Developing Effective Service Policies for Multiclass Queues with Abandonment: Asymptotic Optimality and Approximate Policy Improvement

References

• Argon NT, Ziya S, Righter R (2008) Scheduling impatient jobs in a clearing system with insights on patient triage in mass casualty incidents. Probability Engrg. Informational Sci. 22(3):301–322.Crossref, Google Scholar
• Ata B, Tongarlak MH (2013) On scheduling a multiclass queue with abandonments under general delay costs. Queueing Systems 74(1):65–104.Crossref, Google Scholar
• Atar R, Giat C, Shimkin N (2010) The cμ/θ-rule for many-server queues with abandonment. Oper. Res. 58(5):1427–1439.Link, Google Scholar
• Ayesta U, Jacko P, Novak V (2011) A nearly-optimal index rule for scheduling of users with abandonment. INFOCOM, 2011 Proc. IEEE (IEEE, New York), 2849–2857.Crossref, Google Scholar
• Bassamboo A, Harrison JM, Zeevi A (2005) Dynamic routing and admission control in high-volume service systems: Asymptotic analysis via multi-scale fluid limits. Queueing Systems 51(3):249–285.Crossref, Google Scholar
• Bertsekas DP (2012) Dynamic Programming and Optimal Control: Approximate Dynamic Programming, Vol. 2 (Athena Scientific, Belmont, MA).Google Scholar
• Down DG, Koole G, Lewis ME (2011) Dynamic control of a single-server system with abandonments. Queueing Systems 67(1):63–90.Crossref, Google Scholar
• Garnett O, Mandelbaum A, Reiman M (2002) Designing a call center with impatient customers. Manufacturing Service Oper. Management 4(3):208–227.Link, Google Scholar
• Gaver DP, Jacobs PA, Samorodnitsky G, Glazebrook KD (2006) Modeling and analysis of uncertain time-critical tasking problems. Naval Res. Logist. 53(6):588–599.Crossref, Google Scholar
• Gittins J, Glazebrook KD, Weber RR (2011) Multi-Armed Bandit Allocation Indices (John Wiley & Sons, Chichester, UK).Crossref, Google Scholar
• Glazebrook KD, Niño-Mora J (2001) Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance. Oper. Res. 49(4):609–623.Link, Google Scholar
• Glazebrook KD, Punton EL (2008) Dynamic policies for uncertain time-critical tasking problems. Naval Res. Logist. 55(2):142–155.Crossref, Google Scholar
• Glazebrook KD, Ansell PS, Dunn RT, Lumley RR (2004) On the optimal allocation of service to impatient tasks. J. Appl. Probab. 41(1):51–72.Crossref, Google Scholar
• Harrison MJ, Zeevi A (2004) Dynamic scheduling of a multiclass queue in the Halfin-Whitt heavy traffic regime. Oper. Res. 52(2):243–257.Link, Google Scholar
• Howard R (1960) Dynamic Programming and Markov Processes (MIT Press, Cambridge, MA).Google Scholar
• Jouini O, Pot A, Koole G, Dallery Y (2010) Online scheduling policies for multiclass call centers with impatient customers. Eur. J. Oper. Res. 207(1):258–268.Crossref, Google Scholar
• Kim J, Ward AR (2013) Dynamic scheduling of a GI/GI/1 + GI queue with multiple customer classes. Queueing Systems 75(2):339–384.Crossref, Google Scholar
• Klimov GP (1974) Time-sharing service systems I. Theory Probab. Its Appl. 19(3):532–551.Crossref, Google Scholar
• Klimov GP (1978) Time-sharing service systems II. Theory Probab. Its Appl. 23(2):314–321.Crossref, Google Scholar
• Krishnan KR (1987) Joining the right queue: A Markov decision-rule. Proc. 26th IEEE Conf. Decision Control, Vol. 26 (IEEE, New York), 1863–1868.Crossref, Google Scholar
• Larrañaga M, Ayesta U, Verloop M (2014) Index policies for a multi-class queue with convex holding cost and abandonments. 2014 ACM Internat. Conf. Measurement Model. Comput. Systems (ACM, New York), 125–137.Crossref, Google Scholar
• Li D, Glazebrook KD (2010) An approximate dynamic programing approach to the development of heuristics for the scheduling of impatient jobs in a clearing system. Naval Res. Logist. 57(3):225–236.Crossref, Google Scholar
• Lin KY, Kress M, Szechtman R (2009) Scheduling policies for an antiterrorist surveillance system. Naval Res. Logist. 56(2):113–126.Crossref, Google Scholar
• Niederreiter H (1978) Existence of good lattice points in the sense of Hlawka. Monatshefte für Mathematik 86(3):203–219.Crossref, Google Scholar
• Powell MJD (1987) Radial basis functions for multivariable interpolation: A review. Mason JC, Cox MG, eds. Algorithms for Approximation (Clarendon Press, Oxford, UK), 143–167.Google Scholar
• Powell MJD (1999) Recent research at Cambridge on radial basis functions. Müller MW, Buhmann MD, Mache DH, Felten M, eds. New Developments in Approximation Theory, Vol. 132 (Birkhäuser Verlag, Basel, Switzerland), 215–232.Crossref, Google Scholar
• Powell WB (2011) Approximate Dynamic Programming: Solving the Curses of Dimensionality, 2nd ed. (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
• Puterman ML (1994) Markov Decision Processes: Discrete Stochastic Dynamic Programming (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
• Tijms HC (1994) Stochastic Models: An Algorithmic Approach, Wiley Series in Probability and Mathematical Statistics (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Verloop M (2014) Asymptotic optimal control of multi-class restless bandits. Technical report hal-00743781, Université de Toulouse, France.Google Scholar