The Pht/Pht/∞ Queueing System: Part I—The Single Node

Published Online:https://doi.org/10.1287/ijoc.1040.0070

References

  • Brown M., Ross S. H. Some results for infinite-server Poisson queues. J. Appl. Probab. (1967) 6:453–458CrossrefGoogle Scholar
  • Collings T., Stoneman C. The M/M/∞ queue with varying arrival and service rates. Oper. Res. (1976) 24:760–773LinkGoogle Scholar
  • Eick S. G., Massey W. A., Whitt W. Mtt/G/∞ queues with sinusoidal arrival rates. Management Sci. (1993a) 39:241–252LinkGoogle Scholar
  • Eick S. G., Massey W. A., Whitt W. The physics of the Mtt/G/∞ queue. Oper. Res. (1993b) 41:731–742LinkGoogle Scholar
  • Foley R. D. The nonhomogeneous M/G/∞ queue. Oper. Res. (1984) 19:40–48Google Scholar
  • Glynn P. W., Whitt W. A new view of the heavy-traffic limit theorem for infinite-server queues. Adv. Appl. Probab. (1991) 23:188–209CrossrefGoogle Scholar
  • Harrison J. M., Lemoine A. J. A note on networks of infinite-server queues. J. Appl. Probab. (1981) 18:561–567CrossrefGoogle Scholar
  • Johnson N. L., Kotz S.Urn Models and Their Applications (1977) (John Wiley & Sons, New York) Google Scholar
  • Kao E.An Introduction to Stochastic Processes (1997) (Duxbury Press, Belmont, CA) Google Scholar
  • Lee W. C. Y.Mobile Cellular Telecommunications Systems (1989) (McGraw-Hill, New York) Google Scholar
  • Massey W. A., Whitt W. Networks of infinite-server queues with nonstationary Poisson input. Queueing Systems: Theory Appl. (1993) 13:183–250CrossrefGoogle Scholar
  • Massey W. A., Whitt W. An analysis of the modified offered-load approximation for the nonstationary Erlang loss model. Ann. Appl. Probab. (1994) 4:1145–1160CrossrefGoogle Scholar
  • Mirasol N. M. The output of an M/G/∞ queueing system is Poisson. Oper. Res. (1963) 11:282–284LinkGoogle Scholar
  • Nelson B. L., Taaffe M. R. The [Phtt/Phtt/∞]KK queueing system: Part II—The multiclass network. INFORMS J. Comput. (2004) 16(3):275–283LinkGoogle Scholar
  • Neuts M. F.Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (1981) (The Johns Hopkins University Press, Baltimore, MD) Google Scholar
  • Newell G. F. The M/G/∞ queue. SIAM J. Appl. Math. (1966) 14:86–88CrossrefGoogle Scholar
  • Ong K. L., Taaffe M. R. Approximating nonstationary Ph(t)/M(t)/S/C queueing systems. Ann. Oper. Res. (1987) 8:103–116CrossrefGoogle Scholar
  • Ong K. L., Taaffe M. R. Approximating Ph(t)/Ph(t)/1/c nonstationary queueing systems. Math. Comput. Simulation (1988) 30:441–452CrossrefGoogle Scholar
  • Ong K. L., Taaffe M. R. Nonstationary queues with interrupted Poisson arrivals and unreliable/repairable servers. Queueing Systems: Theory Appl. (1989) 4:27–46CrossrefGoogle Scholar
  • Rothkopf M. H., Oren S. S. A closure approximation for the nonstationary M/M/s queue. Management Sci. (1979) 25:522–534LinkGoogle Scholar
  • Taaffe M. R., Ong K. L., Sheppard S., Pooch U., Pegden C. D. Approximating time-dependent non-exponential queues. Proc. 1984 Winter Simulation Conf. (1984) 175–180Institute of Electrical and Electronic Engineers, Piscataway, NJGoogle Scholar
  • Tijms H. C.Stochastic Models: An Algorithmic Approach (1995) (John Wiley & Sons, Chichester, U.K) Google Scholar
  • Whitt W. On the heavy-traffic limit theorem for the GI/G/∞ queues. Adv. Appl. Probab. (1982) 14:171–190CrossrefGoogle 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.