Stability of feed-forward fluid networks with lévy input

Journal of Applied Probability

Volumn 33, Issue 2, 1996, Pages 513-522

  Kaspi, Haya ^a   Kella, Offer ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Fluid networks; L vy process; Storage models; Subordinator

Indexed keywords

EID: 0030503367     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200099939     Document Type: Article

References (19)

1. ANICK, D., MITRA, D. AND SONDHI, M. M. (1982) Stochastic theory of a data handling system. Bell Sys. Tech. J. 61, 1871-1894.
2. CHEN, H. AND MANDELDAUM, A. (1991) Discrete flow networks: bottleneck analysis and fluid approximations. Math. Operat. Res. 16, 408-446.
3. CHEN, H. AND YAO, D. D. (1992) A fluid model for systems with random disruptions. Operat. Res. 40 (Supplement 2), 239-247.
4. DAI, J. G. (1995) On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Prob. 5, 49-77.
5. DAI, J. G. AND MEYN, S. (1994) Stability and convergence of moments for multiclass queueing networks via fluid limits models. Preprint.
6. DOWN, D. AND MEYN, S. (1992) Stability of multiclass queueing networks. Proc. 26th Annual Conf. on Information Sciences and Systems. Princeton.
7. DOWN, D. AND MEYN, S. (1993) Stability of acyclic multiclass queueing networks. Preprint.
8. GAVER, D. P., JR. AND MILLER, R. G., JR. (1962) Limiting distributions for some storage problems. In Studies in Applied Probability and Management Sciences, pp. 110-126. ed. K. J. Arrow, S. Karlin and H. Scarf. Stanford University Press, Stanford, CA.
9. GLICKMANN, H. (1993) Stochastic Fluid Networks. M.Sc. thesis, Hebrew University.
10. KASPI, H. (1984) Storage processes with Markov additive input and output. Math. Operat. Res. 9, 424-440.
11. KELLA, O. (1993) Parallel and tandem fluid networks with dependent Lévy inputs. Ann. Appl. Prob. 3, 682-695.
12. KELLA, O. AND WHITT, W. (1992a) A storage model with a two-stage random environment. Operat. Res. 40 (supplement 2), 257-262.
13. KELLA, O. AND WHITT, W. (1992b) A tandem fluid network with Lévy input. In Queues and Related Models. pp. 112-128. ed. I. Basawa and U. Bhat. Oxford University Press, Oxford.
14. KELLA, O. AND WHITT, W. (1992c) Useful martingales for stochastic storage processes with Lévy input. J. Appl. Prob. 29, 296-403.
15. MEYER, R. R., ROTHKOPF, M. H. AND SMITH, S. A. (1979) Reliability and inventory in a production-storage system. Management Sci. 25, 799-807.
16. MEYER, R. R., ROTHKOPF, M. H. AND SMITH, S. A. (1983) Erratum to 'Reliability and inventory in a production-storage system. Management Sci. 29, 1346.
17. MILLER, R. G., JR. (1963) Continuous time stochastic storage processes with random linear inputs and outputs. J. Math. Mech. 12, 275-291.
18. MITRA, D. (1988) Stochastic theory of a fluid model of multiple failure-susceptible producers and consumers coupled by a buffer. Adv. Appl. Prob. 20, 646-676.
19. NEWELL, G. F. (1982) Applications of Queueing Theory. Chapman and Hall, London.