Home  Articles  Past volumes  About  Login  Notify  Contact  Search  


References[1] Abate, J., Choudhury, G. L., Whitt, W. (1994). Asymptotics for steadystate tail probabilities in structured Markov queueing models. Stochastic Models 10 99–143. MR1259856 [2] Bassamboo, A., Zeevi, A. (2009). On a datadriven method for staffing large call centers. Oper. Res. 57, 714–726. [3] Choudhury, G. L., Whitt, W. (1994). Heavytraffic asymptotic expansions for the asymptotic decay rates in the BMAP/G/1 queue. Stochastic Models 10 453–498. MR1268561 [4] Coddington, E. A., Levinson, N. (1955). Theory of Ordinary Differential Equations, McGrawHill, New York. MR0069338 [5] Coffman, E. G., Puhalskii, A. A., Reiman, M. I. (1995). Polling systems with zero switchover times: a heavytraffic averaging principle. Annals of Applied Probability 5 681–719. MR1359825 [6] Ethier, S. N., Kurtz, T. G. (1986). Markov Processes: Characterization and Convergence. Wiley, New York. MR0838085 [7] Gurvich, I., Whitt, W. (2009). Queueandidlenessratio controls in manyserver service systems. Math. Oper. Res. 34 (2) 363–396. MR2554064 [8] He, Q. (1995). Differentiability of the matrices R and G in the matrix analytic method. Stochastic Models 11 (1) 123–132. MR1316771 [9] Hunt, P. J., Kurtz, T. G. (1994). Large loss networks. Stochastic Processes and their Applications 53 363–378. MR1302919 [10] Khalil, H. K. (2002). Nonlinear Systems. Prentice Hall, New Jersey. [11] Latouche, G., Ramaswami, V. (1999). Introduction to Matrix Analystic Methods in Stochastic Modeling, Siam and ASA, Philadelphia MR1674122 [12] Marquez, H. J. (2003). Nonlinear Control Systems. Wiley, New York. [13] Neuts, M. F. (1986). The caudal characteristic curve of queues. Adv. Appl. Prob. 18 221–254. MR0827337 [14] Neuts, M. F. (1989). Structured Stochastic Matrices of M∕G∕1 Type and Their Applications, Marcel Dekker, New York. MR1010040 [15] Pang, G., Talreja, R., Whitt, W. (2007). Martingale proofs of manyserver heavytraffic limits for Markovian queues. Probability Surveys 4, 193–267. MR2368951 [16] Perry, O., Whitt, W. (2009). Responding to unexpected overloads in largescale service systems. Management Sci., 55 (8) 1353–1367. [17] Perry, O., Whitt, W. (2010a). A fluid limit for an overloaded X model via an averaging principle. working paper, Columbia University, NY. Available at: http://www.columbia.edu/∼ww2040/allpapers.html [18] Perry, O., Whitt, W. (2010b). Gaussian approximations for an overloaded X model via an averaging principle. working paper, Columbia University, NY.Available at: http://www.columbia.edu/∼ww2040/allpapers.html [19] Perry, O., Whitt, W. (2011). A fluid approximation for service systems responding to unexpected overloads. Operations Res., forthcoming Available at: http://www.columbia.edu/∼ww2040/allpapers.html [20] Stolyar, A. L., Tezcan, T. (2010). Control of systems with flexible multiserver pools: a shadow routing approach. Queueing Systems 66, 1–51. MR2674107 [21] Teschl, G. (2009). Ordinary Differential Equations and Dynamical Systems, Universität Wien. Available online: www.mat.univie.ac.at/∼gerald/ftp/bookode/ode.pdf [22] Whitt, W. (2002). StochasticProcess Limits, New York, Springer MR1876437 [23] Whitt, W. (2004). Efficiencydriven heavytraffic approximations for manyserver queues with abandonments. Management Sci. 50 (10) 1449–1461. 

Home  Articles  Past volumes  About  Login  Notify  Contact  Search Stochastic Systems. ISSN: 19465238 