Fluid limits of many-server queues with reneging

Annals of Applied Probability

Volumn 20, Issue 6, 2010, Pages 2204-2260

  Kang, Weining ^a   Ramanan, Kavita ^b  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^b BROWN UNIVERSITY   (United States)

Author keywords

Abandonment; Call centers; Fluid limits; GI G N queue; Many server queues; Measure valued processes; Reneging; Strong law of large numbers

Indexed keywords

EID: 77957695286     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/10-AAP683     Document Type: Article

References (24)

1. BACCELLI, F. and HEBUTERNE, G. (1981). On queues with impatient customers. In Performance '81 (E. Gelenbe, ed.) 159-179. North-Holland, Amsterdam. MR727303
2. BASSAMBOO, A., HARRISON, J. M. and ZEEVI, A. (2005). Dynamic routing and admission control in high-volume service systems: Asymptotic analysis via multi-scale fluid limits. Queueing Syst. 51 249-285. MR2189595
3. BOXMA, O. J. and DE WAAL, P. R. (1994). Multiserver queues with impatient customers. In Proceedings of ITC 14 743-756. Elsevier, Amsterdam.
4. BROWN, L., GANS, N., MANDELBAUM, A., SAKOV, A., SHEN, H., ZELTYN, S. and ZHAO, L. (2005). Statistical analysis of a telephone call center: A queueing-science perspective. J. Amer. Statist. Assoc. 100 36-50. MR2166068
5. DUPUIS, P. and ELLIS, R. S. (1997). A Weak Convergence Approach to the Theory of Large Deviations. Wiley, New York. MR1431744
6. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes: Characterization and Convergence. Wiley, New York. MR838085
7. GANS, N., KOOLE, G. and MANDELBAUM, A. (2003). Telephone call centers: Tutorial, review and research prospects. Manufacturing Service Oper. Management 5 79-141.
8. GARNETT, O., MANDELBAUM, A. and REIMAN, M. I. (2002). Designing a call center with impatient customers. Manufacturing Service Oper. Management 4 208-227.
9. HARRISON, J. M. (2005). A method for staffing large call centers based on stochastic fluid models. Manufacturing Service Oper. Management 7 20-36.
10. JACOD, J. and SHIRYAEV, A. N. (1987). Limit Theorems for Stochastic Processes. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 288. Springer, Berlin. MR959133
11. JACOBSEN, M. (2006). Point Process Theory and Applications: Markov Point and Piecewise Deterministic Processes. Birkhäuser, Boston, MA. MR2189574
12. KALLENBERG, O. (1975). Random Measures. Akademie Verlag, Berlin. MR0431372
13. KANG, W. N. and RAMANAN, K. (2010). Asymptotic approximations for the stationary distributions of many-server queues. Preprint. Available at http://arxiv.org/abs/1003.3373.
14. KASPI, H. and RAMANAN, K. (2010). Law of large numbers limits for many-server queues. Ann. Appl. Probab. To appear.
15. KASPI, H. and RAMANAN, K. (2010). SPDE limits for many-server queues. Preprint.
16. MANDELBAUM, A.,MASSEY, W. A. and REIMAN, M. I. (1998). Strong approximations for Markovian service networks. Queueing Syst. 30 149-201. MR1663767
17. MANDELBAUM, A. and MOMCILOVIC, P. (2010). Queues with many servers and impatient customers. Preprint.
18. ZELTYN, S. and MANDELBAUM, A. (2005). Call centers with impatient customers: Manyserver asymptotics of the M/M/n +G queue. Queueing Syst. 51 361-402. MR2189598
19. MANDELBAUM, A. and ZELTYN, S. (2009). Staffing many-server queues with impatient customers: Constraint satisfaction in call centers. Oper. Res. 57 1189-1205. MR2583510
20. PARTHASARATHY, K. R. (1967). Probability Measures on Metric Spaces. Probability and Mathematical Statistics 3. Academic Press, New York. MR0226684
21. RAMANAN, K. and REIMAN, M. I. (2003). Fluid and heavy traffic diffusion limits for a generalized processor sharing model. Ann. Appl. Probab. 13 100-139. MR1951995
22. WHITT, W. (2006). Fluid models for multiserver queues with abandonments. Oper. Res. 54 37-54. MR2201245
23. WHITT, W. (2002). Stochastic-process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues. Springer, New York. MR1876437
24. ZHANG, J. (2010). Fluid models of many-server queues with abandonment. Preprint.