Fluid approximation of a controlled multiclass tandem network

Queueing Systems

Volumn 35, Issue 1-4, 2000, Pages 349-380

  Gajrat, A ^a   Hordijk, A ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Fluid optimal control model; Markov decision chain; Pontryagin maximum principle; Stochastic dynamic scheduling; Tandem c rule

Indexed keywords

DECISION THEORY; MARKOV CHAINS; MAXIMUM PRINCIPLE; SCHEDULING; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; STRUCTURAL OPTIMIZATION;

ASYMPTOTICALLY OPTIMAL; DYNAMIC SCHEDULING; FLUID APPROXIMATION; FLUID OPTIMAL CONTROL MODEL; MARKOV DECISION; MARKOV DECISION PROBLEM; STOCHASTIC DYNAMICS; SWITCHING SURFACES;

QUEUEING NETWORKS;

EID: 0034341919     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019162615537     Document Type: Article

References (26)

1. D. Atkins and H. Chen, Performance evaluation of scheduling control of queueing network: Fluid model heuristics, Queueing Systems 21 (1995) 391-413.
2. F. Avram, D. Bertsimas and M. Ricard, Fluid models of sequencing problems in open queueing networks: An optimal control approach, in: Stochastic Networks, eds. F. Kelly and R. Williams, IMA Volumes in Mathematics and its Applications, Vol. 71 (Springer, New York, 1995) pp. 199-234.
3. N. Bäuerle and U. Rieder, Optimal control of single-server fluid networks, Queueing Systems 35 (2000) 185-200 (this volume).
4. H. Chen and A. Mandelbaum, Discrete flow networks: Bottlenecks analysis and fluid approximations, Math. Oper. Res. 16(2) (1991) 408-446.
5. H. Chen and D. Yao, Dynamic scheduling of a multiclass fluid networks, Oper. Res. 41(6) (1993) 1104-1115.
6. J.G. Dai, On positive Harris recurrence for multiclass queueing networks: A unified approach via fluid limit models, Ann. Appl. Probab. 5(1) (1995) 49-77.
7. D. Eng, J. Humphrey and S.P. Meyn, Fluid network models: Linear programs for control and performance bounds, in: 13th World Congress of International Federation of Automatic Control, San Francisco (1996).
8. A. Gajrat, A. Hordijk, V. Malyshev and F. Spieksma, Fluid approximations of Markov decision chains, Markov Process. Related Fields 3 (1997) 129-150.
9. T.C. Green and S. Stidham, Sample-path conservation laws, with applications to scheduling queues and fluid systems, Technical Report (1999).
10. P.J. Holewijn and A. Hordijk, On the convergence of moments in stationary Markov chains, Stochastic Process. Appl. 3 (1975) 55-64.
11. A. Hordijk, Dynamic programming and its applications, Math. Center Tract. 51 (1974).
12. A. Hordijk and G. Koole, On the optimality of LEPT and μc rules for parallel processors and dependent arrival processes, Adv. in Appl. Probab. 25 (1993) 979-996.
13. A. Hordijk and G. Koole, On suboptimal policies in multiclass tandem models, Probab. Engrg. Inform. Sci. 10 (1996) 29-39.
14. I.K. Kleinrock, Queueing systems, Vol. 2: Computer Applications (1976).
15. C. Maglaras, Discrete-review policies for scheduling stochastic networks: Fluid scale asymptotic optimality, submitted to Ann. Appl. Probab. (1997).
16. S.P. Meyn, Stability and optimization of queueing networks and their fluid models, in: Proc. of the Summer Seminar on The Mathematics of Stochastic Manufacturing Systems, Williamsburg, VA (June 17-21, 1996).
17. S.P. Meyn, The policy improvement algorithm for Markov decision processes with general state space, IEEE Trans. Automat. Control (December 1997).
18. J.A. van Mieghem, Dynamic scheduling with convex delay costs: The generalized cμ rule, Ann. Appl. Probab. 5(3) (1995) 808-833.
19. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishenko, The Mathematical Theory of Optimal Processes (Pergamon, Oxford, 1964).
20. M.C. Pullan, A duality theory for separated continuous linear programs, SIAM J. Control Optim. 34(3) (1996) 931-965.
21. M.L. Puterman, Markov Decision Process (Wiley, New York, 1994).
22. H.L. Royden, Real Analysis, 2nd ed. (Collier-Mcmillan Limited, London, 1968).
23. A.N. Rybko and A.L. Stolyar, Ergodicity of stochastic processes describing the operations of open queueing networks, Problems Inform. Transmission 28 (1992) 199-220.
24. A. Seierstad and K. Sydsæter, Sufficient conditions in optimal control theory, Internat. Econom. Rev. 18(2) (1977) 367-391.
25. A. Seierstad and K. Sydsæter, Optimal Control Theory With Economic Applications (North-Holland, Amsterdam, 1987).
26. G. Weiss, Algorithm for minimum wait draining of two station fluid re-entrant line, to appear in Ann. Oper. Res.