An Algorithm to Compute the Waiting Time Distribution for the M/G/1 Queue

References

• Abate J., Whitt W. The Fourier-series method for inverting transforms of probability distributions. Queueing Systems (1992) 10:5–88Crossref, Google Scholar
• Abate J., Whitt W. Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comput. (1995) 7:36–43Link, Google Scholar
• Abate J., Whitt W. Computing Laplace transforms for numerical inversion via continued fractions. INFORMS J. Comput. (1999) 11:394–405Link, Google Scholar
• Crovella M. E., Bestavros A. Self-similarity in the World Wide Web traffic: Evidence and possible causes. IEEE/ACM Trans. Networking (1997) 5:835–847Crossref, Google Scholar
• Crovella M. E., Lipsky L., Andradóttir A. S., Healy K. J., Withers D. H., Nelson B. L.Proc. 1997 Winter Simulation Conf. (1997) (IEEE, Atlanta, GA) 1005–1012Google Scholar
• Crovella M. E., Taqqu M. S., Bestavros A., Adler R., Feldman R., Taqqu M. S. Heavy-tailed probability distributions in the World Wide Web. A Practical Guide to Heavy Tails: Statistical Techniques and Applications (1998) (Birkhäuser, Boston, MA) 3–25Google Scholar
• Embrechts P., Klüppelberg C., Mikosch T.Modelling Extremal Events for Insurance and Finance (1997) (Springer, New York) Crossref, Google Scholar
• Feldmann A., Whitt W. Fitting mixtures of exponentials to long-tail distributions to analyze network performance models. Performance Evaluation (1998) 31:245–279Crossref, Google Scholar
• Fischer M. J., Knepley J. E., Neuts M. F. A numerical solution for some computational problems occurring in queueing theory. Algorithmic Methods in Probability (1977) (North-Holland Publishing Company, New York) 271–285Google Scholar
• Greiner M., Jobmann M., Lipsky L. The importance of power-tail distributions for modeling queueing systems. Oper. Res. (1999) 47:313–326Link, Google Scholar
• Gross D., Harris C. M.Fundamentals of Queueing Theory (1998) 3rd ed.(John Wiley, New York) Google Scholar
• Harris C. M., Marchal W. G. Distribution estimation using Laplace transforms. INFORMS J. Comput. (1998) 10:448–458Link, Google Scholar
• Harris C. M., Brill P. H., Fischer M. J. Internet-type queues with power-tailed interarrival times and computational methods for their analysis. INFORMS J. Comput. (2000) 12:261–271Link, Google Scholar
• Juneja S., Shahabuddin P., Chandra A., Farrington P. A., Nembhard H. B., Nembhard H. B., Evans G. W. Simulating heavy tailed processes using delayed hazard rate twisting. Proc. 1999 Winter Simulation Conf. (1999) (IEEE, Phoenix, AZ) 420–427Crossref, Google Scholar
• Leland W., Taqqu M., Willinger W., Wilson D. On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Trans. Networking (1994) 2:1–13Crossref, Google Scholar
• Lucantoni D. M., Choudhury G. L., Whitt W. The transient BMAP/G/1 queue. Stochastic Models (1994) 10:145–182Crossref, Google Scholar
• Naldi M. Measurement-based modelling of Internet dial-up access connections. Comput. Networks (1999) 31:2381–2390Crossref, Google Scholar
• Neuts M.Structured Stochastic Matrices of M/G/1 Type and Their Applications (1989) (Marcel Dekker, New York) Google Scholar
• Paxson V., Floyd S. Wide-area traffic: The failure of Poisson modeling. IEEE/ACM Trans. Networking (1995) 3:226–244Crossref, Google Scholar
• Shortle J. F., Fischer M. J., Gross D., Masi D. M. B. Using the transform approximation method to analyze queues with heavy-tailed service. J. Probab. Statist. Sci. (2003) 1:15–27Google Scholar
• Sigman K. Appendix: A primer on heavy-tailed distributions. Queueing Systems (1999) 33:261–275Crossref, Google Scholar