Optimal Control of Distributed Parallel Server Systems Under the Halfin and Whitt Regime

Published Online:https://doi.org/10.1287/moor.1070.0277

References

  • Aksin O. Z., Harker P. T. To sell or not to sell: Determining the tradeoffs between service and sales in retail banking phone centers. J. Service Res. (1999) 2:19–33CrossrefGoogle Scholar
  • Armony M. Dynamic routing in large-scale service systems with heterogenous servers. Queueing Systems (2005) 51:287–329CrossrefGoogle Scholar
  • Armony M., Maglaras C. On customer contact centers with a call-back option: Customer decisions, routing rules and system design. Oper. Res. (2004) 52:271–292LinkGoogle Scholar
  • Armony M., Maglaras C. Contact centers with a call-back option and real-time delay information. Oper. Res. (2004) 52:527–545LinkGoogle Scholar
  • Armony M., Mandelbaum A. Design, staffing and control of large service systems: The case of a single customer class and multiple server types. (2004) . Working paper, New York University, New YorkGoogle Scholar
  • Bacelli F., Hebuterne G., Kylstra F. J. On queues with impatient customers. Performance '81 (1981) (Elsevier, Amsterdam) 159–179Google Scholar
  • Billingsley P.Convergence of Probability Measures (1999) (Wiley, New York) CrossrefGoogle Scholar
  • Borst S., Mandelbaum A., Reiman M. Dimensioning large call centers. Oper. Res. (2004) 52:17–34LinkGoogle Scholar
  • Borst S. C., Flockhart A. D., Reiman M. I., Seery J. B. DEFINITY queue to best: Multisite routing simulations. (1996) . Compas Document ID 53921, Bell Laboratories, Lucent Technologies, Murray Hills, NJGoogle Scholar
  • Bramson M. State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems (1998) 30:89–148CrossrefGoogle Scholar
  • Brockmeyer E., Halstrom H. L., Jensen A.The Life and Works of A. K. Erlang (1948) (The Copenhagen Telephone Company, Copenhagen) Google Scholar
  • Chung K. L.A Course in Probability Theory (2001) 3rd ed.(Academic Press, New York) Google Scholar
  • Dai J. G. On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. (1995) 5:49–77CrossrefGoogle Scholar
  • Dai J. G.Stability of Fluid and Stochastic Processing Networks (1999) (MaPhySto, University of Aarhus, Aarhus, Denmark) Google Scholar
  • Dai J. G., Tezcan T. State space collapse in many server diffusion limits of parallel server systems. (2005) . Technical report. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA. http://www.isye.gatech.edu/∼dai/publications/preprints/daiTezcanSSC.pdfGoogle Scholar
  • Ethier S. N., Kurtz T. G.Markov Processes: Characterization and Convergence (1986) (John Wiley and Sons, New York) CrossrefGoogle Scholar
  • Foschini G. J., Salz J. A basic dynamic routing problem and diffusion. IEEE Trans. Comm. (1978) 26:320–327CrossrefGoogle Scholar
  • Gamarnik D., Zeevi A. Validity of heavy traffic steady-state approximations in open queueing networks. Ann. Appl. Probab (2006) 16(1):56–90CrossrefGoogle Scholar
  • Gans N., Koole G., Mandelbaum A. Telephone call centers: Tutorial, review and research prospects. Manufacturing Service Oper. Management (2003) 5:79–141LinkGoogle Scholar
  • Garnett O., Mandelbaum A., Reiman M. Designing a call center with impatient customers. Manufacturing Service Oper. Management (2002) 48:566–583Google Scholar
  • Gurvich I. Design and control of the M/M/N queue with multiclass customers and many servers. (2004) . Master's thesis, Haifa, IsrealGoogle Scholar
  • Gurvich I., Armony M., Mandelbaum A. Staffing and control of large-scale service systems with multiple customer classes and fully flexible servers. Management Sci. (2004) . ForthcomingGoogle Scholar
