Loss Rates for Lévy Processes with Two Reflecting Barriers
Published Online:1 May 2007https://doi.org/10.1287/moor.1060.0226
References
- , Dshalalow J. Stationary distributions via first passage times. Advances in Queueing: Models, Methods and Problems (1995) (CRC Press, Boca Raton, FL) 79–102Google Scholar
- Applied Probability and Queues (2003) (Springer, New York) Google Scholar
- Monotone stochastic recursions and their duals. Probab. Engrg. Inform. Sci. (1996) 10:1–20Crossref, Google Scholar
- Exact buffer overflow calculations for queues via martingales. Queueing Systems (2002) 42:63–90Crossref, Google Scholar
- On an equivalence between loss rates and cycle maxima in queues and dams. Probab. Engrg. Inform. Sci. (2005) 19:241–255Crossref, Google Scholar
- On the first exit time of a completely asymmetric stable process from a finite interval. Bull. London Math. Soc. (1996) 28:514–520Crossref, Google Scholar
- Lévy Processes (1996) (Cambridge University Press, Cambridge, UK) Google Scholar
- Cramér’s estimate for a Lévy process. Statist. Probab. Lett. (1994) 21:363–365Crossref, Google Scholar
- Asymptotic Methods in Queueing Theory (1984) (Wiley, New York) Google Scholar
- , Davis M. H. A., Elliot R. J. Leontief systems, RBV’s and RBM’s. Proc. Imperial College Workshop on Appl. Stochastic Processes (1990) (Gordon and Breach, New York) Google Scholar
- Skorohod-Loynes characterizations of queueing, fluid, and inventory processes. Queueing Systems (2001) 37:233–257Crossref, Google Scholar
- Subexponential loss rates in a GI/GI/1 queue with applications. Queueing Systems (1999) 33:91–123Crossref, Google Scholar
- A Brownian motion with two reflecting barriers and Markov-modulated speed. J. Appl. Probab. (2004) 41:1237–1242Crossref, Google Scholar
- Useful martingales for stochastic storage processes with Lévy input. J. Appl. Probab. (1992) 29:396–403Crossref, Google Scholar
- On the asymptotic relationship between the overflow probability and the loss ratio. Adv. Appl. Probab. (2001) 33:836–863Crossref, Google Scholar
- First passage of reflected strictly stable processes. ALEA (Latin Amer. J. Probab. Math. Statist.) (2006) 2:119–123Google Scholar
- Discussion of a paper of C. B. Winsten. J. Roy. Statist. Soc. Ser. B Statist. Methodol. (1951) 21:22–23Google Scholar
- The Theory of Storage (1959) (Methuen, London, UK) Google Scholar
- Loss rate asymptotics in a GI/G/1 queue with finite buffer. Stochastic Models (2005) 21:913–931Crossref, Google Scholar
- Stochastic Integration and Differential Equations (2004) (Springer, New York) Google Scholar
- Continuous-time monotone stochastic recursions and duality. Adv. Appl. Probab. (2000) 32:426–445Crossref, Google Scholar
- Lévy Processes and Infinitely Divisible Distributions (1999) (Cambridge University Press, Cambridge, UK) Google Scholar
- The equivalence of absorbing and reflecting barrier problems for stochastically monotone Markov processes. Ann. Probab. (1976) 4:914–924Crossref, Google Scholar
- A new look at the Moran dam. J. Appl. Probab. (1993) 30:489–495Crossref, Google Scholar
- Stochastic-Process Limits (2002) (Springer, New York) Crossref, Google Scholar
- A fluid queue with a finite buffer and subexponential inputs. Adv. Appl. Probab. (2002) 32:221–243Crossref, Google Scholar

