Transforming Renewal Processes for Simulation of Nonstationary Arrival Processes

Published Online:https://doi.org/10.1287/ijoc.1080.0316

References

  • Avramidis A. N., Deslauriers A., L'Ecuyer P. Modeling daily arrivals to a telephone call center. Management Sci. (2004) 50(7):896–908LinkGoogle Scholar
  • Channouf N., L'Ecuyer P., Ingolfsson A., Avramidis A. N. The application of forecasting techniques to modeling emergency medical system calls in Calgary, Alberta. Health Care Management Sci. (2007) 10(1):25–45CrossrefGoogle Scholar
  • Chen H., Schmeiser B. W. Simulation of Poisson processes with trigonometric rates. Proc. 1992 Winter Simulation Conf. (1992) Arlington, VA(ACM, New York) 609–617CrossrefGoogle Scholar
  • Çinlar E.Introduction to Stochastic Processes (1975) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
  • Cox D. R., Isham V.Point Processes (1980) (Chapman & Hall, New York) Google Scholar
  • Cox D. R., Lewis P. A. W.The Statistical Analysis of Series of Events (1966) (Methuen, London) CrossrefGoogle Scholar
  • Cox D. R., Smith W. L. On the superposition of renewal processes. Biometrika (1954) 41(1–2):91–99CrossrefGoogle Scholar
  • Gans N., Koole G., Mandelbaum A. Telephone call centers: Tutorial, review, and research prospects. Manufacturing Service Oper. Management (2003) 5(2):79–141LinkGoogle Scholar
  • Gnedenko B. V., Kovalenko I. N.Introduction to Queueing Theory (1989) 2nd ed.(Birkhäuser, Boston) CrossrefGoogle Scholar
  • Harrod S., Kelton W. D. Numerical methods for realizing nonstationary Poisson processes with piecewise-constant instantaneous-rate functions. Simulation (2006) 82(3):147–157CrossrefGoogle Scholar
  • Henderson S. G. Estimation for nonhomogeneous Poisson processes from aggregated data. Oper. Res. Lett. (2003) 31(5):375–382CrossrefGoogle Scholar
  • Jongbloed G., Koole G. Managing uncertainty in call centers using Poisson mixtures. Appl. Stochastic Models Bus. Indust. (2001) 17:307–318CrossrefGoogle Scholar
  • Klein R. W., Roberts S. D. A time-varying Poisson arrival process generator. Simulation (1984) 43(4):193–195CrossrefGoogle Scholar
  • Kuhl M. E., Sumant S. G., Wilson J. R. An automated multiresolution procedure for modeling complex arrival processes. INFORMS J. Comput. (2006) 18(1):3–18LinkGoogle Scholar
  • Kulkarni V. G.Modeling and Analysis of Stochastic Systems (1995) (Chapman & Hall, London) Google Scholar
  • Leemis L. M. Nonparametric estimation of the cumulative intensity function for a nonhomogeneous Poisson process. Management Sci. (1991) 37(7):886–900LinkGoogle Scholar
  • Lewis P. A. W., Shedler G. S. Simulation of nonhomogeneous Poisson processes by thinning. Naval Res. Logist. Quart. (1979) 26(3):403–413CrossrefGoogle Scholar
  • Lucantoni D. M. New results on the single server queue with a batch Markovian arrival process. Comm. Statist. Stochastic Models (1991) 7(1):1–46CrossrefGoogle Scholar
  • Manor O. Bernoulli thinning of a Markov renewal process. Appl. Stochastic Models Data Analysis (1998) 14(3):229–240CrossrefGoogle Scholar
  • Marie R. Calculating equilibrium probabilities for λ(n)/ck/1/n queues. Proc. 1980 Internat. Sympos. Comput. Performance Modelling, Measurement, Evaluation (1980) Toronto(ACM, New York) 117–125CrossrefGoogle Scholar
  • Massey W. A., Parker G. A., Whitt W. Estimating the parameters of a nonhomogeneous Poisson process with linear rate. Telecomm. Systems (1996) 5(2):361–388CrossrefGoogle Scholar
  • Miller D. R. Almost sure comparisons of renewal processes and Poisson processes, with application to reliability theory. Math. Oper. Res. (1979) 4(4):406–413LinkGoogle Scholar
  • Nelson B. L., Taaffe M. R. The Pht/Pht/∞ queueing system: Part I—The single node. INFORMS J. Comput. (2004) 16(3):266–274LinkGoogle Scholar
  • Neuts M. F.Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (1981) (The Johns Hopkins University Press, Baltimore) Google Scholar
  • Ogata Y. On Lewis' simulation method for point processes. IEEE Trans. Inform. Theory (1981) 27(1):23–31CrossrefGoogle Scholar
  • Paxson V., Floyd S. Wide-area traffic: The failure of Poisson modeling. IEEE/ACM Trans. Networking (1995) 3(3):226–244CrossrefGoogle Scholar
  • Rényi A. A characterization of Poisson processes. Magyar Tud. Akad. Mat. Kutató Int. Közl. (1956) 1:519–527Google Scholar
  • Rolski T., Szekli R. Stochastic ordering and thinning of point processes. Stochastic Processes Their Appl. (1991) 37(2):299–312CrossrefGoogle Scholar
  • Ross S. M.Stochastic Processes (1983) (John Wiley & Sons, New York) Google Scholar
  • Sauer C., Chandy K. Approximate analysis of central server models. IBM J. Res. Development (1975) 19:301–313CrossrefGoogle Scholar
  • Shanthikumar J. G. Uniformization and hybrid simulation/analytic models of renewal processes. Oper. Res. (1986) 34(4):573–580LinkGoogle Scholar
  • Smith W. L. On the cumulants of renewal processes. Biometrika (1959) 46(1-2):1–29CrossrefGoogle Scholar
  • Testik M. C., Cochran J. K., Runger G. C. Adaptive server staffing in the presence of time-varying arrivals: A feed-forward control approach. J. Oper. Res. Soc. (2004) 55(3):233–239CrossrefGoogle Scholar
  • Tijms H. C.Stochastic Models: An Algorithmic Approach (1994) (John Wiley & Sons, Chichester, UK) Google Scholar
  • Whitt W. Approximating a point process by a renewal process: The view through a queue, an indirect approach. Management Sci. (1981) 27(6):619–634LinkGoogle Scholar
  • Wu C., Chen H.-L. A consumer purchasing model with learning and departure behaviour. J. Oper. Res. Soc. (2000) 51(5):583–591CrossrefGoogle 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.