ethier SN, Kurtz TG (1986) Markov Processes. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics (John Wiley & Sons Inc., New York).Google Scholar
  • Hansen LP, Sargent TJ (2008) Robustness (Princeton University Press, Princeton, NJ).Google Scholar
  • Hansen LP, Sargent TJ, Turmuhambetova G, Williams N (2006) Robust control and model misspecification. J. Econom. Theory 128(1):45–90.Google Scholar
  • Harrison JM (1988) Brownian models of queueing networks with heterogeneous customer populations. Fleming WH, Lions P-L, eds. Stochastic Differential Systems, Stochastic Control Theory and Applications, IMA Volumes in Mathematics and Its Applications, vol. 10 (Springer, New York), 147–186.Google Scholar
  • Jain A, Lim AEB, Shanthikumar JG (2010) On the optimality of threshold control in queues with model uncertainty. Queueing Systems 65(2):157–174.Google Scholar
  • Karatzas I, Shreve SE (1991) Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, vol. 113, 2nd ed. (Springer-Verlag, New York).Google Scholar
  • Kruk L, Lehoczky J, Ramanan K, Shreve S (2007) An explicit formula for the Skorokhod map on [0, a]. Ann. Probab. 35(5):1740–1768.Google Scholar
  • Kurtz TG (1991) Random time changes and convergence in distribution under the Meyer-Zheng conditions. Ann. Probab. 19(3):1010–1034.Google Scholar
  • Kushner HJ, Martins LF (1991) Numerical methods for stochastic singular control problems. SIAM J. Control Optim. 29(6):1443–1475.Google Scholar
  • Kushner HJ, Martins LF (1993) Limit theorems for pathwise average cost per unit time problems for controlled queues in heavy traffic. Stochastics Stochastics Rep. 42(1):25–51.Google Scholar
  • Lam H (2016) Robust sensitivity analysis for stochastic systems. Math. Oper. Res. 41(4):1248–1275.Google Scholar
  • Maenhout PJ (2004) Robust portfolio rules and asset pricing. Rev. Financial Stud. 17(4):951–983.Google Scholar
  • Martins LF, Kushner HJ (1990) Routing and singular control for queueing networks in heavy traffic. SIAM J. Control Optim. 28(5):1209–1233.Google Scholar
  • Meyer PA, Zheng WA (1984) Tightness criteria for laws of semimartingales. Ann. Inst. H. Poincaré Probab. Statist. 20(4):353–372.Google Scholar
  • Petersen IR, James MR, Dupuis P (2000) Minimax optimal control of stochastic uncertain systems with relative entropy constraints. IEEE Trans. Automatic. Control 45(3):398–412.Google Scholar
  • Plambeck E, Kumar S, Harrison JM (2001) A multiclass queue in heavy traffic with throughput time constraints: Asymptotically optimal dynamic controls. Queueing Systems 39(1):23–54.Google Scholar
  • Protter PE (2004) Stochastic Integration and Differential Equations, Applications of Mathematics (New York), vol. 21, 2nd ed. (Springer-Verlag, Berlin).Google Scholar
  • Stroock DW (1987) Lectures on Stochastic Analysis: Diffusion Theory, London Mathematical Society Student Texts, vol. 6 (Cambridge University Press, Cambridge, UK).Google Scholar
  • Whitt W (2006) Staffing a call center with uncertain arrival rate and absenteeism. Production Oper. Management 15(1):88–102.Google Scholar
  • Whitt W, You W (2018) Using robust queueing to expose the impact of dependence in single-server queues. Oper. Res. 66(1):184–199.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.