Hazard Rate Scaling of the Abandonment Distribution for the GI/M/n + GI Queue in Heavy Traffic

References

• Baccelli F, Hebuterne G, Kylstra FJ. On queues with impatient customers. Performance 81 (1981) (North-Holland Publishing Company, Amsterdam) 159–179Google Scholar
• Billingsley P. Convergence of Probability Measures (1999) (John Wiley and Sons, New York) Crossref, Google Scholar
• Boxma OJ, de Waal PR. Multiserver queues with impatient customers. ITC (1994) 14:743–756Google Scholar
• Brandt A, Brandt M. On the M(n)/M(n)/s queue with impatient calls. Performance Evaluation (1999) 35(1--2):1–18Crossref, Google Scholar
• Brandt A, Brandt M. Asymptotic results and a Markovian approximation for the M(n)/M(n)/s + GI system. Queueing Systems: Theory Appl. (2000) 41(1--2):73–94Google Scholar
• Dai JG, He S. Customer abandonment in many-server queues. Math. Oper. Res. (2010) 35(2):347–362Link, Google Scholar
• Dai JG, He S, Tezcan T. Many-server diffusion limits for G/Ph/n/ + GI queues. Ann. Appl. Probability (2010) 20(5):1854–1890Crossref, Google Scholar
• Edwards CH, Penny DE. Calculus with Analytic Geometry (1994) (Prentice Hall, NJ) Google Scholar
• Ethier S, Kurtz T. Markov Processes: Characterization and Convergence (1986) (John Wiley & Sons, New York) Crossref, Google Scholar
• Gans N, Koole G, Mandelbaum A. Telephone call centers: Tutorial, review and research prospects. Manufacturing Service Oper. Management (2003) 5(2):79–141Link, Google Scholar
• Garnett O, Mandelbaum A, Reiman M. Designing a call center with impatient customers. Manufacturing Service Oper. Management (2002) 4(3):208–227Link, Google Scholar
• Halfin S, Whitt W. Heavy-traffic limits for queues with many exponential servers. Oper. Res. (1981) 29(3):567–588Link, Google Scholar
• Haugen R, Skogan E. Queueing systems with stochastic time out. IEEE Trans. Comm. (1980) 28(12):1984–1989Crossref, Google Scholar
• Kang W, Ramanan K. Fluid limits of many-server queues with reneging. Ann. Appl. Probability (2010) 20(6):2204–2260Crossref, Google Scholar
• Mandelbaum A, Momčilovic P. Queues with many servers and impatient customers. Math. Oper. Res. (2012) 37(1):41–65Link, Google Scholar
• Mandelbaum A, Zeltyn S. Staffing many-server queues with impatient customers: Constraint satisfaction in call centers. Oper. Res. (2009) 57(5):1189–1205Link, Google Scholar
• Palm C. Methods of judging the annoyance caused by congestion. Tele (1953) 2:189–208Google Scholar
• Palm C. Research on telephone traffic carried by full availability groups. Tele (1957) 1:1–107Google Scholar
• Pang G, Talreja R, Whitt W. Martingale proofs of many-server heavy-traffic limits for Markovian queues. Probability Surveys (2007) 4:193–267Crossref, Google Scholar
• Reed JE, Ward AR. Approximating the GI/GI/1 + GI queue with a nonlinear drift diffusion: Hazard rate scaling in heavy traffic. Math. Oper. Res. (2008) 33(3):606–644Link, Google Scholar
• Reiman MI, Disney RL, Ott TJ. The heavy-traffic diffusion approximation for sojourn times in Jackson networks. Applied Probability—Computer Sciences, the Interface II (1982) (Birkhäuser, Boston) 409–422Crossref, Google Scholar
• Ward AR, Glynn PW. A diffusion approximation for a Markovian queue with reneging. Queueing Systems: Theory Appl. (2003) 43(1--2):103–128Crossref, Google Scholar
• Ward AR, Glynn PW. A diffusion approximation for a GI/GI/1 queue with balking or reneging. Queueing Systems: Theory Appl. (2005) 50(4):371–400Crossref, Google Scholar
• Whitt W. Stochastic-Process Limits (2002) (Springer, New York) Crossref, Google Scholar
• Whitt W. Engineering solution of a basic call center model. Management Sci. (2005a) 51(2):221–235Link, Google Scholar
• Whitt W. Heavy-traffic limits for the G/H2/n/m queue. Math. Oper. Res. (2005b) 30(1):1–27Link, Google Scholar
• Zeltyn S, Mandelbaum A. Call centers with impatient customers: Many-server asymptotics of the M/M/n + G queue. Queueing Systems: Theory Appl. (2005) 51(3--4):361–402Crossref, Google Scholar