Fair dynamic routing in large-scale heterogeneous-server systems

Operations Research

Volumn 58, Issue 3, 2010, Pages 624-637

  Armony, Mor ^a   Ward, Amy R ^b  

^a NEW YORK UNIVERSITY   (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC OPTIMALITY; CLASS 1; DIFFUSION LIMITS; DYNAMIC ROUTING; KEY ISSUES; OPTIMIZATION PROBLEMS; SERVER SYSTEM; SERVICE CAPACITY; STOCHASTIC NETWORKS; TIME ALLOCATION; TRAFFIC INTENSITY; UTILITY FUNCTIONS;

DIFFUSION; OPTIMIZATION;

SERVERS;

EID: 77953605713     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1090.0777     Document Type: Article

References (44)

1. Altman, E. 1999. Constrained Markov Decision Processes. Chapman & Hall/CRC, Boca Raton, FL.
2. Armony, M. 2005. Dynamic routing in large-scale service systems with heterogeneous servers. Queueing Systems 51(3-4) 287-329.
3. Armony, M., I. Gurvich. 2009. When promotions meet operations: Cross selling and its effect on call-center performance. Manufacturing Service Oper. Management, ePub ahead of print December 29, 2009, http://msom.journal.informs. org/cgi/content/abstract/msom.1090.0281v1.
4. Armony, M., A. Mandelbaum. 2010. Routing and staffing in large-scale service systems: The case of homogeneous impatient customers and heterogeneous servers. Oper. Res. Forthcoming.
5. Atar, R. 2005. Scheduling control for queueing systems with many servers: Asymptotic optimality in heavy traffic. Ann. Appl. Probab. 15(4) 2606-2650. (Pubitemid 43106166)
6. Atar, R. 2008. Central limit theorem for a many-server queue with random service rates. Ann. Appl. Probab. 18(4) 1548-1568.
7. Atar, R., A. Shwartz. 2008. Efficient routing in heavy traffic under partial sampling of service times. Math. Oper. Res. 33(4) 899-909.
8. Atar, R., A. Mandelbaum, M. Reiman. 2004. Scheduling a multi-class queue with many i.i.d. servers: Asymptotic optimality in heavytraffic. Ann. Appl. Probab. 14(3) 1084-1134.
9. Atar, R., Y. Y. Shaki, A. Shwartz. 2009. A blind policy for equalizing cumulative idleness. Working paper, Technion, Haifa, Israel.
10. Avi-Itzhak, B., H. Levy, D. Raz. 2010. Quantifying fairness in queueing systems: Principles and applications. Probab. Engrg. Informational Sci. Forthcoming.
11. Bell, S. L., R. J. Williams. 2001. Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy. Ann. Appl. Probab. 11 608-649.
12. Bell, S. L., R. J. Williams. 2005. Dynamic scheduling of a parallel server system in heavy traffic with complete resource pooling: Asymptotic optimality of a threshold policy. Electronic J. Probab. 10 1044-1115.
13. Bhulai, S., G. Koole. 2003. A queueing model for call blending in call centers. IEEE Trans. Automatic Control 48 1434-1438.
14. Browne, S., W. Whitt. 1995. Piecewise-linear diffusion processes. J. H. Dshalalow, ed. Advances in Queueing: Theory, Methods, and Open Problems. CRC Press, Boca Raton, FL, 463-480.
15. Cabral, F. B. 2005. The slow server problem for uninformed customers. Queueing Systems 50(4) 353-370
16. Cabral, F. B. 2007. Queues with heterogeneous servers and uninformed customers: Who works the most? arxiv 0706.0560v1.
17. Cohen-Charash, Y., P. E. Spector. 2001. The role of justice in organizations: A meta-analysis. Organ. Behav. Human Decision Processes 86(2) 278-321.
18. Colquitt, J. A., D. E. Conlon, M. J. Wesson, C. O. L. H. Porter, K. Y. Ng. 2001. Justice at the millennium: A meta-analytic review of 25 years of organizational justice research. J. Appl. Psych. 86(3) 425-445.
19. Dai, J., T. Tezcan. 2005. State space collapse in many-server diffusion limits of parallel server systems. Working paper, Georgia Institute of Technology, Atlanta.
