Fluid Queues with Heavy-Tailed M/G/∞ Input

References

• Asmussen S., Klüppelberg C. Large deviations results for subexponential tails, with applications to insurance risk. Stochastic Proc. Appl. (1996) 64:103–125Crossref, Google Scholar
• Beran J., Sherman R., Taqqu M. S., Willinger W. Long-range dependence in variable-bit-rate video traffic. IEEE Trans. Comm. (1995) 43:1566–1579Crossref, Google Scholar
• Boxma O. J. Fluid queues and regular variation. Performance Evaluation (1996) 27 & 28:699–712Crossref, Google Scholar
• Boxma O. J., Dumas V. Fluid queues with heavy-tailed activity period distributions. Comput. Commun. (1998) 21:1509–1529Crossref, Google Scholar
• Crovella M., Bestavros A. Self-similarity in World Wide Web traffic: Evidence and possible causes. Proc. ACM Sigmetrics’96 (1996) Philadelphia, PA(ACM, New York) 160–169Crossref, Google Scholar
• Duffield N. G. Queueing at large resources driven by long-tailed M/G/∞-modulated processes. Queueing Systems (1998) 28:245–266Crossref, Google Scholar
• Duffield N. G., O’Connell N. Large deviations and overflow probabilities for the general single server queue, with applications. Proc. Cambridge Philos. Soc. (1995) 118:363–374Crossref, Google Scholar
• Dumas V., Simonian A. Asymptotic bounds for the fluid queue fed by subexponential on/off sources. Adv. Appl. Probab. (2000) 32:244–255Crossref, Google Scholar
• Glynn P. W., Whitt W. Logarithmic asymptotics for steady-state tail probabilities in a single-server queue. J. Appl. Probab. (1994) 31A:131–156Crossref, Google Scholar
• Jelenković P. R. Network multiplexer with truncated heavy-tailed arrival streams. Proc. INFOCOM’99 (1999) New York(IEEE, Piscataway, NJ) 625–632Crossref, Google Scholar
• Jelenković P. R. Subexponential loss rates in a GI/GI/1 queue with applications. Queueing Systems (1999) 33:91–123Crossref, Google Scholar
• Jelenković P. R., Lazar A. A. Asymptotic results for multiplexing subexponential on-off processes. Adv. Appl. Prob. (1999) 31:394–421Crossref, Google Scholar
• Jelenković P. R., Momčilović P. Asymptotic loss probability in a finite buffer queue with heterogeneous heavy-tailed fluid on-off processes. Ann. Appl. Probab. (2003) 13:576–603Crossref, Google Scholar
• Leland W. E., Taqqu M. S., Willinger W., Wilson D. V. On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Trans. Networking (1994) 2:1–15Crossref, Google Scholar
• Likhanov N., Park K., Willinger W. Bounds on the buffer occupancy probability with self-similar input traffic. Self-Similar Network Traffic and Performance Evaluation (2000) (Wiley, New York) 193–213Crossref, Google Scholar
• Likhanov N., Mazumdar R. R. Loss asymptotics in large buffers fed by heterogeneous long-tailed sources. Adv. Appl. Probab. (2000) 32:1168–1189Crossref, Google Scholar
• Likhanov N., Tsybakov B., Georganas N. D. Analysis of an ATM buffer with self-similar (“fractal”) traffic. Proc. INFOCOM’95 (1995) Boston, MA(IEEE, Piscataway, NJ) 985–992Crossref, Google Scholar
• Liu Z., Nain P., Towsley D., Zhang Z.-L. Asymptotic behavior of a multiplexer fed by a long-range dependent process. J. Appl. Probab. (1999) 36:105–118Crossref, Google Scholar
• Mandjes M. A note on fluid queues with M/G/∞ input. Oper. Res. Lett. (2001) 28:233–242Crossref, Google Scholar
• Park K., Willinger W.Self-Similar Network Traffic and Performance Evaluation (2000) (Wiley, New York) Crossref, Google Scholar
• Parulekar M., Makowski A. M., Park K., Willinger W. Buffer asymptotics for M/G/∞ input processes. Self-Similar Network Traffic and Performance Evaluation (2000) (Wiley, New York) 215–248Google Scholar
• Paxson V., Floyd S. Wide area traffic: The failure of Poisson modeling. IEEE/ACM Trans. Networking (1995) 3:226–244Crossref, Google Scholar
• Prasolov V. V. Problems and Theorems in Linear Algebra. AMS Translations of Mathematical Monographs (1994) 134(American Mathematical Society, Providence, RI) Crossref, Google Scholar
• Resnick S., Samorodnitsky G. Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues. Queueing Systems (1999) 33:43–71Crossref, Google Scholar
• Resnick S., Samorodnitsky G. Steady state distribution of the buffer content for M/G/∞ input fluid queues. Bernoulli (2001) 7:191–210Crossref, Google Scholar
• Sigman K. Special issue on queues with heavy-tailed distributions. Queueing Systems (1999) 33(1–3Google Scholar
• Willinger W., Taqqu M. S., Sherman R., Wilson D. V. Self-similarity through high-variability: Statistical analysis of Ethernet LAN traffic at the source level. IEEE/ACM Trans. Networking (1997) 5:71–86Crossref, Google Scholar
• Zwart B., Borst S. C., Dębicki K. Subexponential asymptotics of hybrid fluid and ruin models. Ann. Appl. Probab. (2005) 15:500–517Crossref, Google Scholar
• Zwart B., Borst S. C., Mandjes M. Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows. Ann. Appl. Probab. (2004) 14:903–957Crossref, Google Scholar