Queueing Systems

, Volume 89, Issue 1–2, pp 3–14 | Cite as

A broad view of queueing theory through one issue

  • Ward Whitt


This is an overview and appreciation of the contributions to this special issue.


Service systems Sharing delay information Heavy traffic Time-varying arrival rates Closure approximations Reflected Le’vy processes 

Mathematics Subject Classification

60K25 90B22 


  1. 1.
    Aksin, O.Z., Armony, M., Mehrotra, V.: The modern call center: a multi-disciplinary perspective on operations management research. Prod. Oper. Manag. 16, 665–688 (2007)CrossRefGoogle Scholar
  2. 2.
    Aras, A.K., Chen, X., Liu, Y.: Many-server Gaussian limits for overloaded queues with customer abandonment and nonexponential service times. Queueing Syst. (2018).
  3. 3.
    Asmussen, S.: Applied Probability and Queues, 2nd edn. Springer, New York (2003)Google Scholar
  4. 4.
    Asmussen, S., Boxma, O.J.: Editorial introduction: 100 years of queueing, the Erlang centennial. Queueing Syst. 62, 1–2 (2009)CrossRefGoogle Scholar
  5. 5.
    Asmussen, S., Glynn, P.W.: Stochastic Simulation. Springer, New York (2007)Google Scholar
  6. 6.
    Asmussen, S., Ivanovs, J.: Discretization error for a two-sided reflected Lévy process. Queueing Syst. (2018).
  7. 7.
    Asmussen, S., Glynn, P.W., Pitman, J.: Discretization error in simulation of one-dimensional reflecting Brownian motion. Ann. Appl. Probab. 5(4), 875–896 (1995)CrossRefGoogle Scholar
  8. 8.
    Asmussen, S., Anderson, L.N., Glynn, P.W., Pihlsgaard, M.: Lévy process with two sided reflection. In: Barndorff-Nielsen, O.E., Bertoin, J., Jacod, J., Klűppelberg, C. (eds.) Lévy Matters V, pp. 67–182. Springer, New York (2015)Google Scholar
  9. 9.
    Billingsley, P.: Convergence of Probability Measures, 2nd edn. Wiley, New York (1999)CrossRefGoogle Scholar
  10. 10.
    Borodin, A.N., Salminen, P.: A Handbook of Brownian Motion: Facts and Formulae, 2nd edn. Sppringer Basel, New York (2015)Google Scholar
  11. 11.
    Borovkov, A.A.: Some limit theorems in the theory of mass service, II. Theor. Prob. Appl. 10, 375–500 (1965)CrossRefGoogle Scholar
  12. 12.
    Brockmeyer, E., Halstrom, H.L., Jensen, A.: The Life and Works of A. K. Erlang. Academy of Technical Sciences, Copenhagen (1948)Google Scholar
  13. 13.
    Brown, L., Gans, N., Mandelbaum, A., Sakov, A., Shen, H., Zeltyn, S., Zhao, L.: Statistical analysis of a telephone call center: a queueing-science perspective. J. Am. Stat. Assoc. 100, 36–50 (2005)CrossRefGoogle Scholar
  14. 14.
    Chen, H., Yao, D.D.: Fundamentals of Queueing Networks. Springer, New York (2001)CrossRefGoogle Scholar
  15. 15.
    Cohen, J.W.: The Single Server Queue, 2nd edn. North-Holland, Amsterdam (1982)Google Scholar
  16. 16.
    Dallery, Y., Gershwin, B.: Manufacturing flow line systems: a review of models and analytical results. Queueing Syst. 12, 3–94 (1992)CrossRefGoogle Scholar
  17. 17.
    Debicki, K., Mandjes, M.: Queues and Lévy Fluctuation Theory. Springer, London (2015)CrossRefGoogle Scholar
  18. 18.
    Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Springer, New York (2013). reprinted from 1988Google Scholar
  19. 19.
    Foderaro, L.W.: Navigation apps are truning quiet neighborhoods into traffic nightmares. The New York Times, (December 24, 2017). New York Regional SectionGoogle Scholar
  20. 20.
    Foss, S.: Editorial. Queueing Syst. 64(1), 1–3 (2010)CrossRefGoogle Scholar
  21. 21.
    Garnett, O., Mandelbaum, A., Reiman, M.I.: Designing a call center with impatient customers. Manuf. Serv. Oper. Manag. 4(3), 208–227 (2002)CrossRefGoogle Scholar
  22. 22.
    Glynn, P.W., Wang, R.J.: On the rate of convergence to equilibrium for reflected Brownian motion. Queueing Syst. (2018).
  23. 23.
    Harrison, J.M.: Brownian Motion and Stochastic Flow Systems. Wiley, New York (1985)Google Scholar
  24. 24.
    Harrison, J.M.: Brownian Models of Performance and Control. Cambridge University Press, New York (2013)CrossRefGoogle Scholar
  25. 25.
    Hassin, R.: Rational Queueing. CRC Press, Boca Raton (2016)CrossRefGoogle Scholar
