State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems

References

• Armony M. Dynamic routing in large-scale service systems with heterogenous servers. Queueing Systems (2005) 51:287–329Crossref, Google Scholar
• Armony M., Maglaras C. Contact centers with a call-back option and real-time delay information. Oper. Res. (2004) 52:527–545Link, Google Scholar
• Armony M., Maglaras C. On customer contact centers with a call-back option: Customer decisions, routing rules and system design. Oper. Res. (2004) 52:271–292Link, Google Scholar
• Ata B., Kumar S. Heavy traffic analysis of open processing networks with complete resource pooling: Asymptotic optimality of discrete review policies. Ann. Appl. Probab. (2005) 15:331–391Crossref, Google Scholar
• Atar R. A diffusion model of scheduling control in queueing systems with many servers. Ann. Appl. Probab. (2005) 15:820–852Crossref, Google Scholar
• Atar R. Scheduling control for queueing systems with many servers: Asymptotic optimality in heavy traffic. Ann. Appl. Probab. (2005) 15:2606–2650Crossref, Google Scholar
• Atar R., Mandelbaum A., Reiman M. Scheduling a multi-class queue with many exponential servers: Asymptotic optimality in heavy-traffic. Ann. Appl. Probab. (2004) 14:1084–1134Crossref, Google Scholar
• Billingsley P.Convergence of Probability Measures (1999) 2nd ed.(John Wiley & Sons, New York) Wiley Series in Probability and StatisticsCrossref, Google Scholar
• Borovkov A. A. On limit laws for service processes in multi-channel systems. Siberian Math. J. (1967) 8:983–1004Crossref, Google Scholar
• Bramson M. State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems (1998) 30:89–148Crossref, Google Scholar
• Bramson M., Dai J. G. Heavy traffic limits for some queueing networks. Ann. Appl. Probab. (2001) 11:49–90Crossref, Google Scholar
• Chen H., Yao D. D.Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization (2001) (Springer, New York) Crossref, Google Scholar
• Dai J. G. On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. (1995) 5:49–77Crossref, Google Scholar
• Dai J. G., Lin W. Maximum pressure policies in stochastic processing networks. Oper. Res. (2005) 53:197–218Link, Google Scholar
• Dai J. G., Lin W. Asymptotic optimality of maximum pressure policies in stochastic processing networks. Ann. Appl. Probab. (2008) 18:2239–2299Crossref, Google Scholar
• Dai J. G., Tezcan T. Optimal control of parallel server systems with many servers in heavy traffic. Queueing Systems (2008) 59:95–134Crossref, Google Scholar
• Dai J. G., He S., Tezcan T. Many-server diffusion limits for G/Ph/n + GI queues. Ann. Appl. Probab. (2010) 20:1854–1890Crossref, Google Scholar
• Davis M. H. A. Piecewise-deterministic Markov processes: A general class of nondiffusion stochastic models. J. Roy. Statist. Soc. Ser. B (1984) 46(3):353–388Crossref, Google Scholar
• Ethier S. N., Kurtz T. G.Markov Processes: Characterization and Convergence (1986) (John Wiley & Sons, New York) Crossref, Google Scholar
• Fleming P., Stolyar A. L., Simon B. Heavy traffic limit for a mobile phone system model. Proc. 2nd Internat. Conf. Telecommunication Systems, Modeling Anal. (1994) Nashville, TN:317–327Google Scholar
• Gans N., Koole G., Mandelbaum A. Telephone call centers: Tutorial, review and research prospects. Manufacturing Service Oper. Management (2003) 5:79–141Link, Google Scholar
• Garnett O., Mandelbaum A., Reiman M. Designing a call center with impatient customers. Manufacturing Service Oper. Management (2002) 48:566–583Google Scholar
• Gross D., Harris C. M.Fundamentals of Queueing Theory (1998) 3rd ed.(Wiley & Sons, New York) Wiley Series in Probability and StatisticsGoogle Scholar
• Gurvich I., Whitt W. Service-level differentiation in many-server service systems via queue-ratio routing. Oper. Res. (2010) 58(2):316–328Link, Google Scholar
