Approximations and Optimal Control for State-Dependent Limited Processor Sharing Queues

Published Online:https://doi.org/10.1287/stsy.2021.0087

References

  • Adusumilli KM, Hasenbein JJ (2010) Dynamic admission and service rate control of a queue. Queueing Systems 66(2):131–154.Google Scholar
  • Agrawal R, Carey MJ, Livny M (1985) Models for studying concurrency control performance: Alternatives and implications. SIGMOD Rec. 14(4):108–121.Google Scholar
  • Ata B, Shneorson S (2006) Dynamic control of an M/M/1 service system with adjustable arrival and service rates. Management Sci. 52(11):1778–1791.LinkGoogle Scholar
  • Avi-Itzhak B, Halfin S (1988) Expected response times in a non-symmetric time sharing queue with a limited number of service positions. Proc. ITC.Google Scholar
  • Batt RJ, Terwiesch C (2014) Doctors under load: An empirical study of state-dependent service times. Working paper, University of Wisconsin-Madison, Madison.Google Scholar
  • Bertsekas D (2007) Dynamic Programming and Optimal Control, vol. 1-2, 3rd ed. (Athena Scientific).Google Scholar
  • Blake R (1982) Optimal control of thrashing. Proc. ACM SIGMETRICS Conf. on Measurements and Modeling of Comput. Systems. Seattle, Washington, SIGMETRICS ’82 (Association for Computing Machinery, New York), 1–10.Google Scholar
  • Brumelle SL (1971) Some inequalities for parallel-server queues. Oper. Res. 19(2):402–413.LinkGoogle Scholar
  • Daley D, Rolski T (1984) Some comparibility results for waiting times in single- and many-server queues. J. Appl. Probabilities 21:887–900.Google Scholar
  • Denning PJ, Kahn KC, Leroudier J, Potier D, Suri R (1976) Optimal multiprogramming. Acta Inform. 7:197–216.Google Scholar
  • Elnikety S, Nahum E, Tracy J, Zwaenepoel W (2004) A method for trasparent admission control and request scheduling in e-commerce web sites. Proc. 13th Internat. Conf. World Wide Web, WWW ’04 (Association for Computing Machinery, New York), 276–286.Google Scholar
  • Gamarnik D, Momčilović P (2008) Steady-state analysis of a multiserver queue in the halfin-whitt regime. Adv. Appl. Probabilities 40(2):548–577.Google Scholar
  • George JM, Harrison JM (2001) Dynamic control of a queue with adjustable service rate. Oper. Res. 49(5):720–731.LinkGoogle Scholar
  • Gupta V, Harchol-Balter M (2009) Self-adaptive admission control policies for resource-sharing systems. SIGMETRICS Perform. Eval. Rev. (Association for Computing Machinery, New York), 37(1):311–322.Google Scholar
  • Halfin S, Whitt W (1981) Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29(3):567–588.LinkGoogle Scholar
  • Harrison JM, Taksar MI (1983) Instantaneous control of Brownian motion. Math. Oper. Res. 8(3):439–453.LinkGoogle Scholar
  • Harrison JM, Sellke TM, Taylor AJ (1983) Impulse control of Brownian motion. Math. Oper. Res. 8(3):454–466.LinkGoogle Scholar
  • Heiss HU, Wagner R (1991) Adaptive load control in transaction processing systems. Proc. 17th Internat. Conf. on Large Data Bases.Google Scholar
  • Hernández-Lerma O, Lasserre JB (1995) Discrete-Time Markov Control Processes (Springer, Berlin).Google Scholar
  • Janssen A, Leeuwaarden JV, Sanders J (2013) Scaled control in the qed regime. Performance Evaluation 70(10):750–769.Google Scholar
  • Köllerström J (1974) Heavy traffic theory for queues with several servers. I. J. Appl. Probabilities 11:544–552.Google Scholar
  • Krichagina E (1992) Asymptotic analysis of queueing networks. Stochastics Stochastic Rep. 40:43–76.Google Scholar
  • Krichagina EV, Puhalskii AA (1997) A heavy-traffic analysis of a closed queueing system with a GI/∞ service center. Queueing Systems 25(1-4):235–280.Google Scholar
  • Kushner HJ, Dupuis P (2001) Numerical Methods for Stochastic Control Problems in Continuous Time (Springer, Berlin).Google Scholar
  • Lee N, Kulkarni V (2014) Optimal arrival rate and service rate control of multi-server queues. Queueing Systems 76(1):37–50.Google Scholar
  • Lee C, Puhalskii AA (2015) Non-Markovian state dependent networks in critical loading. Stochastic Models 31(1):43–66.Google Scholar
  • Mandelbaum A, Pats G (1998) State-dependent stochastic networks. Part i. Approximations and applications with continuous diffusion limits. Ann. Appl. Probabilities 8(2):569–646.Google Scholar
  • Mandl P (1968) Analytical Treatment of One-Dimensional Markov Processes (Academia, Springer, Berlin).Google Scholar
  • Nair J, Wierman A, Zwart B (2010) Tail-robust scheduling via limited processor sharing. Performance Evaluation 67(11):978–995.Google Scholar
  • Puterman M (1977) Optimal control of diffusion processes with reflection. J. Optim. Theory Appl. 22(1):103–116.Google Scholar
  • Puterman ML, Brumelle SL (1979) On the convergence of policy iteration in stationary dynamic programming. Math. Oper. Res. 4(1):60–69.LinkGoogle Scholar
  • Reed JE (2009) The G/GI/N queue in the Halfin-Whitt regime. Ann. Appl. Probabilities 19(6):2211–2269.Google Scholar
  • Rege K, Sengupta M (1985) Sojourn time distribution in a multiprogrammed computer system. ATT Tech. J. 64:1077–1090.Google Scholar
  • Ward AR, Kumar S (2008) Asymptotically optimal admission control of a queue with impatient customers. Math. Oper. Res. 33(1):167–202.LinkGoogle Scholar
  • Welsh M, Culler D, Brewer E (2001) Seda: An architecture for well-conditioned, scalable Internet services. SIGOPS Oper. Systems Rev. 35(5):230–243.Google Scholar
  • Yamada K (1995) Diffusion approximation for open state-dependent queueing networks in the heavy traffic situation. Ann. Appl. Probabilities 5(4):958–982.Google Scholar
  • Yamazaki G, Sakasegawa H (1987) An optimal design problem for limited processor sharing systems. Management Sci. 33(8):1010–1019.LinkGoogle Scholar
  • Zhang J, Zwart B (2008) Steady state approximations of limited processor sharing queues in heavy traffic. Queueing Systems 60:227–246.Google Scholar
  • Zhang J, Dai JG, Zwart B (2009) Law of large number limits of limited processor-sharing queues. Math. Oper. Res. 34(4):937–970.LinkGoogle Scholar
  • Zhang J, Dai JG, Zwart B (2011) Diffusion limits of limited processor-sharing queues. Ann. Appl. Probabilities 21(2):745–799.Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.