Robust Queue Inference from Waiting Times

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
• Asanjarani A, Nazarathy Y, Taylor P (2021) A survey of parameter and state estimation in queues. Queueing Systems 97(1):39–80.Crossref, Google Scholar
• Bandi C, Bertsimas D (2012) Tractable stochastic analysis in high dimensions via robust optimization. Math. Programming 134(1):23–70.Crossref, Google Scholar
• Bandi C, Bertsimas D, Youssef N (2015) Robust queueing theory. Oper. Res. 63(3):676–700.Link, Google Scholar
• Bandi C, Trichakis N, Vayanos P (2019) Robust multiclass queuing theory for wait time estimation in resource allocation systems. Management Sci. 65(1):152–187.Link, Google Scholar
• Basawa IV, Bhat UN, Lund R (1996) Maximum likelihood estimation for single server queues from waiting time data. Queueing Systems 24:155–167.Crossref, Google Scholar
• Bayraksan G, Love DK (2015) Data-driven stochastic programming using phi-divergences. The Operations Research Revolution (INFORMS, Catonsville, MD), 1–19.Link, Google Scholar
• Ben-Tal A, Nemirovski A (2001) Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications (SIAM, Philadelphia).Crossref, Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Ben-Tal A, Den Hertog D, De Waegenaere A, Melenberg B, Rennen G (2013) Robust solutions of optimization problems affected by uncertain probabilities. Management Sci. 59(2):341–357.Link, Google Scholar
• Bennett KP, Mangasarian OL (1993) Bilinear separation of two sets in n-space. Comput. Optim. Appl. 2(3):207–227.Crossref, Google Scholar
• Bertsimas D, Brown DB (2009) Constructing uncertainty sets for robust linear optimization. Oper. Res. 57(6):1483–1495.Link, Google Scholar
• Bertsimas D, Natarajan K (2007) A semidefinite optimization approach to the steady-state analysis of queueing systems. Queueing Systems 56(1):27–39.Crossref, Google Scholar
• Bertsimas D, Thiele A (2006) A robust optimization approach to inventory theory. Oper. Res. 54(1):150–168.Link, Google Scholar
• Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.Crossref, Google Scholar
• Bertsimas D, Gupta V, Kallus N (2018) Data-driven robust optimization. Math. Programming 167(2):235–292.Crossref, Google Scholar
• Bezanson J, Edelman A, Karpinski S, Shah VB (2017) Julia: A fresh approach to numerical computing. SIAM Rev. 59(1):65–98.Crossref, Google Scholar
• Bingham N, Pitts SM (1999) Nonparametric inference from M/G/l busy periods. Stochastic Models 15(2):247–272.Crossref, Google Scholar
• Brown M (2002) An M/G/∞ estimation problem. Ann. Math. Statist. 41(2):651–654.Crossref, Google Scholar
• Burer S (2009) On the copositive representation of binary and continuous nonconvex quadratic programs. Math. Programming 120(2):479–495.Crossref, Google Scholar
• Chen W, Sim M, Sun J, Teo CP (2010) From CVaR to uncertainty set: Implications in joint chance-constrained optimization. Oper. Res. 58(2):470–485.Link, Google Scholar
• Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.Link, Google Scholar
• Duchi JC, Glynn PW, Namkoong H (2021) Statistics of robust optimization: A generalized empirical likelihood approach. Math. Oper. Res. 46(3):946–969.Link, Google Scholar
• Ehrgott M (2005) Multicriteria Optimization, vol. 491 (Springer Science & Business Media, Boston).Google Scholar
• Fatehi S, Wagner MR (2022) Crowdsourcing last-mile deliveries. Manufacturing Service Oper. Management 24(2):791–809.Link, Google Scholar
• Fearnhead P (2004) Filtering recursions for calculating likelihoods for queues based on inter-departure time data. Statist. Comput. 14(3):261–266.Crossref, Google Scholar
• Gao R, Kleywegt A (2023) Distributionally robust stochastic optimization with Wasserstein distance. Math. Oper. Res. 48(2):603–655.Link, Google Scholar
• Gnedenko BV, Kolmogorov AN (1954) Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Boston).Google Scholar
• Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4):902–917.Link, Google Scholar
• Goldenshluger A (2016) Nonparametric estimation of the service time distribution in the M/G/∞ queue. Adv. Appl. Probability 48(4):1117–1138.Crossref, Google Scholar
• Goldenshluger A (2018) The M/G/∞ estimation problem revisited. Bernoulli 24(4A):2531–2568.Crossref, Google Scholar