• Gurvich I., Armony M., Mandelbaum A. Service level differentiation in call centers with fully flexible servers. Management Sci. (2005) 54:279–294Link, Google Scholar
• Halfin S., Whitt W. Heavy-traffic limits for queues with many exponential servers. Oper. Res. (1981) 29:567–588Link, Google Scholar
• Harrison J. M.Brownian Motion and Stochastic Flow Systems (1985) (John Wiley & Sons, New York) Google Scholar
• Harrison J. M., Fleming W., Lions P. L. Brownian models of queueing networks with heterogeneous customer populations. Stochastic Differential Systems, Stochastic Control Theory and Their Applications (1988) 10(Springer-Verlag, New York) 147–186The IMA Volumes in Mathematics and Its ApplicationsCrossref, Google Scholar
• Harrison J. M. Brownian models of open processing networks: Canonical representation of workload. Ann. Appl. Probab. (2000) 10:75–103Crossref, Google Scholar
• Harrison J. M., Zeevi A. Dynamic scheduling of a multiclass queue in the Halfin and Whitt heavy traffic regime. Oper. Res. (2004) 52:243–257Link, Google Scholar
• Iglehart D. L. Weak convergence of compound stochastic process. Stochastic Processes Appl. (1973) 1:11–31Crossref, Google Scholar
• Maglaras C. Discrete-review policies for scheduling stochastic networks: Trajectory tracking and fluid-scale asymptotic optimality. Ann. Appl. Probab. (2000) 10(3):897–929Crossref, Google Scholar
• Maglaras C., Zeevi A. Pricing and capacity sizing for systems with shared resources: Approximate solutions and scaling relations. Management Sci. (2003) 49:1018–1038Link, Google Scholar
• Maglaras C., Zeevi A. Diffusion approximations for a multiclass Markovian service system with “guaranteed” and “best-effort” service levels. Math. Oper. Res. (2004) 29(4):786–813Link, Google Scholar
• Maglaras C., Zeevi A. Pricing and design of differentiated services: Approximate analysis and structural insights. Oper. Res. (2005) 53:242–262Link, Google Scholar
• Mandelbaum A., Momčilović P. Queues with many servers and impatient customers. (2009) . Technical report, Technion, Haifa, IsraelGoogle Scholar
• Mandelbaum A., Stolyar A. L. Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ-rule. Oper. Res. (2004) 52:836–855Link, Google Scholar
• Mandelbaum A., Massey W. A., Reiman M. Strong approximations for Markovian service networks. Queueing Systems (1998) 30:149–201Crossref, Google Scholar
• Pang G., Talreja R., Whitt W. Martingale proofs of many-server heavy-traffic limits for markovian queues. Probab. Surveys (2007) 4:193–267Crossref, Google Scholar
• Puhalskii A., Reiman M. The multiclass GI/PH/N queue in the Halfin-Whitt regime. Adv. Appl. Probab. (2000) 32:564–595Crossref, Google Scholar
• Randhawa R. S., Kumar S. Multiserver loss systems with subscribers. Math. Oper. Res. (2009) 34(1):142–179Link, Google Scholar
• Reed J. The G/GI/N queue in the Halfin-Whitt regime. Ann. Appl. Probab. (2009) 19:2211–2269Crossref, Google Scholar
• Ross S.Stochastic Processses (1996) (John Wiley & Sons, New York) Google Scholar
• Stolyar A. L. Optimal routing in output-queued flexible server systems. Probab. Engrg. Informational Sci. (2005) 19:141–189Crossref, Google Scholar
• Tezcan T. Optimal control of distributed parallel server systems under the Halfin and Whitt regime. Math. Oper. Res. (2008) 33:51–90Link, Google 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. (2010) 58(1):94–110Link, Google Scholar
• Whitt W. On the heavy-traffic limit theorem for GI/G/∞ queues. Adv. Appl. Probab. (1982) 14:171–190Crossref, Google Scholar
• Whitt W.Stochastic-Process Limits (2002) (Springer, New York) Crossref, Google Scholar
• Whitt W. A diffusion approximation for the G/GI/n/m queue. Oper. Res. (2004) 52:922–941Link, Google Scholar
• Whitt W. Heavy-traffic limits for the G/H2*/n/m queue. Math. Oper. Res. (2005) 30:1–27Link, Google Scholar
• Williams R. J. Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse. Queueing Systems (1998) 30:27–88Crossref, Google Scholar