A Skorokhod Problem formulation and large deviation analysis of a processor sharing model

Queueing Systems

Volumn 28, Issue 1-3, 1998, Pages 109-124

  Dupuis, Paul ^a   Ramanan, Kavita ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Large deviation estimates; Processor sharing; Skorokhod problem

Indexed keywords

MAPPING;

DISTRIBUTING PROCESSING; EXISTENCE AND UNIQUENESS; GENERALIZED PROCESSOR SHARING; LARGE DEVIATION ANALYSIS; LARGE DEVIATION ESTIMATES; PROCESSOR SHARING; PROCESSOR-SHARING MODEL; SKOROKHOD PROBLEM;

HIGH SPEED NETWORKS;

EID: 0032396011     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019186720196     Document Type: Article

References (14)

1. D. Anick, D. Mitra and M.M. Sondhi, Stochastic theory of a data-handling system and multiple sources, Bell Syst. Tech. J. 61 (1982) 1871-1894.
2. H. Chen and A. Mandelbaum, Discrete flow networks: Bottleneck analysis and fluid approximations, Math. Oper. Res. 2 (1991) 408-446.
3. P. Dupuis and R.S. Ellis, A Weak Convergence Approach to the Theory of Large Deviations (Wiley, New York, 1997).
4. P. Dupuis, R.S. Ellis and A. Weiss, Large deviations for Markov processes with discontinuous statistics I: General upper bounds, Ann. Probab. 19 (1991) 1280-1297.
5. P. Dupuis and H. Ishii, On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications, Stochastics 35 (1991) 31-62.
6. P. Dupuis and A. Nagurney, Dynamical systems and variational inequalities, Ann. Oper. Res. 44 (1993) 9-42.
7. P. Dupuis and K. Ramanan, Convex duality and the Skorokhod Problem, LCDS Technical Report 96-5, Brown University (1996).
8. M.I. Freidlin and A.D. Wentsell, Random Perturbations of Dynamical Systems (Springer, New York, 1984).
9. J.M. Harrison and M.I. Reiman, Reflected Brownian motion on an orthant, Ann. Probab. 9 (1981) 302-308.
10. P.-L. Lions and A.-S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Commun. Pure Appl. Math. 37 (1984) 511-553.
11. 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).
12. I.C. Paschalidis, Large deviations in high speed communication networks, Ph.D. thesis, MIT, Cambridge, MA (1996).
13. A. Shwartz and A. Weiss, Large Deviations for Performance Analysis: Queues, Communication and Computing (Chapman and Hall, New York, 1995).
14. Z.L. Zhang, D. Towsley and J. Kurose, Statistical analysis of the generalized processor sharing scheduling discipline, IEEE J. Selected Areas Commun. 13 (1995) 1071-1080.