Skip to main content
SpringerLink
Log in

A broad view of queueing theory through one issue

  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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)

    Article  Google Scholar 

  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). https://doi.org/10.1007/s11134-018-9575-0

  3. Asmussen, S.: Applied Probability and Queues, 2nd edn. Springer, New York (2003)

    Google Scholar 

  4. Asmussen, S., Boxma, O.J.: Editorial introduction: 100 years of queueing, the Erlang centennial. Queueing Syst. 62, 1–2 (2009)

    Article  Google Scholar 

  5. Asmussen, S., Glynn, P.W.: Stochastic Simulation. Springer, New York (2007)

    Google Scholar 

  6. Asmussen, S., Ivanovs, J.: Discretization error for a two-sided reflected Lévy process. Queueing Syst. (2018). https://doi.org/10.1007/s11134-018-9576-z

  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)

    Article  Google Scholar 

  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. Billingsley, P.: Convergence of Probability Measures, 2nd edn. Wiley, New York (1999)

    Book  Google Scholar 

  10. Borodin, A.N., Salminen, P.: A Handbook of Brownian Motion: Facts and Formulae, 2nd edn. Sppringer Basel, New York (2015)

    Google Scholar 

  11. Borovkov, A.A.: Some limit theorems in the theory of mass service, II. Theor. Prob. Appl. 10, 375–500 (1965)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  14. Chen, H., Yao, D.D.: Fundamentals of Queueing Networks. Springer, New York (2001)

    Book  Google Scholar 

  15. Cohen, J.W.: The Single Server Queue, 2nd edn. North-Holland, Amsterdam (1982)

    Google Scholar 

  16. Dallery, Y., Gershwin, B.: Manufacturing flow line systems: a review of models and analytical results. Queueing Syst. 12, 3–94 (1992)

    Article  Google Scholar 

  17. Debicki, K., Mandjes, M.: Queues and Lévy Fluctuation Theory. Springer, London (2015)

    Book  Google Scholar 

  18. Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Springer, New York (2013). reprinted from 1988

    Google Scholar 

  19. Foderaro, L.W.: Navigation apps are truning quiet neighborhoods into traffic nightmares. The New York Times, (December 24, 2017). New York Regional Section

  20. Foss, S.: Editorial. Queueing Syst. 64(1), 1–3 (2010)

    Article  Google Scholar 

  21. Garnett, O., Mandelbaum, A., Reiman, M.I.: Designing a call center with impatient customers. Manuf. Serv. Oper. Manag. 4(3), 208–227 (2002)

    Article  Google Scholar 

  22. Glynn, P.W., Wang, R.J.: On the rate of convergence to equilibrium for reflected Brownian motion. Queueing Syst. (2018). https://doi.org/10.1007/s11134-018-9574-1

  23. Harrison, J.M.: Brownian Motion and Stochastic Flow Systems. Wiley, New York (1985)

    Google Scholar 

  24. Harrison, J.M.: Brownian Models of Performance and Control. Cambridge University Press, New York (2013)

    Book  Google Scholar 

  25. Hassin, R.: Rational Queueing. CRC Press, Boca Raton (2016)

    Book  Google Scholar 

  26. Hassin, R., Haviv, M.: To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Springer, New York (2003)

    Book  Google Scholar 

  27. Ibrahim, R.: Sharing delay information in service systems: a literature survey. Queueing Syst. (2018). https://doi.org/10.1007/s11134-018-9577-y

  28. Iglehart, D.L.: Limit diffusion approximations for the many-server queue and the repairman problem. J. Appl. Probab. 2, 429–441 (1965)

    Article  Google Scholar 

  29. Ivanovs, J.: Zooming in on a Lévy process at its supremum. Ann. Appl. Prob. (2018) arXiv:1610.904471v3

  30. Karlin, S., Taylor, H.M.: A Second Course in Stochastic Processes. Academic Press, New York (1981)

    Google Scholar 

  31. Kaspi, H., Ramanan, K.: SPDE limits of many-server queues. Ann. Appl. Probab. 23, 145–229 (2013)

    Article  Google Scholar 

  32. Kingman, J.F.C.: The single server queue in heavy traffic. Proc. Camb. Phil. Soc. 77, 902–904 (1961)

    Article  Google Scholar 

  33. Kingman, J.F.C.: On queues in heavy traffic. J. R. Stat. Soc. B 24, 383–392 (1962)

    Google Scholar 

  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)

  35. Kingman, J.F.C.: The first Erlang century—and the next. Queueing Syst. 63, 3–12 (2009)

    Article  Google Scholar 

  36. Kolmogorov, A.N.: On Skorohod convergence. Theory Probab. Appl. 1, 215–222 (1956)

    Article  Google Scholar 

  37. Linetsky, V.: On the transition densities for reflected diffusions. Adv. Appl. Probab. 37(2), 435–460 (2005)

    Article  Google Scholar 

  38. Mandelbaum, A., Massey, W.A., Reiman, M.I.: Strong approximations for Markovian service networks. Queueing Syst. 30, 149–201 (1998)

    Article  Google Scholar 

  39. Massey, W.A., Pender, J.: Gaussian skewness approximation for dynamic rate multi-server queues with abandonment. Queueing Syst. 75, 243–277 (2013)

    Article  Google Scholar 

  40. Massey, W.A., Pender, J.: Dynamic rate Erlang—a queues. Queueing Syst. (2018). https://doi.org/10.1007/s11134-018-9581-2

  41. Naor, P.: The regulation of queue size by levying tolls. Econometrica 37(1), 15–24 (1969)

    Article  Google Scholar 

  42. Prabhu, N.U.: Editorial introduction. Queueing Syst. 1(1), 1–4 (1986)

    Article  Google Scholar 

  43. Prohorov, YuV: Convergence of random proccesses and limit theorems in probability. Theory Probab. Appl. 1, 157–214 (1956)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  45. Skorohod, A.V.: Limit theorems for stochastic processes. Theory Probab. Appl. 1, 261–290 (1956)

    Article  Google Scholar 

  46. Stein, C.: Approximate Computation of Expectations. Institute of Mathematical Statistics, Hayward, California (1986). Lecture Notes - Monograph Series 7

  47. Stidham, S.: The Optimal Design of Queues. CRC Press, Boca Raron, FL (2009)

    Book  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

  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). https://doi.org/10.1007/s11134-018-9578-x

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, Columbia University, New York, NY, 10027, USA

    Ward Whitt

Authors
  1. Ward Whitt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ward Whitt.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Whitt, W. A broad view of queueing theory through one issue. Queueing Syst 89, 3–14 (2018). https://doi.org/10.1007/s11134-018-9580-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11134-018-9580-3

Keywords

Mathematics Subject Classification

Search

Navigation