Heavy traffic analysis of controlled multiplexing systems

Queueing Systems

Volumn 28, Issue 1-3, 1998, Pages 79-107

  Kushner, Harold J ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Controlled multiplexing; Ergodic cost problem; Heavy traffic; Multiplexing systems

Indexed keywords

COST FUNCTIONS; MULTIPLEXING EQUIPMENT; OPTIMAL CONTROL SYSTEMS;

ANALYSIS AND CONTROLS; COST PROBLEMS; HEAVY TRAFFIC LIMIT; HEAVY TRAFFICS; HIGH-SPEED TELECOMMUNICATIONS; MUTUALLY INDEPENDENTS; OPTIMAL CONTROL PROBLEM; UNCONTROLLED SYSTEMS;

COST BENEFIT ANALYSIS;

EID: 0032381844     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019194922013     Document Type: Article

References (24)

1. D. Anick, D. Mitra and M.M. Sondhi, Stochastic theory of a data handling system with multiple sources, Bell Syst. Tech. J. 61 (1982) 1971-1894.
2. P. Billingsley, Convergence of Probability Measures (Wiley, New York, 1968).
3. S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence (Wiley, New York, 1986).
4. J.M. Harrison and R.J. Williams, Brownian models of open queueing networks with homogeneous customer populations, Stochastics Stochastics Rep. 22 (1987) 77-115.
5. D.L. Iglehart and W. Whitt, Multiple channel queues in heavy traffic, Adv. in Appl. Probab. 2 (1970) 150-177.
6. D. Jarvis and H.J. Kushner, Codes for optimal stochastic control: documentation and users guide, Technical Report, Brown University, Lefschetz Center for Dynamical Systems Report 96-3 (1996). Documentation and codes are available on the internet: www.dam.brown.edu, then open Lefschetz Center.
7. C. Knessl and J.A. Morrison, Heavy traffic analysis of a data handling system with multiple sources, SIAM J. Appl. Math. 51 (1991) 187-213.
8. T.G. Kurtz, Approximation of Population Processes, CBMS-NSF Regional Conf. Series in Appl. Math., Vol. 36 (SIAM, Philadelphia, PA, 1981).
9. H.J. Kushner, Optimality conditions for the average cost per unit time problem with a diffusion model, SIAM J. Control Optim. 16 (1978) 330-346.
10. H.J. Kushner, Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems, Vol. 3, Systems and Control (Birkhäuser, Boston, 1990).
11. H.J. Kushner, Analysis of controlled multiplexing systems via numerical stochastic control techniques, IEEE J. Selected Areas Commun. 13 (1995) 1207-1218.
12. H.J. Kushner, Control of trunk line systems in heavy traffic, SIAM J. Control Optim. 33 (1995) 765-803.
13. H.J. Kushner and P. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time (Springer, Berlin/New York, 1992).
14. H.J. Kushner, D. Jarvis and J. Yang, Controlled and optimally controlled multiplexing systems: A numerical exploration, Queueing Systems 20 (1995) 255-291.
15. H.J. Kushner and L.F. Martins, Numerical methods for stochastic singular control problems, SIAM J. Control Optim. 29 (1991) 1443-1475.
16. H.J. Kushner and L.F. Martins, Heavy traffic analysis of a data transmission system with many independent sources, SIAM J. Appl. Math. 53 (1993) 1095-1122.
17. H.J. Kushner and L.F. Martins, Limit theorems for pathwise average cost per unit time problems for queues in heavy traffic, Stochastics Stochastics Rep. 42 (1993) 25-51.
18. H.J. Kushner and L.F. Martins, Numerical methods for controlled and uncontrolled multiplexing and queueing systems, Queueing Systems 16 (1994) 241-285.
19. H.J. Kushner and L.F. Martins, Heavy traffic analysis of a controlled multi class queueing network via weak convergence theory, SIAM J. Control Optim. 34 (1996) 1781-1797.
20. H.J. Kushner and K.M. Ramachandran, Optimal and approximately optimal control policies: for queues in heavy traffic, SIAM J. Control Optim. 27 (1989) 1293-1318.
21. R. Liptser and A.N. Shiryaev, Statistics of Random Processes (Springer, Berlin/New York, 1977).
22. L.F. Martins and H.J. Kushner, Routing and singular control for queueing networks in heavy traffic, SIAM J. Control Optim. 28 (1990) 1209-1233.
23. M.R. Reiman, Open queueing networks in heavy traffic, Math. Oper. Res. 9 (1984) 441-458.
24. D.W. Stroock and S.R.S. Varadhan, Multidimensional Diffusion Processes (Springer, New York, 1979).