• Goldenshluger A, Koops DT (2019) Nonparametric estimation of service time characteristics in infinite-server queues with nonstationary poisson input. Stochastic Systems 9(3):183–207.Link, Google Scholar
• Hall P, Park J (2004) Nonparametric inference about service time distribution from indirect measurements. J. Royal Statist. Soc. Ser. B Statist. Methodology 66(4):861–875.Crossref, Google Scholar
• Hansen MB, Pitts SM (2006) Nonparametric inference from the M/G/1 workload. Bernoulli 12(4):737–759.Crossref, Google Scholar
• Harchol-Balter M (2021) Open problems in queueing theory inspired by datacenter computing. Queueing Systems 97(1):3–37.Crossref, Google Scholar
• Harrison JM (1973) The heavy traffic approximation for single server queues in series. J. Appl. Probability 10(3):613–629.Crossref, Google Scholar
• Hong LJ, Huang Z, Lam H (2021) Learning-based robust optimization: Procedures and statistical guarantees. Management Sci. 67(6):3447–3467.Link, Google Scholar
• Janson S (2011) Stable distributions. Preprint, submitted December 1, https://arxiv.org/abs/1112.0220.Google Scholar
• Kingman J (1962) Some inequalities for the queue GI/G/1. Biometrika 49(3):315–324.Crossref, Google Scholar
• Lam H, Zhou E (2017) The empirical likelihood approach to quantifying uncertainty in sample average approximation. Oper. Res. Lett. 45(4):301–307.Crossref, Google Scholar
• Larson RC (1990) The queue inference engine: Deducing queue statistics from transactional data. Management Sci. 36(5):586–601.Link, Google Scholar
• Larson RC, Cahn MF, Shell MC (1993) Improving the New York City arrest-to-arraignment system. Interfaces 23(1):76–96.Link, Google Scholar
• Lindley DV (1952) The theory of queues with a single server. Math. Proc. Cambridge Philosophical Soc. 48:277–289.Crossref, Google Scholar
• Lobo MS, Vandenberghe L, Boyd S, Lebret H (1998) Applications of second-order cone programming. Linear Algebra Appl. 284(1–3):193–228.Crossref, Google Scholar
• Mangasarian OL (1995) The linear complementarity problem as a separable bilinear program. J. Global Optim. 6(2):153–161.Crossref, Google Scholar
• Mohajerin Esfahani P, Kuhn D (2018) Data-driven distributionally robust optimization using the wasserstein metric: Performance guarantees and tractable reformulations. Math. Programming 171(1):115–166.Crossref, Google Scholar
• Pardalos PM, Rosen JB (1986) Methods for global concave minimization: A bibliographic survey. SIAM Rev. 28(3):367–379.Crossref, Google Scholar
• Petrik M, Zilberstein S (2011) Robust approximate bilinear programming for value function approximation. J. Machine Learn. Res. 12:3027–3063.Google Scholar
• Pólik I, Terlaky T (2007) A survey of the S-lemma. SIAM Rev. 49(3):371–418.Crossref, Google Scholar
• Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J. Risk 2:21–42.Crossref, Google Scholar
• Ross JV, Taimre T, Pollett PK (2007) Estimation for queues from queue length data. Queueing Systems 55(2):131–138.Crossref, Google Scholar
• Schweer S, Wichelhaus C (2015) Nonparametric estimation of the service time distribution in the discrete-time GI/G/∞ queue with partial information. Stochastic Processing Appl. 125(1):233–253.Crossref, Google Scholar
• Wang TY, Ke JC, Wang KH, Ho SC (2006) Maximum likelihood estimates and confidence intervals of an M/M/R queue with heterogeneous servers. Math. Methods Oper. Res. 63(2):371–384.Crossref, Google Scholar
• Whitt W (2012) Fitting birth-and-death queueing models to data. Statist. Probability Lett. 82(5):998–1004.Crossref, Google Scholar
• Whitt W, You W (2017) Using robust queueing to expose the impact of dependence in single-server queues. Oper. Res. 66(1):184–199.Link, Google Scholar
• Whitt W, You W (2019) Time-varying robust queueing. Oper. Res. 67(6):1766–1782.Link, Google Scholar
• Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
• Wong W (2021) How RFID solutions improve patient safety and hospital workflow. Accessed February 12, 2022, https://healthtechmagazine.net/article/2021/01/how-rfid-solutions-improve-patient-safety-and-hospital-workflow.Google Scholar
• Zhang Q, Cheng L, Boutaba R (2010) Cloud computing: State-of-the-art and research challenges. J. Internet Service Appl. 1(1):7–18.Crossref, Google Scholar