Abstract
This is an overview and appreciation of the contributions to this special issue.
Keywords
Service systems Sharing delay information Heavy traffic Time-varying arrival rates Closure approximations Reflected Le’vy processesMathematics Subject Classification
60K25 90B22References
- 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.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)CrossRefGoogle 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)CrossRefGoogle 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)CrossRefGoogle 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)CrossRefGoogle 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)CrossRefGoogle Scholar
- 14.Chen, H., Yao, D.D.: Fundamentals of Queueing Networks. Springer, New York (2001)CrossRefGoogle 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)CrossRefGoogle Scholar
- 17.Debicki, K., Mandjes, M.: Queues and Lévy Fluctuation Theory. Springer, London (2015)CrossRefGoogle Scholar
- 18.Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Springer, New York (2013). reprinted from 1988Google Scholar
- 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.Foss, S.: Editorial. Queueing Syst. 64(1), 1–3 (2010)CrossRefGoogle 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)CrossRefGoogle 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)CrossRefGoogle Scholar
- 25.Hassin, R.: Rational Queueing. CRC Press, Boca Raton (2016)CrossRefGoogle Scholar
- 26.Hassin, R., Haviv, M.: To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Springer, New York (2003)CrossRefGoogle 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)CrossRefGoogle 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)CrossRefGoogle Scholar
- 32.Kingman, J.F.C.: The single server queue in heavy traffic. Proc. Camb. Phil. Soc. 77, 902–904 (1961)CrossRefGoogle 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)Google Scholar
- 35.Kingman, J.F.C.: The first Erlang century—and the next. Queueing Syst. 63, 3–12 (2009)CrossRefGoogle Scholar
- 36.Kolmogorov, A.N.: On Skorohod convergence. Theory Probab. Appl. 1, 215–222 (1956)CrossRefGoogle Scholar
- 37.Linetsky, V.: On the transition densities for reflected diffusions. Adv. Appl. Probab. 37(2), 435–460 (2005)CrossRefGoogle Scholar
- 38.Mandelbaum, A., Massey, W.A., Reiman, M.I.: Strong approximations for Markovian service networks. Queueing Syst. 30, 149–201 (1998)CrossRefGoogle Scholar
- 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.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)CrossRefGoogle Scholar
- 42.Prabhu, N.U.: Editorial introduction. Queueing Syst. 1(1), 1–4 (1986)CrossRefGoogle Scholar
- 43.Prohorov, YuV: Convergence of random proccesses and limit theorems in probability. Theory Probab. Appl. 1, 157–214 (1956)CrossRefGoogle 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)CrossRefGoogle Scholar
- 45.Skorohod, A.V.: Limit theorems for stochastic processes. Theory Probab. Appl. 1, 261–290 (1956)CrossRefGoogle Scholar
- 46.Stein, C.: Approximate Computation of Expectations. Institute of Mathematical Statistics, Hayward, California (1986). Lecture Notes - Monograph Series 7Google Scholar
- 47.Stidham, S.: The Optimal Design of Queues. CRC Press, Boca Raron, FL (2009)CrossRefGoogle 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)CrossRefGoogle 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)Google Scholar
- 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
Copyright information
© Springer Science+Business Media, LLC, part of Springer Nature 2018