20. de Vericourt, F., Y.-P. Zhou. 2006. On the incomplete results for the heterogeneous server problem. Queueing Systems 52(3) 189-191.
21. Fleming, W. H., H. M. Soner. 1993. Controlled Markov Processes and Viscosity Solutions. Springer, New York.
22. Gans, N., Y.-P. Zhou. 2003. A call-routing problem with service-level constraints. Oper. Res. 51 255-271.
23. Glazebrook, K., J. Nino-Mora. 2001. Parallel scheduling of multiclass m/m/m queues: Approximate and heavy-traffic optimization of achievable performance. Oper. Res. 49(4) 609-623.
24. Gurvich, I., W. Whitt. 2009a. Queue-and-idleness-ratio controls in manyserver service systems. Math. Oper. Res. 34(2) 363-396.
25. Gurvich, I., W. Whitt. 2009b. Scheduling flexible servers with convex delay costs in many-server service systems. Manufacturing Service Oper. Management 11(2) 237-253.
26. Gurvich, I., W. Whitt. 2010. Service-level differentiation in manyserver service systems via queue-ratio routing. Oper. Res. 58(2) 316-328.
27. Gurvich, I., M. Armony, A. Mandelbaum. 2008. Service level differentiation in call centers with fully flexible servers. Management Sci. 54(2) 279-294.
28. Halfin, S., W. Whitt. 1981. Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29(3) 567-588.
29. Harrison, J. M. 1988. Brownian models of queueing networks with heterogeneous customer populations. W. Fleming, P. L. Lions, eds. Stochastic Differential Systems, Stochastic Control Theory and Applications. IMA Volumes in Mathematics and Its Applications, Vol.10. Springer-Verlag, New York, 147-186.
30. Harrison, J. M. 1998. Heavy traffic analysis of a system with parallel servers: Asymptotic optimality of discrete-review policies. Ann. Appl. Probab. 8 822-848.
31. Kushner, H. J., P. Dupuis. 2001. Numerical Methods for Stochastic Control Problems in Continuous Time. Springer, New York.
32. Larsen, R. L., A. K. Agrawala. 1983. Control of a heterogeneous twoserver exponential queueing system. IEEE Trans. Software Engrg. 522-526.
33. Lin, W., P. R. Kumar. 1984. Optimal control of a queueing system with two heterogeneous servers. IEEE Trans. Automatic Control 29 696-703.
34. Lu, H.-M., C.-C. Wu, W. Lin. 2007. Improving inter-server fairness in active queue management. IEEE Comm. Lett. 11(11) 910-912.
35. Mandelbaum, A., S. Stolyar. 2004. Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized c,-rule. Oper. Res. 52(6) 836-855.
36. Puterman, M. L. 1994. Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons, Inc., New York.
37. Rubinovich, M. 1983. The slow server problem. J. Appl. Probab. 28 205-213.
38. Stockbridge, R. H. 1991. A martingale approach to the slow server problem. J. Appl. Probab. 28 480-486.
39. Stolyar, S. 2005. Optimal routing in output-queued flexible server systems. Probab. Engrg. Informational Sci. 19(2) 141-189.
40. Teh, Y.-C., A. R. Ward. 2002. Critical thresholds for dynamic routing in queueing networks. Queueing Systems 42 297-315.
41. Tezcan, T. 2007. Asymptotically optimal control of many-server heterogeneous service systems with hyperexponential service times. Working paper, University of Illinois at Urbana-Champaign, Urbana, IL.
42. Tseytlin, Y. 2007. Queueing systems with heterogeneous servers: Improving patients' flow in hospitals. Master's thesis, Technion, Haifa, Israel. http://iew3.technion.ac.il/serveng/references/proposal-Yulia.pdf.
43. Whitt, W. 2006. The impact of increased employee retention upon performance in a customer contact center. Manufacturing Service Oper. Management 8(3) 221-234.
44. Wierman, A. 2007. Fairness and classification. Performance Eval. Rev. 34(4) 4-12.