  26. 26.
    Hassin, R., Haviv, M.: To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Springer, New York (2003)CrossRefGoogle Scholar
  27. 27.
    Ibrahim, R.: Sharing delay information in service systems: a literature survey. Queueing Syst. (2018).
  28. 28.
    Iglehart, D.L.: Limit diffusion approximations for the many-server queue and the repairman problem. J. Appl. Probab. 2, 429–441 (1965)CrossRefGoogle Scholar
  29. 29.
    Ivanovs, J.: Zooming in on a Lévy process at its supremum. Ann. Appl. Prob. (2018) arXiv:1610.904471v3
  30. 30.
    Karlin, S., Taylor, H.M.: A Second Course in Stochastic Processes. Academic Press, New York (1981)Google Scholar
  31. 31.
    Kaspi, H., Ramanan, K.: SPDE limits of many-server queues. Ann. Appl. Probab. 23, 145–229 (2013)CrossRefGoogle Scholar
  32. 32.
    Kingman, J.F.C.: The single server queue in heavy traffic. Proc. Camb. Phil. Soc. 77, 902–904 (1961)CrossRefGoogle Scholar
  33. 33.
    Kingman, J.F.C.: On queues in heavy traffic. J. R. Stat. Soc. B 24, 383–392 (1962)Google Scholar
  34. 34.
    Kingman, J.F.C.: The heavy-traffic approximation in the theory of queues. In: Smith, W.L., Wilkinson, W.E. (eds.) Proceedings of the Symposium on Congestion Theory, chapter 6, pp. 137–159. University of North Carolina Press, Chapel Hill, NC (1965)Google Scholar
  35. 35.
    Kingman, J.F.C.: The first Erlang century—and the next. Queueing Syst. 63, 3–12 (2009)CrossRefGoogle Scholar
  36. 36.
    Kolmogorov, A.N.: On Skorohod convergence. Theory Probab. Appl. 1, 215–222 (1956)CrossRefGoogle Scholar
  37. 37.
    Linetsky, V.: On the transition densities for reflected diffusions. Adv. Appl. Probab. 37(2), 435–460 (2005)CrossRefGoogle Scholar
  38. 38.
    Mandelbaum, A., Massey, W.A., Reiman, M.I.: Strong approximations for Markovian service networks. Queueing Syst. 30, 149–201 (1998)CrossRefGoogle Scholar
  39. 39.
    Massey, W.A., Pender, J.: Gaussian skewness approximation for dynamic rate multi-server queues with abandonment. Queueing Syst. 75, 243–277 (2013)CrossRefGoogle Scholar
  40. 40.
    Massey, W.A., Pender, J.: Dynamic rate Erlang—a queues. Queueing Syst. (2018).
  41. 41.
    Naor, P.: The regulation of queue size by levying tolls. Econometrica 37(1), 15–24 (1969)CrossRefGoogle Scholar
  42. 42.
    Prabhu, N.U.: Editorial introduction. Queueing Syst. 1(1), 1–4 (1986)CrossRefGoogle Scholar
  43. 43.
    Prohorov, YuV: Convergence of random proccesses and limit theorems in probability. Theory Probab. Appl. 1, 157–214 (1956)CrossRefGoogle Scholar
  44. 44.
    Puhalskii, A.A.: On the \(M_t/M_t/K_t+M_t\) queue in heavy traffic. Math. Methods Oper. Res. 78, 119–148 (2013)CrossRefGoogle Scholar
  45. 45.
    Skorohod, A.V.: Limit theorems for stochastic processes. Theory Probab. Appl. 1, 261–290 (1956)CrossRefGoogle Scholar
  46. 46.
    Stein, C.: Approximate Computation of Expectations. Institute of Mathematical Statistics, Hayward, California (1986). Lecture Notes - Monograph Series 7Google Scholar
  47. 47.
    Stidham, S.: The Optimal Design of Queues. CRC Press, Boca Raron, FL (2009)CrossRefGoogle Scholar
  48. 48.
    van Vuuren, M., Adan, I.J.B.F., Resing-Sassen, S.A.E.: Performance analysis of multi-server tandem queues with finite buffers and blocking. OR Spectrum 27, 315–338 (2005)CrossRefGoogle Scholar
  49. 49.
    Wang, R., Glynn, P.W.: On the marginal standard error rule and testing of the initial transient deletion methods. ACM Trans Model Comput. Simul. 27(1), 1–30 (2016)Google Scholar
  50. 50.
    Zychlinski, N., Mandelbaum, A., Momcilovic, P., Cohen, I.: Bed blocking in hospitals due to scarece capacity in geriatric institutions – cost minimization via fluid models. Working paper, the Technion, Haifa, Israel (2017)Google Scholar
  51. 51.
    Zychlinski, N., Mandelbaum, A., Momcilovic, P.: Time-varying tandem queues with blocking: modeling, analysis and operational insights for fluid models with reflection. Queueing Syst. (2018).

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA

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