Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue

References

  • Abate J., Whitt W. Asymptotics for M/G/1 low-priority waiting-time tail probabilities. Queueing Systems Theory Appl. (1997) 25(1/4):173–223CrossrefGoogle Scholar
  • Agrawal R., Makowski A., Nain P. On a reduced load equivalence for fluid queues under subexponentiality. Queueing Systems Theory Appl. (1999) 33(1/3):5–41CrossrefGoogle Scholar
  • Anantharam V. Scheduling strategies and long-range dependence. Queueing Systems Theory Appl. (1999) 33(1/3):73–89CrossrefGoogle Scholar
  • Asmussen S.Applied Probability and Queues (1987) (Wiley, New York) Google Scholar
  • Asmussen S., Klüppelberg C., Sigman K. Sampling at subexponential times, with queueing applications. Stochastic Processes Appl. (1999) 79:265–286CrossrefGoogle Scholar
  • Athreya K. B., Ney P. E.Branching Processes (1972) (Springer, New York) CrossrefGoogle Scholar
  • Baccelli F., Towsley D. The customer response times in the processor sharing queue are associated. Queueing Systems Theory Appl. (1990) 7:269–282CrossrefGoogle Scholar
  • Baltrunas A. On the asymptotics of one-sided large deviation probabilities. Lithuanian Math. J. (1995) 35(1):11–17CrossrefGoogle Scholar
  • Borst S., Boxma O., Jelenković P. Reduced-load equivalence and induced burstiness in GPS queues with long-tailed traffic flows. Queueing Systems Theory Appl. (2003) 43(4):273–306CrossrefGoogle Scholar
  • Chen H., Kella O., Weiss G. Fluid approximations for a processor sharing queue. Queueing Systems Theory Appl. (1997) 27(1/2):99–125CrossrefGoogle Scholar
  • Chistyakov V. P. A theorem on sums of independent positive random variables and its application to branching random processes. Theory Probab. Appl. (1964) 9:640–648CrossrefGoogle Scholar
  • Coffman E. G., Muntz R. R., Trotter H. Waiting time distributions for processor-sharing systems. J. Assoc. Comput. Math. (1970) 17(1):123–130CrossrefGoogle Scholar
  • Foss S., Korshunov D. Sampling at random time with a heavy-tailed distribution. Markov Process Related Fields (2000) 6:543–568Google Scholar
  • Goldie C. M., Klüppelberg C., Adler R., Feldman R., Taqqu M. S. Subexponential distributions. A Practical Guide to Heavy Tails: Statistical Techniques for Analysing Heavy Tailed Distributions (1998) (Birkhäuser, Boston, MA) 435–459Google Scholar
  • Grishechkin S. GI/G/1 processor sharing queue in heavy traffic. Adv. Appl. Probab. (1994) 26:539–555CrossrefGoogle Scholar
  • Jelenković P. Network multiplexer with truncated heavy-tailed arrival streams. Proc. IEEE Infocom. (1999) (IEEE Computer Society, New York) 625–632CrossrefGoogle Scholar
  • Jelenković P., Lazar A. Asymptotic results for multiplexing subexponential on-off processes. Adv. Appl. Probab. (1999) 31(2):394–421CrossrefGoogle Scholar
  • Kelly F.Reversibility and Stochastic Networks (1979) (Wiley, New York) Google Scholar
  • Kelly F., Maulloo A., Tan D. Rate control for communication networks: Shadow prices, proportional fairness and stability. J. Oper. Res. Soc. (1998) 49:237–252CrossrefGoogle Scholar
  • Klüppelberg C. Subexponential distributions and integrated tails. J. Appl. Probab. (1988) 25:132–141CrossrefGoogle Scholar
  • Klüppelberg C. Subexponential distributions and characterizations of related classes. Probab. Theory and Related Fields (1989) 82:259–269CrossrefGoogle Scholar
  • Kotopoulos C., Likhanov N., Mazumdar R. Asymptotic analysis of the GPS system fed by heterogeneous long-tailed sources. Proc. IEEE Infocom. (2001) Anchorage, AKCrossrefGoogle Scholar
