In Search of Sensitivity in Network Optimization

Queueing Systems

Volumn 44, Issue 4, 2003, Pages 313-363

  Chen, Mike ^a   Pandit, Charuhas ^a   Meyn, Sean ^a  

^a United States of America   (United States)

Author keywords

Optimal control; Queueing networks; Routing; Scheduling

Indexed keywords

OPTIMAL CONTROL SYSTEMS; QUEUEING NETWORKS; SCHEDULING; SENSITIVITY ANALYSIS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS;

OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS; OPTIMAL POLICIES; OPTIMAL SOLUTIONS; ROUTING; STATISTICAL INFORMATION; STEADY STATE PERFORMANCE; STOCHASTIC NETWORKS;

STOCHASTIC MODELS;

EID: 0042524509     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/A:1025130105303     Document Type: Article

References (56)

1. S. Asmussen, Queueing simulation in heavy traffic, Math. Oper. Res. 17 (1992) 84-111.
2. F. Avram, D. Bertsimas and M. Ricard, An optimal control approach to optimization of multiclass queueing networks, in: Proc. of Workshop on Queueing Networks of the Mathematical Institute, eds. F. Kelly and R. Williams, Minneapolis, 1994, IMA Volumes in Mathematics and its Applications, Vol. 71 (Springer, New York, 1995).
3. F.L Baccelli, G. Cohen and G.J. Olsder, Synchronization and Linearity: An Algebra for Discrete Event Systems, Wiley Series in Probability and Mathematical Statistics (Wiley, New York, 1992).
4. S.L. Bell and R.J. Williams, Dynamic scheduling of a system with two parallel servers: Asymptotic optimality of a continuous review threshold policy in heavy traffic, in: Proc. of the 38th Conf. on Decision and Control, Phoenix, AZ, 1999, pp. 1743-1748.
5. P. Billingsley, Convergence of probability measures, Wiley Series in Probability and Statistics: Probability and Statistics, 2nd ed. (Wiley-Interscience, New York, 1999).
6. V.S. Borkar and S.P. Meyn, Value functions and simulation in stochastic networks, in: 42th IEEE Conf. on Decision and Control, 2003, submitted.
7. M. Bramson, State space collapse with application to heavy traffic limits for multiclass queueing networks, Queueing Systems 30 (1998) 89-148.
8. M. Bramson and R.J. Williams, On dynamic scheduling of stochastic networks in heavy traffic and some new results for the workload process, in: Proc. of the 39th Conf. on Decision and Control, 2000.
9. H. Chen and A. Mandelbaum, Discrete flow networks: bottleneck analysis and fluid approximations, Math. Oper. Res. 16(2) (1991) 408-446.
10. H. Chen and D.D. Yao, Dynamic scheduling of a multiclass fluid network, Oper. Res. 41(6) (1993) 1104-1115.
11. H. Chen and D.D. Yao, Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization, Stochastic Modelling and Applied Probability (Springer, New York, 2001).
12. M. Chen, R. Dubrawski and S.P. Meyn, Management of demand-driven production systems (2002) submitted for publication.
13. R.L. Cruz, A calculus for network delay, part I: Network elements in isolation, IEEE Trans. Inform. Theory 31 (1991) 114-131.
14. J.G. Dai, On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models, Ann. Appl. Probab. 5(1) (1995) 49-77.
15. J.G. Dai and S.P. Meyn, Stability and convergence of moments for multiclass queueing networks via fluid limit models, IEEE Trans. Automat. Control 40 (November 1995) 1889-1904.
16. D. Down, S.P. Meyn and R.L. Tweedie, Exponential and uniform ergodicity of Markov processes, Ann. Probab. 23(4) (1995) 1671-1691.
17. P. Dupuis and H. Kushner, Numerical Methods for Stochastic Control Problems in Continuous Time, Applications of Mathematics, Vol. 24 (Springer, New York, 2001).
18. J.D. Eng, Humphrey and S.P. Meyn, Fluid network models: Linear programs for control and performance bounds, in: Proc. of the 13th IFAC World Congress, eds. J. Cruz, J. Gertler and M. Peshkin, Vol. B, San Francisco, CA, 1996, pp. 19-24.
19. S.B. Gershwin, Manufacturing Systems Engineering (Prentice-Hall, Englewood Cliffs, NJ, 1993).
20. J.M. Harrison, Brownian Motion and Stochastic Flow Systems (Wiley, New York, 1985).
21. J.M. Harrison, Brownian models of queueing networks with heterogeneous customer populations, in: Stochastic Differential Systems, Stochastic Control Theory and Applications, Minneapolis, MN, 1986 (Springer, New York, 1988) pp. 147-186.
22. J.M. Harrison, Brownian models of open processing networks: Canonical representations of work-load, Ann. Appl. Probab. 10 (2000) 75-103.
23. J.M. Harrison, Stochastic networks and activity analysis, in: Analytic Methods in Applied Probability, In Memory of Fridrih Karpelevich, ed. Y. Suhov (Amer. Math. Soc., Providence, RI, 2002).
24. J.M. Harrison and L.M. Wein, Scheduling networks of queues: Heavy traffic analysis of a two-station closed network, Oper. Res. 38(6) (1990) 1052-1064.
25. S.G. Henderson, Variance reduction via an approximating Markov process, Ph.D. thesis, Stanford University, Stanford, CA, USA (1997).
26. S.G. Henderson and P.W. Glynn, Approximating martingales for variance reduction in Markov process simulation, Math. Oper. Res. 27(2) (2002) 253-271.
