Queue-and-idleness-ratio controls in many-server service systems

Mathematics of Operations Research

Volumn 34, Issue 2, 2009, Pages 363-396

  Gurvich, Itay ^a   Whitt, Ward ^b  

^a NORTHWESTERN UNIVERSITY   (United States)

^b Columbia University ^*  (United States)

Author keywords

Control of queueing systems; Diffusion limits; Halfin Whitt regime; Heavy traffic; QED regime; State space collapse

Indexed keywords

DIFFUSION LIMITS; HALFIN-WHITT REGIME; HEAVY-TRAFFIC; QED REGIME; STATE-SPACE COLLAPSE;

CUSTOMER SATISFACTION; QUEUEING NETWORKS; SALES;

QUEUEING THEORY;

EID: 67649981768     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1080.0366     Document Type: Article

References (31)

1. Armony, M. 2005. Dynamic routing in large-scale service systems with heterogenous servers. Queueing Systems 51(3-4) 287-329.
2. Armony, M., C. Maglaras. 2004. Contact centers with a call-back option and real-time delay information. Oper. Res. 52(4) 527-545.
3. Armony, M., C. Maglaras. 2004. On customer contact centers with a call-back option: Customer decisions, routing rules, and system design. Oper. Res. 52(2) 271-292.
4. Atar, R. 2005. Scheduling control for queueing systems with many servers: Asymptotic optimality in heavy traffic. Ann. Appl. Probab. 15(4) 2606-2650.
5. Billingsley, P. 1968. Convergence of Probability Measures. J. Wiley & Sons, New York.
6. Bramson, M. 1998. State space collapse with applications to heavy-traffic limits for multiclass queueing networks. Queueing Systems 30 89-148.
7. Browne, S., W. Whitt. 1995. Piecewise-linear diffusion processes. J. H. Dshalalow, ed. Advances in Queueing: Theory, Methods, and Open Problems. CRC Press, Inc., Boca Raton, FL, 463-480.
8. Budhiraja, A., C. Lee. 2008. Stationary distribution convergence for generalized Jackson networks in heavy traffic. Math. Oper. Res. 34(1) 45-56.
9. Dai, J. G. 1995. On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. 5 49-77.
10. Dai, J. G., T. Tezcan. 2008. Optimal control of parallel server systems with many servers in heavy traffic. Queueing Systems 59(2) 95-134.
11. Dai, J. G., T. Tezcan. 2009. Dynamic control of N-systems with many servers: Asymptotic optimality of a static priority policy in heavy traffic. Oper. Res. Forthcoming.
12. Dai, J. G., T. Tezcan. 2009. State space collapse in many-server diffusion limits of parallel server systems. Math. Oper. Res. Forthcoming.
13. Gamarnik, D., A. Zeevi. 2006. Validity of heavy traffic steady-state approximations in generalized Jackson networks. Ann. Appl. Probab. 16 56-90.
14. Gans, N., G. Koole, A. Mandelbaum. 2003. Telephone call centers: Tutorial, review, and research prospects. Manufacturing Service Oper. Management 5(2) 79-141.
15. Garnett, O., A. Mandelbaum, M. Reiman. 2002. Designing a call center with impatient customers. Manufacturing Service Oper. Management 4(3) 208-227.
16. Gurvich, I., W. Whitt. 2007. Service-level differentiation in many-server service systems via queue-ratio routing. Oper. Res. Forthcoming.
17. Gurvich, I., W. Whitt. 2009. Scheduling flexible servers with convex delay costs in many-server service systems. Manufacturing Service Oper. Management. 11(2) 237-253.
18. Gurvich, I., M. Armony, A. Mandelbaum. 2008. Service-level differentiation in call centers with fully flexible servers. Management Sci. 54(2) 279-294.
19. Halfin, S., W. Whitt. 1981. Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29(3) 567-588.
20. Karatzas, I., S. E. Shreve. 1991. Brownian Motion and Stochastic Calculus, 2nd ed. Springer-Verlag, New York.
21. Lipster, R. Sh., A. N. Shirayev. 1989. Theory of Martingales. Kluwer Academic Publishers, Boston.
22. Mandelbaum, A., S. Stolyar. 2004. Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ-rule. Oper. Res. 52 836-855.
23. Pang, G., R. Talrejea, W Whitt. 2007. Martingale proofs of many-server heavy-traffic limits for Markovian queues. Probab. Surveys 4 193-267.
24. Protter, P. 1992. Stochastic Integration and Differential Equations - A New Approach. Springer-Verlag, New York.
25. Puhalskii, A. 1994. On the invariance principle for the first passage time. Math. Oper. Res. 19(4) 946-954.
26. Royden, H. L. 1968. Real Analysis, 2nd ed. Macmillan, London.
27. Talreja, R., W. Whitt. 2008. Heavy-traffic limits for waiting times in many-server queues with abandonments. Working paper, Columbia University, New York.
28. Tezcan, T. 2008. Optimal control of distributed parallel server systems under the Halfin and Whitt regime. Math. Oper. Res. 33(1) 51-90.
29. Van der Vaart, A. W 2006. Martingales, diffusions and financial mathematics - lecture notes. Available at: http://www.math.vu.nl/sto/onderwijs/ mdfm/.
30. Whitt, W 2002. Stochastic-Process limits: An Introduction to Stochastic-Process Limits and Their Application to Queues. Springer-Verlag, New York.
31. Williams, R. J. 1998. Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse. Queueing Systems 30(1-2) 27-88.