  • Halfin S., Whitt W. Heavy-traffic limits for queues with many exponential servers. Oper. Res. (1981) 29:567–588LinkGoogle Scholar
  • Harrison J. M., López M. J. Heavy traffic resource pooling in parallel-server systems. Queueing Systems Theory Appl. (1999) 33(4):339–368CrossrefGoogle Scholar
  • Jagerman D. L. Some properties of Erlang loss function. Bell Systems Tech. J. (1974) 53:525–551CrossrefGoogle Scholar
  • Kogan Y., Levy Y., Milito R. A. Call routing to distributed queues: Is FIFO really better than MED? Telecomm. Systems (1997) 7(1–3):299–312CrossrefGoogle Scholar
  • Law A. M., Kelton W. D.Simulation Modeling and Analysis (2000) 3rd ed.(McGraw-Hill)Google Scholar
  • Laws C. N. Resource pooling in queueing networks with dynamic routing. Adv. Appl. Probab. (1992) 24:699–724CrossrefGoogle Scholar
  • Levin G. Battling agent burnout. Connections (2004) OctoberGoogle Scholar
  • Mandelbaum A., Stolyar A. L. Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ-rule. Oper. Res. (2004) 52(6):836–855LinkGoogle Scholar
  • Puhalskii A. On the invariance principle for the first passage time. Math. Oper. Res. (1994) 19(4):946–954LinkGoogle Scholar
  • Puhalskii A., Reiman M. The multiclass GI/PH/N queue in the Halfin-Whitt regime. Adv. Appl. Probab. (2000) 32:564–595CrossrefGoogle Scholar
  • Reiman M. I. Some diffusion approximations with state space collapse. Proc. Internat. Seminar on Modeling and Performance Eval. Methodology (1983) (Springer-Verlag, Berlin) 209–240Google Scholar
  • Stolyar A. L. Maxweight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic. Ann. Appl. Probab. (2004) 14:1–53CrossrefGoogle Scholar
  • Stolyar A. L. Optimal routing in output-queued flexible server systems. Probab. Engrg. Inform. Sci. (2005) 19:141–189CrossrefGoogle Scholar
  • Teh Y., Ward A. R. Critical thresholds for dynamic routing in queueing networks. Queueing Systems: Theory Appl. (2002) 42:297–316CrossrefGoogle Scholar
  • Tezcan T. State space collapse in many-server diffusion limits of parallel server systems and applications. (2006) . Ph.D. thesis, Georgia Institute of Technology, Atlanta, GAGoogle Scholar
  • Tezcan T., Dai J. G. Dynamic control of N-systems with many servers: Asymptotic optimality of a static priority policy in heavy traffic. Oper. Res. (2006) . ForthcomingGoogle Scholar
  • Utchitelle L. Answering “800” calls, extra income buy no security. New York Times (2002) . (March 27) Section A, col. 5, p. 1Google Scholar
  • Van Mieghem J. A. Dynamic scheduling with convex delay costs: The generalized cμ-rule. Ann. Appl. Probab. (1995) 5:809–833CrossrefGoogle Scholar
  • Weber R. R. On the optimal assignment of customers to parallel servers. J. Appl. Probab. (1978) 15(2):406–413CrossrefGoogle Scholar
  • Whitt W. Deciding which queue to join: Some counterexamples. Oper. Res. (1986) 34(1):55–62LinkGoogle Scholar
  • Whitt W.Stochastic-Process Limits (2002) (Springer, New York) CrossrefGoogle Scholar
  • Whitt W. A diffusion approximation for the G/GI/n/m queue. Oper. Res. (2004) 52(6):922–941LinkGoogle Scholar
  • Whitt W. Heavy-traffic limits for the G/H2*/n/m queue. Math. Oper. Res. (2005) 30:1–27LinkGoogle Scholar
  • Winston W. Optimality of the shortest line discipline. J. Appl. Probab. (1977) 14(1):181–189CrossrefGoogle Scholar
  • Wolff R. W. Poisson arrivals see time averages. Oper. Res. (1982) 30(2):223–231LinkGoogle Scholar
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