Brownian Control Problems for a Multiclass M/M/1 Queueing Problem with Model Uncertainty
Published Online:19 Apr 2019https://doi.org/10.1287/moor.2018.0944
References
- [1] (2014) Control of the multiclass G/G/1 queue in the moderate deviation regime. Ann. Appl. Probab. 24(5):2033–2069.Crossref, Google Scholar
- [2] (2016) A differential game for a multiclass queueing model in the moderate-deviation heavy-traffic regime. Math. Oper. Res. 41(4):1354–1380.Link, Google Scholar
- [3] (2017) Asymptotically optimal control for a multiclass queueing model in the moderate deviation heavy traffic regime. Ann. Appl. Probab. 27(5):2862–2906.Crossref, Google Scholar
- [4] (2016) On the non-Markovian multiclass queue under risk-sensitive cost. Queueing Systems 84(3-4):265–278.Crossref, Google Scholar
- [5] (2017) Optimality of the generalized cμ rule in the moderate deviation regime. Queueing Systems 87(1):113–130.Crossref, Google Scholar
- [6] (2014) An asymptotic optimality result for the multiclass queue with finite buffers in heavy traffic. Stochastic Systems 4(2):556–603.Link, Google Scholar
- [7] (2015) Minimizing the probability of lifetime ruin under ambiguity aversion. SIAM J. Control Optim. 53(1):58–90.Crossref, Google Scholar
- [8] (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.Crossref, Google Scholar
- [9] (2014) Risk-sensitive control for the multiclass many-server queues in the moderate deviation regime. Math. Oper. Res. 39(3):908–929.Link, Google Scholar
- [10] (2014) Robust rare-event performance analysis with natural non-convex constraints. Proc. 2014 Winter Simulation Conf. (IEEE Press, New York), 595–603.Crossref, Google Scholar
- [11] (2006) Diffusion approximations for controlled stochastic networks: An asymptotic bound for the value function. Ann. Appl. Probab. 16(4):1962–2006.Crossref, Google Scholar
- [12] (2012) Controlled stochastic networks in heavy traffic: Convergence of value functions. Ann. Appl. Probab. 22(2):734–791.Crossref, Google Scholar
- [13] (2013) Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification. ESAIM Math. Model. Numer. Anal. 47(3):635–662.Crossref, Google Scholar
- [14] (2017) Asymptotic analysis of a multiclass queueing control problem under heavy-traffic with model uncertainty. Working paper, Cornell University, Ithaca, NY.Google Scholar
- [15] (2006) Controlled Markov Processes and Viscosity Solutions, 2nd ed. Stochastic Modelling and Applied Probability, vol. 25 (Springer, New York).Google Scholar
- [16] (2008) Robustness (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
- [17] (2006) Robust control and model misspecification. J. Econom. Theory 128(1):45–90.Crossref, Google Scholar
- [18] (1988) Brownian models of queueing networks with heterogeneous customer populations. Fleming W, Lions PL, eds. Stochastic Differential Systems, Stochastic Control Theory and Applications, IMA Volumes in Mathematics and its Applications, vol. 10 (Springer, New York), 147–186.Crossref, Google Scholar
- [19] (2000) Brownian models of open processing networks: Canonical representation of workload. Ann. Appl. Probab. 10(1):75–103.Crossref, Google Scholar
- [20] (2003) A broader view of Brownian networks. Ann. Appl. Probab. 13(3):1119–1150.Crossref, Google Scholar
- [21] (1983) Instantaneous control of Brownian motion. Math. Oper. Res. 8(3):439–453.Link, Google Scholar
- [22] (1997) Dynamic control of Brownian networks: State space collapse and equivalent workload formulations. Ann. Appl. Probab. 7(3):747–771.Crossref, Google Scholar
- [23] (2005) Workload reduction of a generalized Brownian network. Ann. Appl. Probab. 15(4):2255–2295.Crossref, Google Scholar
- [24] (2010) On the optimality of threshold control in queues with model uncertainty. Queueing Systems 65(2):157–174.Crossref, Google Scholar
- [25] (2007) An explicit formula for the Skorokhod map on [0,a]. Ann. Probab. 35(5):1740–1768.Crossref, Google Scholar
- [26] (2016) Robust sensitivity analysis for stochastic systems. Math. Oper. Res. 41(4):1248–1275.Link, Google Scholar
- [27] (2004) Robust portfolio rules and asset pricing. Rev. Financial Stud. 17(4):951–983.Crossref, Google Scholar
- [28] (2001) A multiclass queue in heavy traffic with throughput time constraints: Asymptotically optimal dynamic controls. Queueing Systems 39(1):23–54.Crossref, Google Scholar
- [29] (2003) Handbook of Exact Solutions for Ordinary Differential Equations, 2nd ed. (Chapman & Hall/CRC, Boca Raton, FL).Google Scholar
- [30] (1967) Maximum Principles in Differential Equations (Prentice-Hall, Englewood Cliffs, NJ).Google Scholar
- [31] (2013) Optimal scheduling in the hybrid-cloud. De Turck F, Diao Y, Hong CS, Medhi D, Sadre R, eds. Proc. 2013 IFIP/IEEE Internat. Sympos. Integrated Network Management, Ghent, Belgium, 51–59.Google Scholar
- [32] (2014) A note on the strong formulation of stochastic control problems with model uncertainty. Electronic Comm. Probab. 19(81):1–10.Google Scholar
- [33] (1980) Introduction to Numerical Analysis (Springer-Verlag, New York).Crossref, Google Scholar

