Queues with many servers and impatient customers

Mathematics of Operations Research

Volumn 37, Issue 1, 2012, Pages 41-65

  Mandelbaum, Avishai ^a   Momčilović, Petar ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b University of Florida   (United States)

Author keywords

Abandonment; Diffusion approximation; Halfin Whitt regime; Multiserver queue; QED regime

Indexed keywords

ABANDONMENT; DIFFUSION APPROXIMATIONS; HALFIN-WHITT REGIME; MULTI-SERVER QUEUE; QED REGIME;

COMPUTER APPLICATIONS; RESEARCH;

QUEUEING THEORY;

EID: 84858699374     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1110.0530     Document Type: Article

References (34)

1. Baccelli, F., P. Bremaud. 2003. Elements of Queueing Theory, 2nd ed. Springer-Verlag, Berlin.
2. Bhattacharya, P., A. Ephremides. 1991. Stochastic monotonicity properties of multiserver queues with impatient customers. J. Appl. Probab. 28(3) 673-682.
3. Billingsley, P. 1995. Probability and Measure, 3rd ed. Wiley, New York.
4. Borovkov, A. A. 1967. On limit laws for service processes in multichannel systems. Siberian Math. J. 8(5) 746-763.
5. Browne, S., W. Whitt. 1995. Piecewise-linear diffusion processes. J. H. Dshalalow, ed. Probability and Stochastic Series: Advances in Queueing: Theory, Methods and Open Problems. CRC Press, Boca Raton, FL, 463-480.
6. Chung, K. L. 1974. A Course in Probability Theory, 2nd ed. Academic Press, San Diego.
7. Dai, J., S. He. 2010. Customer abandonment in many-server queues. Math. Oper. Res. 35(2) 347-362.
8. Decreusefond, L., P. Moyal. 2008. A functional central limit theorem for the M/GI/. queue. Ann. Appl. Probab. 18(6) 2156-2178.
9. Erlang, A. K. 1948. On the rational determination of the number of circuits. E. Brockmeyer, H. L. Halstrom, A. Jensen, eds. The Life and Works of A. K. Erlang. Copenhagen Telephone Company, Copenhagen, 216-221.
10. Gamarnik, D., P. Momčilović. 2008. Steady-state analysis of a multiserver queue in the Halfin-Whitt regime. Adv. Appl. Probab. 40(2) 548-577.
11. Gans, N., G. Koole, A. Mandelbaum. 2003. Telephone call centers: Tutorial, review, and research prospects. Manufacturing Service Oper. Management 5(2) 79-141.
12. Garnett, O., A. Mandelbaum, M. Reiman. 2002. Designing a call center with impatient customers. Manufacturing Service Oper. Management 4(3) 208-227.
13. Green, R. A., P. C. Wyer, J. Giglio. 2002. ED walkout rate correlated with ED length of stay but not with ED volume or hospital census (abstract). Acad. Emergency Medicine 9(5) 514.
14. Halfin, S., W. Whitt. 1981. Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29(3) 567-588. (Pubitemid 12437583)
15. Iglehart, D. L. 1973. Weak convergence of compound stochastic processes. Stochastic Process. Appl. 1(1) 11-31.
16. Jagerman, D. 1974. Some properties of the Erlang loss function. Bell System Techn. J. 53(3) 525-551.
17. Jelenković, P., A. Mandelbaum, P. Momčilović. 2004. Heavy traffic limits for queues with many deterministic servers. Queueing Syst. Theory Appl. 47(1-2) 53-69. (Pubitemid 38919346)
18. Kang, W., K. Ramanan. 2010. Fluid limits of many-server queues with reneging. Ann. Appl. Probab. 20(6) 2204-2260.
19. Kaspi, H., K. Ramanan. 2011. Law of large numbers limits for many-server queues. Ann. Appl. Probab. 21(1) 33-114.
20. Krichagina, E., A. Puhalskii. 1997. A heavy-traffic analysis of a closed queueing system with a GI=. service center. Queueing Syst. Theory Appl. 25(1-4) 235-280. (Pubitemid 127534246)
21. Mandelbaum, A., P. Momčilović. 2008. Queues with many servers: The virtual waiting-time process in the QED regime. Math. Oper. Res. 33(3) 561-586.
22. Mandelbaum, A., S. Zeltyn. 2004. The impact of customers' patience on delay and abandonment: Some empirically-driven experiments with the M/M/N CG queue. OR Spectrum 26(3) 377-411. (Pubitemid 40549762)
23. Mandelbaum, A., S. Zeltyn. 2007. The M/M/n C G queue: Summary of performance measures. http://iew3.technion.ac.il/serveng/References/.
24. Mandelbaum, A., S. Zeltyn. 2009. Staffing many-server queues with impatient customers: Constraint satisfaction in call centers. Oper. Res. 57(5) 1189-1205.
25. Puhalskii, A. 1994. On the invariance principle for the first passage time. Math. Oper. Res. 19(4) 946-954.
26. Puhalskii, A., J. Reed. 2010. On many-server queues in heavy traffic. Ann. Appl. Probab. 20(1) 129-195.
27. Reed, J. 2009. The G/GI/N queue in the Halfin-Whitt regime. Ann. Appl. Probab. 19(6) 2211-2269.
28. Reed, J., R. Talreja. 2009. Distribution-valued heavy-traffic limits for the G/GI/. queue. Preprint, New York University, New York.
29. Reed, J., T. Tezcan. 2009. Hazard rate scaling for the GI/M/n + GI queue. Preprint, New York University, New York.
30. Talreja, R., W. Whitt. 2009. Heavy-traffic limits for waiting times in many-server queues with abandonment. Ann. Appl. Probab. 19(6) 2137-2175.
31. Whitt, W. 2002. Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues. Springer, New York.
32. Whitt, W. 2004. Efficiency-driven heavy-traffic approximations for many-server queues with abandonments. Management Sci. 50(10) 1449-1461.
33. Zeltyn, S. 2005. Call centers with impatient customers: Exact analysis and many-server asymptotics of the M/M/n C G queue. Ph.D. thesis, Technion, Haifa, Israel.
34. Zeltyn, S., A. Mandelbaum. 2005. Call centers with impatient customers: Many-server asymptotics of the M/M/nCG queue. Queueing Syst. Theory Appl. 51(3-4) 361-402. (Pubitemid 41813337)