Nearly Periodic Behavior in the Overloaded G/D/s + GI Queue

References

• Asmussen, S. (2003). Applied Probability and Queues, second edition, Springer, New York. MR1978607Google Scholar
• Bassamboo, A., Ranhawa, R. S. (2010). On the accuracy of fluid models for capacity sizing in queueing systems with impatient customers. Operations Res. 58 1398–1413. MR2560543Link, Google Scholar
• Borovkov, A. A. (1967). On limit laws for service processes in multi-channel systems (in Russian). Siberian Math J. 8 746–763. MR0222973Google Scholar
• Choudhury, G. L., Mandelbaum, A., Reiman, M. I., Whitt, W. (1997). Fluid and diffusion limits for queues in slowly changing environments. Stochastic Models 13 121–146. MR1430932Google Scholar
• Courtois, P. J. (1977). Decomposability, Academic Press, New York. MR0479702Google Scholar
• Erramilli, A., Forys, L. J. (1991). Oscillations and chaos in a flow model of a switching system. IEEE J. Sel. Areas Commun. 9 171–178.Google Scholar
• Feller, W. (1971). An Introduction to Probability Theory and its Applications, second edition, Wiley, New York. MR0270403Google Scholar
• Gamarnik, D., Zeevi, A. (2006). Validity of heavy-traffic steady-state approximations in generalized Jackson networks. Ann. Appl. Prob. 16 56–90. MR2209336Google Scholar
• Garnett, O., Mandelbaum, A., Reiman, M. I. (2002) Designing a call center with impatient customers. Manufacturing Service Oper. Management 4 208–227.Link, Google Scholar
• Gibbens, R. J., Hunt, P. J., Kelly, F. P. (1990). Bistability in communication networks. In Disorder in Physical Systems: A Volume in Honour of John M. Hammersley, G. Grimmett and D. Welsh (eds.), Oxford University Press, 113–127. MR1064558Google Scholar
• Glynn, P. W., Whitt, W. (1991). A new view of the heavy-traffic limit for infinite-server queues. Adv. Appl. Prob. 23 188–209. MR1091098Google Scholar
• Gurvich, I. (2009). Validity of heavy-traffic steady-state approximations in multiclass queueing networks: sufficient conditions involving state-space collapse. Working paper, Northwestern University.Google Scholar
• Halfin, S., Whitt, W. (1981). Heavy-traffic limits for queues with many exponential servers. Operations Res. 29 567–588. MR0629195Link, Google Scholar
• Jelenković, P., Mandelbaum, A., Momčilović, P. (2004). Heavy-traffic limits for queues with many deterministic servers. Queueing Systems 47 53–69. MR2074672Google Scholar
• Kang, W., Ramanan, K. (2010). Fluid limits of many-server queues with reneging. Ann. Appl. Prob. 20 2204–2260. MR2759733Google Scholar
• Kaspi, H., Ramanan, K. (2011). Law of large numbers limits for many-server queues. Ann. Appl. Prob. 21 33–114. MR2759196Google Scholar
• Krichagina, E. V., Puhalskii, A. A. (1997). A heavy-traffic analysis of a closed queueing system with a GI/∞ service center. Queueing Systems 25 235–280. MR1458591Google Scholar
• Lindvall, T. (1992). Lectures on the Coupling method, Wiley, New York. MR1180522Google Scholar
• Liu, Y., Whitt, W. (2010a). The Gt/GI/s + GI many-server fluid queue. Columbia University, NY, NY, 2010. http://www.columbia.edu/~ww2040/allpapers.htmlGoogle Scholar
• Liu, Y., Whitt, W. (2010b). A network of time-varying many-server fluid queues with customer abandonment. Operations Res., forthcoming. http://www.columbia/~ww2040/allpapers.html.Google Scholar
• Liu, Y., Whitt, W. (2011). Large-time asymptotics for the Gt/Mt/st + GIt many-server fluid queue with customer abandonment. Queueing Systems 67 145–182. MR2771198Google Scholar
• Miller, D. (1972). Existence of limits in regenerative stochastic processes. Ann. Math. Statist. 43 1273–1280. MR0312592Google Scholar
• Pang, G., Whitt, W. (2010). Two-parameter heavy-traffic limits for infinite-server queues. Queueing Systems 65 325–364. MR2671058Google Scholar
• Reed, J. (2009). The G/GI/N queue in the Halfin-Whitt regime. Ann. Appl. Prob. 19 2211–2269. MR2588244Google Scholar
• Reed, J., Talreja, R. (2009). Distribution-valued heavy-traffic limits for the G/GI/∞ queue, working paper, New York University, New York, NY.Google Scholar
• Sigman, K., Whitt, W. (2011a). Heavy-traffic limits for nearly deterministic queues. J. Appl. Prob., forthcoming. http://www.columbia.edu/~ww2040/allpapers.htmlGoogle Scholar
• Sigman, K., Whitt, W. (2011b) Heavy-traffic limits for nearly deterministic queues: stationary distributions. Queueing Systems, forthcoming. http://www.columbia.edu/~ww2040/allpapers.htmlGoogle Scholar
• Stolyar, A.L., Yudovina, E. Systems with large flexible server pools: Instability of “natural” load balancing. Bell Labs Technical Memo, December 2010. http://arxiv.org/abs/1012.4140Google Scholar
• Takács, L. (1956). On a probability problem arising in the theory of counters. Proc. Camb. Phil. Soc. 52 488–498. MR0081585Google Scholar
• Takács, L. (1962). Introduction to the Theory of Queues, Oxford University Press, New York. MR0133880Google Scholar
• Whitt, W. (1972). Embedded renewal processes in the GI/G/s queue. J. Appl. Prob. 9 650–658. MR0341670Google Scholar
• Whitt, W. (1981). Comparing counting processes and queues. Adv. Appl. Prob. 13 207–22. MR0595895Google Scholar
• Whitt, W. (1983). Untold horrors of the waiting room. What the equilibrium distribution will never tell about the queue-length process. Management Science 29 395–408. MR0704592Link, Google Scholar
• Whitt, W. (2002). Stochastic-Process Limits, Springer, New York. MR1876437Google Scholar
• Whitt, W. (2004). Efficiency-Driven heavy-traffic approximations for many-server queues with abandonments. Management Sci. 50 1449–1461.Link, Google Scholar
• Whitt, W. (2005). Heavy-traffic limits for the G/H2 ∗ /n/m queue. Math. Oper. Res. 30 1–27. MR2125135Link, Google Scholar
• Whitt, W. (2006). Fluid models for multiserver queues with abandonments. Operations Research 54 37–54. MR2201245Link, Google Scholar
• Willie, H. (1998). Periodic steady state of loss systems. Adv. Appl. Prob. 30 152–166. MR1618825Google Scholar