On the time-dependent moments of Markovian queues with reneging

1. Abate, J., Whitt, W.: Transient behavior of regulated Brownian motion, I: starting at the origin. Adv. Appl. Probab. 19, 560–598 (1987)

   Article  Google Scholar 

2. Abate, J., Whitt, W.: Transient behavior of regulated Brownian motion, II: non-zero initial conditions. Adv. Appl. Probab. 19, 599–631 (1987)

   Article  Google Scholar 

3. Abate, J., Whitt, W.: Transient behavior of the M/M/1 queue: starting at the origin. Queueing Syst. 2, 41–65 (1987)

   Article  Google Scholar 

4. Abate, J., Whitt, W.: Transient behavior of the M/M/1 queue via Laplace transforms. Adv. Appl. Probab. 20, 145–178 (1988)

   Article  Google Scholar 

5. Abate, J., Whitt, W.: Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comput. 7, 36–43 (1995)

   Article  Google Scholar 

6. Abate, J., Whitt, W.: Calculating transient characteristics of the Erlang loss model by numerical transform inversion. Stoch. Models 14, 663–680 (1998)

   Article  Google Scholar 

7. Andersen, L.N., Mandjes, M.: Structural properties of reflected Lévy processes. Queueing Syst. 63, 301–322 (2009)

   Article  Google Scholar 

8. Borovkov, A.: Asymptotic Methods in Queueing Theory. Wiley, New York (1984)

   Google Scholar 

9. Boxma, O.J., Perry, D., Stadje, W., Zacks, S.: The busy period of an M/G/1 queue with customer impatience. J. Appl. Probab. 47, 130–145 (2010)

   Article  Google Scholar 

10. Fralix, B.H., Riaño, G.: A new look at transient versions of Little’s law, and M/G/1 preemptive Last-Come-First-Served queues. J. Appl. Probab. 47, 459–473 (2010)

    Article  Google Scholar 

11. Gross, D., Shortle, J.F., Thompson, J.M., Harris, C.M.: Fundamentals of Queueing Theory. Wiley, New York (2008)

    Google Scholar 

12. Kallenberg, O.: Random Measures. Akademie-Verlag, Berlin (1983)

    Google Scholar 

13. Kallenberg, O.: Foundations of Modern Probability. Springer, New York (2002)

    Google Scholar 

14. Lindvall, T.: Lectures on the Coupling Method. Dover, New York (2002)

    Google Scholar 

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

    Article  Google Scholar 

16. Reed, J., Ward, A., Zhan, D.: On the generalized Skorokhod problem (2011, submitted). http://people.stern.nyu.edu/jreed

17. Ricciardi, L.M., Sacerdote, L.: On the probability densities of an Ornstein–Uhlenbeck process with a reflecting boundary. J. Appl. Probab. 24, 355–369 (1985)

    Article  Google Scholar 

18. Serfozo, R.F.: Introduction to Stochastic Networks. Springer, New York (1999)

    Book  Google Scholar 

19. Srikant, R., Whitt, W.: Simulation run lengths to estimate blocking probabilities. ACM Trans. Model. Comput. Simul. 6, 7–52 (1996)

    Article  Google Scholar 

20. Ward, A.R.: Asymptotic analysis of queueing systems with reneging: a survey of results for FIFO, single-class models. Surv. Oper. Res. Manag. Sci. 17, 1–14 (2012)

    Google Scholar 

21. Ward, A.R., Glynn, P.W.: A diffusion approximation for a Markovian queue with reneging. Queueing Syst. 43, 103–128 (2002)

    Article  Google Scholar 

22. Ward, A.R., Glynn, P.W.: Properties of the reflected Ornstein–Uhlenbeck process. Queueing Syst. 44, 109–123 (2003)

    Article  Google Scholar 

23. Ward, A.R., Glynn, P.W.: A diffusion approximation for a GI/GI/1 queue with balking or reneging. Queueing Syst. 50, 371–400 (2005)

    Article  Google Scholar 

Download references