The Impact of Dependent Service Times on Large-Scale Service Systems

References

• Asmussen S.Applied Probability and Queues (2003) 2nd ed.(Springer, New York) Google Scholar
• Berkes I., Philipp W. An almost sure invariance principle for empirical distribution function of mixing random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete (1977) 41(2):115–137Crossref, Google Scholar
• Berkes I., Hörmann S., Schauer J. Asymptotic results for the empirical process of stationary sequences. Stoch. Proc. Appls. (2009) 119(4):1298–1324Crossref, Google Scholar
• Eckberg A. E. Generalized peakedness of teletraffic processes. Proc. 10th Internat. Teletraffic Congress (1983) Montreal, CanadaGoogle Scholar
• Eick S. G., Massey W. A., Whitt W. Mt/G/∞ queues with sinusoidal arrival rates. Management Sci. (1993a) 39(2):241–252Link, Google Scholar
• Eick S. G., Massey W. A., Whitt W. The physics of the Mt/G/∞ queue. Oper. Res. (1993b) 41(4):731–742Link, Google Scholar
• Falin G. The Mk/G/∞ batch arrival queue with heterogeneous dependent demands. J. Appl. Prob. (1994) 31(3):841–846Crossref, Google Scholar
• Feldman Z., Mandelbaum A., Massey W. A., Whitt W. Staffing of time-varying queues to achieve time-stable performance. Management Sci. (2008) 54(2):324–338Link, Google Scholar
• Feller W.An Introduction to Probability Theory and Its Applications (1971) 2nd ed.(John Wiley & Sons, New York) Google Scholar
• Fendick K. W., Saksena V. R., Whitt W. Dependence in packet queues. IEEE Trans. Commun. (1989) 37(11):1173–1183Crossref, Google Scholar
• Green L. V., Kolesar P. J., Whitt W. Coping with time-varying demand when setting staffing requirements for a service system. Production Oper. Management (2007) 16(1):13–29Crossref, Google Scholar
• Halfin S., Whitt W. Heavy-traffic limits for queues with many exponential servers. Oper. Res. (1981) 29(3):567–588Link, Google Scholar
• Jacobs P. A. Heavy traffic results for single-server queues with dependent (EARMA) service and interarrival times. Adv. Appl. Prob. (1980) 12(2):517–529Crossref, Google Scholar
• Jacobs P. A., Lewis P. A. W. A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1). Adv. Appl. Prob. (1977) 9(9):87–104Crossref, Google Scholar
• Jacobs P. A., Lewis P. A. W. Discrete time series generated by mixtures. Correlational and run properties. J. Roy. Statist., Ser. B (1978) 40(1):94–105Google Scholar
• Jacobs P. A., Lewis P. A. W. Stationary autoregressive discrete moving average time series generated by mixtures. J. Times Series Anal. (1983) 4(1):19–36Crossref, Google Scholar
• Jagerman D. L., Melamed B. Burstiness descriptors of traffic streams: Indices of dispersion and peakedness. Proc. 1994 Conf. Inform. Sci. Systems (1994) Princeton, NJ:24–28Google Scholar
• Jennings O. B., Mandelbaum A., Massey W. A., Whitt W. Server staffing to meet time-varying demand. Management Sci. (1996) 42(10):1383–1394Link, Google Scholar
• Krichagina E. V., Puhalskii A. A. A heavy-traffic analysis of a closed queueing system with a GI/1 service center. Queueing Systems (1997) 25(1–4):235–280Crossref, Google Scholar
• Lawrence A. J., Lewis P. A. W. The exponential autoregressive-moving average EARMA(p, q) process. J. Roy. Stat. Soc. Ser. B (1980) 42(2):150–161Google Scholar
• Mark B. L., Jagerman D. L., Ramamurthy G. Peakedness measures for traffic characterization in high-speed networks. Proc. INFOCOM '97. Sixteenth Annual Joint Conf. IEEE Comput. Commun. Soc. (1997) (IEEE Computer Society, Washington, DC) 427–435Crossref, Google Scholar
• Massey W. A., Whitt W. Networks of infinite-server queues with nonstationary Poisson input. Queueing Systems (1993) 13(1):183–250Crossref, Google Scholar
• Massey W. A., Whitt W. Stationary-process approximations for the nonstationary Erlang loss model. Oper. Res. (1996) 44(6):976–983Link, Google Scholar
• Nelson B. L., Taaffe M. R. The Pht/Pht/∞ queueing system: Part I—The single node. INFORMS J. Comput. (2004) 16(3):266–274Link, Google Scholar
• Pang G., Whitt W. Two-parameter heavy-traffic limits for infinite-server queues. Queueing Systems (2010) 65(4):325–364Crossref, Google Scholar
• Pang G., Whitt W. Infinite-server queues with batch arrivals and dependent service times. Probab. Engrg. Informational Sci. (2012a) . ForthcomingGoogle Scholar
• Pang G., Whitt W. Two-parameter heavy-traffic limits for infinite-server queues with dependent service times. Queueing Systems (2012b) (Forthcoming. )Google Scholar
• Sim C. H. First-order autoregressive models for gamma and exponential processes. J. Appl. Prob. (1990) 27(2):325–332Crossref, Google Scholar
• Whitt W. Bivariate distributions with given marginals. Ann. Statistics (1976) 4(6):1280–1289Crossref, Google Scholar
• Whitt W. Approximating a point process by a renewal process: Two basic methods. Oper. Res. (1982) 30(1):125–147Link, Google Scholar
• Whitt W. Comparing batch delays and customer delays. Bell System Tech. J. (1983) 62(7):2001–2009Crossref, Google Scholar
• Whitt W. Heavy traffic approximations for service systems with blocking. AT&T Bell Lab. Tech. J. (1984) 63(5):689–708Crossref, Google Scholar
• Whitt W.Stochastic-Process Limits (2002) (Springer, New York) Crossref, Google Scholar
• Whitt W. A diffusion approximation for the G/GI/n/m queue. Oper. Res. (2004) 52(6):922–941Link, Google Scholar