27. S.G. Henderson and S.P. Meyn, Variance reduction for simulation in multiclass queueing networks, IIE Trans. Oper. Engrg. (2003) to appear.
28. S.G. Henderson, S.P. Meyn and V. Tadic, Performance evaluation and policy selection in multiclass networks, Discrete Event Dynamic Systems: Theory and Applications, Special Issue on Learning and Optimization Methods in Discrete Event Dynamic Systems (2002) to appear.
29. F.C. Kelly and C.N. Laws, Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling, Queueing Systems 13 (1993) 47-86.
30. I. Kontoyiannis and S.P. Meyn, Spectral theory and limit theorems for geometrically ergodic Markov processes, Ann. Appl. Probab. 13 (2003) 304-362; presented at The INFORMS Applied Probability Conference, New York, July 2001.
31. I. Kontoyiannis and S.P. Meyn, Spectral theory and limit theorems for geometrically ergodic Markov processes, Ann. Appl. Probab. 13 (2003) 304-362; presented at The INFORMS Applied Probability Conference, New York, July 2001.
32. S. Kumar and M. Muthuraman, A numerical method for solving singular Brownian control problems, in: Proc. of the 39th Conf. on Decision and Control, 2000.
33. H.J. Kushner, Heavy Traffic Analysis of Controlled Queueing and Communication Networks, Stochastic Modelling and Applied Probability (Springer, New York, 2001).
34. H.J. Kushner and K.M. Ramchandran, Optimal and approximately optimal control policies for queues in heavy traffic, SIAM J. Control Optim. 27 (1989) 1293-1318.
35. X. Luo and D. Bertsimas, A new algorithm for state-constrained separated continuous linear programs, SIAM J. Control Optim. 37 (1998) 177-210.
36. C. Maglaras, Dynamic scheduling in multiclass queueing networks: Stability under discrete-review policies, Queueing Systems 31 (1999) 171-206.
37. C. Maglaras, Discrete-review policies for scheduling stochastic networks: Trajectory tracking and fluid-scale asymptotic optimally, Ann. Appl. Probab. 10 (2000).
38. 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.
39. L.F. Martins, S.E. Shreve and H.M. Soner, Heavy traffice convergence of a controlled, multiclass queueing system, SIAM J. Control Optim. 34(6) (1996) 2133-2171.
40. S.P. Meyn, The policy iteration algorithm for average reward Markov decision processes with general state space, IEEE Trans. Automat. Control 42 (1997); also presented at The 35th IEEE Conf. on Decision and Control, Kobe, Japan, December 1996.
41. S.P. Meyn, The policy iteration algorithm for average reward Markov decision processes with general state space, IEEE Trans. Automat. Control 42 (1997); also presented at The 35th IEEE Conf. on Decision and Control, Kobe, Japan, December 1996.
42. S.P. Meyn, Stability and optimization of queueing networks and their fluid models, in: Mathematics of Stochastic Manufacturing Systems, Williamsburg, VA, 1996 (Amer. Math. Soc., Providence, RI, 1997) pp. 175-199.
43. S.P. Meyn, Sequencing and routing in multiclass queueing networks. Part I: Feedback regulation, SIAM J. Control Optim. 40(3) (2001) 741-776.
44. S.P. Meyn, Stability, performance evaluation, and optimization, in: Markov Decision Processes: Models, Methods, Directions, and Open Problems, eds. E. Feinberg and A. Shwartz (Kluwer, Dordrecht, 2001) pp. 43-82.
45. S.P. Meyn, Sequencing and routing in multiclass queueing networks. Part II: Workload relaxations, SIAM J. Control Optim. (2003) to appear; also presented at The 2000 IEEE Internat. Symposium on Information Theory, Sorrento, Italy, June 25 June 30 2003.
46. S.P. Meyn, Sequencing and routing in multiclass queueing networks. Part II: Workload relaxations, SIAM J. Control Optim. (2003) to appear; also presented at The 2000 IEEE Internat. Symposium on Information Theory, Sorrento, Italy, June 25 June 30 2003.
47. S.P. Meyn and R.L. Tweedie, Marov Chains and Stochastic Stability (Springer, London, 1993).
48. J. Perkins, Control of push and pull manufacturing systems, Ph.D. thesis, University of Illinois, Urbana, IL (1993), Technical Report No. UILU-ENG-93-2237 (DC-155).
49. M.I. Reiman, Open queueing networks in heavy traffic, Math. Oper. Res. 9 (1984) 441-458.
50. M.I. Reiman, A multiclass queue in heavy traffic, Adv. in Appl. Probab. 20 (1988) 179-207.
51. L.C.G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales, Vol. I: Foundations, 2nd ed. (Cambridge Univ. Press, Cambridge, 2000).
52. A. Shwartz and A. Weiss, Large Deviations for Performance Analysis: Queues, Communication and Computing (Chapman and Hall, London, UK, 1995).
53. M.H. Veatch, Using fluid solutions in dynamic scheduling (2001) submitted for publication.
54. G. Weiss, Optimal draining of a fluidre-entrant line, in: IMA Volumes in Mathematics and its Applications, Vol. 71, eds. F. Kelly and R. Williams (Springer, New York, 1995) pp. 91-103.
55. G. Weiss, A simplex based algorithm to solve separated continuous linear programs, Technical Report, Department of Statistics, University of Haifa, Israel (2001).
56. W. Whitt, Planning queueing simulations, Managm. Sci. 35 (1994) 1341-1366.