Convex duality and the Skorokhod Problem. II

Probability Theory and Related Fields

Volumn 115, Issue 2, 1999, Pages 197-236

  Dupuis, Paul ^a   Ramanan, Kavita ^b  

^a BROWN UNIVERSITY   (United States)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033438733     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050270     Document Type: Article

References (19)

1. N. Bourbaki. Groupes et Algebres de Lie. Hermann, Paris, 1968.
2. A. Buddhiraja and P. Dupuis. Necessary and sufficient conditions for the stability of constrained processes. To appear in SIAM J. on Appl. Math.
3. P. Dupuis and H. Ishii. Invariant sets for collections of oblique projections. Technical Report, University of Massachusetts, 1991.
4. P. Dupuis and H. Ishii. On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stochastics, 35:31-62, 1991.
5. P. Dupuis and K. Ramanan. A Skorokhod problem formulation and large deviation analysis of a processor sharing model. Queueing Systems, 28:109-124, 1998.
6. P. Dupuis and K. Ramanan. Convex duality and the Skorokhod Problem - I. To appear in Prob. Theor. and Rel. Fields, 1999.
7. P. Dupuis and K. Ramanan. Convex duality and the Skorokhod Problem. LCDS Technical Report 97-1, Brown University, 1997.
8. J. M. Harrison and M. I. Reiman. Reflected Brownian motion on an orthant. Ann. of Prob., 9:302-308, 1981.
9. V. S. Kozyakin, A. Mandelbaum, and A. A. Vladimirov. Absolute stability and dynamic complementarity. Technical report, Technion, Haifa, Israel, 1993.
10. N.O'Connell. Large deviations for queue lengths at a multi-buffered resource. Technical report HPL-BRIMS 96-010, BRIMS, Hewlett-Packard Labs, Bristol, England, 1996.
11. A. K. Parekh and R. G. Gallager. A generalized processor sharing approach to flow control in integrated services networks: the multiple node case. IEEE/ACM Transaction on Networking, 2:137-150, 1993.
12. I. C. Paschalidis. Large Deviations in High Speed Communication Networks. PhD thesis, MIT, Cambridge, Massachusetts, 1996.
13. W. P. Peterson. Diffusion approximations for networks of queues with multiple customer types. Math. of Oper. Res., 9:90-118, 1991.
14. M. I. Reiman. Open queueing networks in heavy traffic. Math. of Oper. Res., 9:441-458, 1984.
15. R. T. Rockafellar. Convex Analysis. Princeton University Press, Princeton, 1970.
16. A. V. Skorokhod. Stochastic equations for diffusions in a bounded region. Theor. of Prob. and its Appl., 6:264-274, 1961.
17. A. F. Veinott Jr. Discrete dynamic programming with sensitive discount optimality criteria. Ann. Math. Statist., 40:1635-1660, 1969.
18. R. J. Williams. Semimartingale reflecting Brownian motions in an orthant. Stochastic Networks, IMA Volumes in Mathematics and Its Applications, F. P. Kelley and R. J. Williams, editors, 125-137, 1995.
19. Z. L. Zhang, D. Towsley, and J. Kurose. Statistical analysis of the generalized processor sharing scheduling discipline. IEEE J. on Selected Areas in Communications, 13:1071-1080, 1995.