  • Liu Z., Niclausse N., Jalpa-Villanueva C., Gelenbe E. Web traffic modeling and performance comparison between HTTP 1.0 and HTTP 1.1. Systems Performance Evaluation: Methodologies and Applications (2000) (CRC Press, Boca Raton, FL) 177–189Google Scholar
  • Liu Z., Niclausse N., Jalpa-Villanueva C. Traffic model and performance evaluation of Web servers. Performance Evaluation (2001) 46(2–3):77–100CrossrefGoogle Scholar
  • Massoulié L., Roberts J. Bandwidth sharing: Objectives and algorithms. Proc. IEEE Infocom. (1999) New YorkCrossrefGoogle Scholar
  • Morrison J. A. Response-time distribution for a processor sharing system. SIAM J. Appl. Math. (1985) 45(1):152–167CrossrefGoogle Scholar
  • Nagaev A. V. Integral limit theorems taking large deviations into account when Cramér's condition does not hold I, II. Theory Probab. Appl. (1969) 14:51–64193208CrossrefGoogle Scholar
  • Nagaev A. V. On a property of sums of independent random variables. Theory Probab. Appl. (1977) 22(2):326–338CrossrefGoogle Scholar
  • Nagaev S. V. Large deviations of sums of independent random variables. Ann. Probab. (1979) 7(5):745–789CrossrefGoogle Scholar
  • Núñez-Queija R. Processor-Sharing Models for Integrated-Services Networks. (2000) . Ph.D. thesis. Eindhoven University of Technology, Eindhoven, The NetherlandsGoogle Scholar
  • Núñez-Queija R. Queues with equally heavy sojourn time and service requirement distributions. (2002) . CWI Research Report PNA-R0201. Amsterdam, The NetherlandsGoogle Scholar
  • Ott T. J. The sojourn-time distribution in the M/G/1 queue with processor sharing. J. Appl. Probab. (1984) 21:360–378CrossrefGoogle Scholar
  • Pakes A. G. On the tails of waiting-time distribution. J. Appl. Probab. (1975) 12:555–564CrossrefGoogle Scholar
  • Park K., Willinger W.Self-Similar Network Traffic and Performance Evaluation (2000) (Wiley, New York) CrossrefGoogle Scholar
  • Resnick S., Samorodnitsky G. Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues. Queueing Systems Theory Appl. (1999) 33(1/3):43–71CrossrefGoogle Scholar
  • Sakata M., Noguchi S., Oizumi J. Analysis of a processor shared queueing model for time sharing systems. Proc. 2nd Hawaii Internat. Conf. on System Sci. (1969) 625–628Google Scholar
  • Schassberger R. A new approach to the M/G/1 processor sharing queue. Adv. Appl. Probab. (1984) 16:202–213CrossrefGoogle Scholar
  • Sengupta B. An approximation for the sojourn-time distribution for the GI/G/1 processor sharing queue. Comm. Statist. Stochastic Models (1992) 8:35–57CrossrefGoogle Scholar
  • Squillante M., Yao D., Zhang L. Web traffic modeling and Web server performance analysis. Proc. IEEE 38th Conf. Decision and Control (1999) Phoenix, AZ:4432–4437CrossrefGoogle Scholar
  • Ward A., Whitt W., MacDonald D. J., Glynn P. W., Turner S. J. Predicting response times in processor-sharing queues. Proc. of the Fields Institute Conf. Comm. Networks (2000) (American Mathematical Society, Providence, RI) 1–29CrossrefGoogle Scholar
  • Wolff R. W.Stochastic Modeling and Theory of Queues (1989) (Prentice Hall, Englewood Cliffs, NJ) Google Scholar
  • Yashkov S. F. A derivation of response time distribution for a M/G/1 processor sharing queue. Problems Control Inform. Theory (1983) 12:133–148Google Scholar
  • Yashkov S. F. Mathematical problems in the theory of shared-processor systems. J. Soviet Math. (1992) 58:101–147CrossrefGoogle Scholar
  • Yashkov S. F. On heavy traffic limit theorem for the M/G/1 processor-sharing queue. Comm. Statist. Stochastic Models (1993) 9:467–471CrossrefGoogle Scholar
  • Zwart A. P., Boxma O. J. Sojourn time asymptotics in the M/G/1 processor sharing queue. Queueing Systems Theory Appl. (2000) 35(1/4):141–166CrossrefGoogle Scholar
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