Refined Models for Efficiency-Driven Queues with Applications to Delay Announcements and Staffing

References

• Akşin Z, Armony M, Mehrotra V (2007) The modern call center: A multi-disciplinary perspective on operations management research. Production Oper. Management 16(6):665–688.Crossref, Google Scholar
• Akşin Z, Ata B, Emadi SM, Su C-L (2016) Impact of delay announcements in call centers: An empirical approach. Oper. Res. 65(1):242–265.Link, Google Scholar
• Allon G, Bassamboo A (2011) The impact of delaying the delay announcements. Oper. Res. 59(5):1198–1210.Link, Google Scholar
• Armony M, Shimkin N, Whitt W (2009) The impact of delay announcements in many-server queues with abandonment. Oper. Res. 57(1):66–81.Link, Google Scholar
• Bassamboo A, Randhawa RS (2010) On the accuracy of fluid models for capacity sizing in queueing systems with impatient customers. Oper. Res. 58(5):1398–1413.Link, Google Scholar
• Brown L, Gans N, Mandelbaum A, Sakov A, Shen H, Zeltyn S, Zhao L (2005) Statistical analysis of a telephone call center: A queueing-science perspective. J. Amer. Statist. Assoc. 100(469):36–50.Crossref, Google Scholar
• Dai JG, He S, Tezcan T (2010) Many-server diffusion limits for G/Ph/n + GI queues. Ann. Appl. Probab. 20(5):1854–1890.Crossref, Google Scholar
• Ethier SN, Kurtz TG (1986) Markov Processes, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics (John Wiley & Sons, New York).Crossref, Google Scholar
• Gans N, Koole G, Mandelbaum A (2003) Telephone call centers: Tutorial, review, and research prospects. Manufacturing Service Oper. Management 5(2):79–141.Link, Google Scholar
• Garnett O, Mandelbaum A, Reiman M (2002) Designing a call center with impatient customers. Manufacturing Service Oper. Management 4(3):208–227.Link, Google Scholar
• Hassin R, Haviv M (2003) To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems (Springer, New York).Crossref, Google Scholar
• He S (2015) Diffusion approximation for efficiency-driven queues: A space-time scaling approach. Working paper, http://arxiv.org/abs/1506.06309v3.Google Scholar
• Hui MK, Tse DK (1996) What to tell consumers in waits of different lengths: An integrative model of service evaluation. J. Marketing 60(2):81–90.Crossref, Google Scholar
• Ibrahim R, Armony M, Bassamboo A (2016) Does the past predict the future? The case of delay announcements in service systems. Management Sci. 63(6):1762–1780.Link, Google Scholar
• Jouini O, Akşin Z, Dallery Y (2011) Call centers with delay information: Models and insights. Manufacturing Service Oper. Management 13(4):534–548.Link, Google Scholar
• Kang W, Pang G (2011) Fluid limit of a many-server queueing network with abandonment. Working paper.Google Scholar
• Kang W, Pang G (2013) Equivalence of fluid models for Gt/GI/N + GI queues. Working paper.Google Scholar
• Kang W, Ramanan K (2010) Fluid limits of many-server queues with reneging. Ann. Appl. Probab. 20(6):2204–2260.Crossref, Google Scholar
• Krichagina EV, Puhalskii AA (1997) A heavy-traffic analysis of a closed queueing system with a GI/∞ service center. Queueing Syst. 25(1–4):235–280.Crossref, Google Scholar
• Li G, Huang JZ, Shen H (2015) Nonparametric two-way hazards model with application to call center waiting times. Working paper, University of North Carolina.Google Scholar
• Liu Y, Whitt W (2011a) Large-time asymptotics for the Gt/Mt/st + GIt many-server fluid queue with abandonment. Queueing Syst. 67(2):145–182.Crossref, Google Scholar
• Liu Y, Whitt W (2011b) A network of time-varying many-server fluid queues with customer abandonment. Oper. Res. 59(4):835–846.Link, Google Scholar
• Liu Y, Whitt W (2012a) The Gt/GI/st + GI many-server fluid queue. Queueing Syst. 71(4):405–444.Crossref, Google Scholar
• Liu Y, Whitt W (2012b) A many-server fluid limit for the queueing model experiencing periods of overloading. Oper. Res. Lett. 40(5):307–312.Crossref, Google Scholar
• Liu Y, Whitt W (2014a) Algorithms for time-varying networks of many-server fluid queues. INFORMS J. Comput. 26(1):59–73.Link, Google Scholar
• Liu Y, Whitt W (2014b) Many-server heavy-traffic limit for queues with time-varying parameters. Ann. Appl. Probab. 24(1):378–421.Crossref, Google Scholar
• Long Z, Zhang J (2014) Convergence to equilibrium states for fluid models of many-server queues with abandonment. Oper. Res. Lett. 42(6–7):388–393.Crossref, Google Scholar
• Maister D (1985) The psychology of waiting lines. Czepiel J, Solomon M, Suprenant C, eds. The Service Encounter: Managing Employee/Customer Interaction in Service Businesses (Lexington Books, Lexington, MA), 113–123.Google Scholar
• Mandelbaum A, Momčilović P (2012) Queues with many servers and impatient customers. Math. Oper. Res. 37(1):41–65.Link, Google Scholar
• Mandelbaum A, Zeltyn S (2009) Staffing many-server queues with impatient customers: Constraint satisfaction in call centers. Oper. Res. 57(5):1189–1205.Link, Google Scholar
• Mandelbaum A, Zeltyn S (2013) Data-stories about (im)patient customers in tele-queues. Queueing Syst. 75(2–4):115–146.Crossref, Google Scholar
• Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24.Crossref, Google Scholar
• Perry O, Whitt W (2009) Responding to unexpected overloads in large-scale service systems. Management Sci. 55(8):1353–1367.Link, Google Scholar
• Reed JE, Tezcan T (2012) Hazard rate scaling of the abandonment distribution for the GI/M/n + GI queue in heavy traffic. Oper. Res. 60(4):981–995.Link, Google Scholar
• Reed JE, Ward AR (2008) Approximating the GI/GI/1 + GI queue with a nonlinear drift diffusion: Hazard rate scaling in heavy traffic. Math. Oper. Res. 33(3):606–644.Link, Google Scholar
• Whitt W (2004) Efficiency-driven heavy-traffic approximations for many-server queues with abandonments. Management Sci. 50(10): 1449–1461.Link, Google Scholar
• Whitt W (2006) Fluid models for multiserver queues with abandonments. Oper. Res. 54(1):37–54.Link, Google Scholar
• Yu Q, Allon G, Bassamboo A (2017) How do delay announcements shape customer behavior? An empirical study. Management Sci. 63(1):1–20.Link, Google Scholar
• Zeltyn S, Mandelbaum A (2005) Call centers with impatient customers: Many-server asymptotics of the M/M/n + G queue. Queueing Syst. 51(3–4):361–402.Crossref, Google Scholar
• Zhang J (2013) Fluid models of many-server queues with abandonment. Queueing Syst. 73(2):147–193.Crossref, Google Scholar