Quasi-Product Forms for Lévy-Driven Fluid Networks

References

• Asmussen S.Applied Probability and Queues (2003) 2nd ed.(Springer, New York) Google Scholar
• Avram F., Palmowski Z., Pistorius M. A two-dimensional ruin problem on the positive quadrant. (2006) . PreprintGoogle Scholar
• Bertoin J. Sur la décomposition de la trajectoire d’un processus de Lévy spectralement positif en son infimum. Ann. Inst. Henri Poincaré Probab. Statist. (1991) 27:537–547Google Scholar
• Bertoin J.Lévy Processes (1996) (Cambridge University Press, Cambridge, UK) Google Scholar
• Chaumont L., Doney R. A. On Lévy processes conditioned to stay positive. Electron. J. Probab. (2005) 10:948–961Crossref, Google Scholar
• Dębicki K., Mandjes M., van Uitert M. A tandem queue with Lévy input: A new representation of the downstream queue length. Probab. Engrg. Inform. Sci. (2007) 21:83–107Crossref, Google Scholar
• Dieker A. B. Applications of factorization embeddings for Lévy processes. Adv. Appl. Probab. (2006) 38:768–791Crossref, Google Scholar
• Dieker A. B., Mandjes M. Extremes of Markov-additive processes with one-sided jumps, with queueing applications. (2006) . PreprintGoogle Scholar
• Doney R. A.Tanaka’s Construction for Random Walks and Lévy Processes, Séminaire de Probabilités XXXVIII (2005) (Springer, Berlin, Germany) 1–4Google Scholar
• Doney R. A., Kyprianou A. E. Overshoots and undershoots of Lévy processes. Ann. Appl. Probab. (2006) 16:91–106Crossref, Google Scholar
• Dufresne F., Gerber H. The surpluses immediately before and at ruin, and the amount of the claim causing ruin. Insurance Math. Econom. (1988) 7:193–199Crossref, Google Scholar
• Elwalid A., Mitra D. Analysis, approximations and admission control of a multi-service multiplexing system with priorities. Proc. IEEE INFOCOM (1995) 463–472Crossref, Google Scholar
• Greenwood P., Pitman J. Fluctuation identities for Lévy processes and splitting at the maximum. Adv. Appl. Probab. (1980) 12:893–902Crossref, Google Scholar
• Harrison J. M. The diffusion approximation for tandem queues in heavy traffic. Adv. Appl. Probab. (1978) 10:886–905Crossref, Google Scholar
• Harrison J. M., Reiman M. I. Reflected Brownian motion on an orthant. Ann. Probab. (1981) 9:302–308Crossref, Google Scholar
• Harrison J. M., Williams R. J. Brownian models of open queueing networks with homogeneous customer populations. Stochastics (1987) 22:77–115Crossref, Google Scholar
• Harrison J. M., Williams R. J. Brownian models of feedforward queueing networks: Quasireversibility and product form solutions. Ann. Appl. Probab. (1992) 2:263–293Crossref, Google Scholar
• Jacobsen M. Splitting times for Markov processes and a generalised Markov property for diffusions. Zeitschrift für Wahrscheinlichkeitstheorie Verwandte Gebiete (1974) 30:27–43Crossref, Google Scholar
• Jaiswal N. K.Priority Queues (1968) (Academic Press, New York) Google Scholar
• Kella O. Parallel and tandem fluid networks with dependent Lévy inputs. Ann. Appl. Probab. (1993) 3:682–695Crossref, Google Scholar
• Kella O. Stability and nonproduct form of stochastic fluid networks with Lévy inputs. Ann. Appl. Probab. (1996) 6:186–199Crossref, Google Scholar
• Kella O. Stochastic storage networks: Stationarity and the feedforward case. J. Appl. Probab. (1997) 34:498–507Crossref, Google Scholar
• Kella O. Non-product form of two-dimensional fluid networks with dependent Lévy inputs. J. Appl. Probab. (2000) 37:1117–1122Crossref, Google Scholar
• Kella O. Reflecting thoughts. Statist. Probab. Lett. (2006) 76:1808–1811Crossref, Google Scholar
• Kella O., Whitt W.A Tandem Fluid Network with Lévy Input. Queueing and Related Models (1992) (Oxford University Press, New York) 112–128Google Scholar
• Kella O., Whitt W. Useful martingales for stochastic storage processes with Lévy input. J. Appl. Probab. (1992) 29:396–403Crossref, Google Scholar
• Kersting G., Memişoǧlu K. Path decompositions for Markov chains. Ann. Probab. (2004) 32:1370–1390Crossref, Google Scholar
• Konstantopoulos T., Last G., Lin S.-J. On a class of Lévy stochastic networks. Queueing Syst. (2004) 46:409–437Crossref, Google Scholar
• Kyprianou A. E., Palmowski Z.A Martingale Review of Some Fluctuation Theory for Spectrally Negative Lévy Processes (2005) (Springer, Berlin, Germany) 16–29Crossref, Google Scholar
• Lieshout P., Mandjes M. Tandem Brownian queues. (2006) . Technical Report PNA-R0604, CWI, Amsterdam, The NetherlandsGoogle Scholar
• Millar P. W. Zero-one laws and the minimum of a Markov process. Trans. Amer. Math. Soc. (1977) 226:365–391Crossref, Google Scholar
• Millar P. W. A path decomposition for Markov processes. Ann. Probab. (1978) 6:345–348Crossref, Google Scholar
• Piera F. J., Mazumdar R. R., Guillemin F. M. On product-form stationary distributions for reflected diffusions with jumps in the positive orthant. Adv. Appl. Probab. (2005) 37:212–228Crossref, Google Scholar
• Prabhu N. U.Stochastic Storage Processes (1998) (Springer, New York) Crossref, Google Scholar
• Robert P.Stochastic Networks and Queues (2003) (Springer, Berlin, Germany) Crossref, Google Scholar
• Salminen P., Norros I. On busy periods of the unbounded Brownian storage. Queueing Syst. (2001) 39:317–333Crossref, Google Scholar
• Whitt W.Stochastic-Process Limits (2002) (Springer, New York) Crossref, Google Scholar