Two workload properties for Brownian networks

Queueing Systems

Volumn 45, Issue 3, 2003, Pages 191-221

  Bramson, M ^a   Williams, R J ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Brownian control problem; Brownian network; Dynamic scheduling; Equivalent workload formulation; Leontief matrix; Open multiclass queueing network; Open stochastic processing network; Unitary network

Indexed keywords

SCHEDULING; STOCHASTIC SYSTEMS;

BROWNIAN; CONTROL PROBLEMS; DYNAMIC SCHEDULING; EQUIVALENT WORKLOAD FORMULATION; LEONTIEF; MULTI-CLASS QUEUEING NETWORKS; STOCHASTIC PROCESSING NETWORKS;

BROWNIAN MOVEMENT;

EID: 3543052886     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/A:1027372517452     Document Type: Article

References (40)

1. B. Ata and S. Kumar, Heavy traffic analysis of open processing networks with complete resource pooling: Asymptotic optimality of discrete review policies, Preprint.
2. S.L. Bell and R.J. Williams, Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy, Ann. Appl. Probab. 11 (2001) 608-649.
3. S.L. Bell and R.J. Williams, Dynamic scheduling of a multiserver system with complete resource pooling: Asymptotic optimality of a threshold policy in heavy traffic, Preprint.
4. A. Berman and R.J. Plemmons, Non-Negative Matrices in the Mathematical Sciences (SIAM, Philadelphia, PA, 1994).
5. D. Bertsekas and R. Gallagher, Data Networks (Prentice-Hall, Englewood Cliffs, NJ, 1992).
6. D. Bertsimas and J.N. Tsitsiklis, Introduction to Linear Optimization (Athena Scientific, Belmont, MA, 1997).
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 IEEE Conf. on Decision and Control, December 2000, pp. 516-521.
9. J.A. Buzacott and J.G. Shantikumar, Stochastic Analysis of Manufacturing Systems (Prentice-Hall, Englewood Cliffs, NJ, 1993).
10. H. Chen, P. Yang and D. Yao, Control and scheduling in a two-station queueing network: Optimal policies and heuristics, Queueing Systems 18 (1994) 301-332.
11. G.B. Dantzig, The programming of interdependent activities: Mathematical model, in: Activity Analysis of Production and Allocation, ed. T.C. Koopmans (Wiley, New York, 1951) pp. 19-32.
12. R. Hariharan, M.S. Moustafa and S. Stidham, Jr., Scheduling in a multi-class series of queues with deterministic service times, Queueing Systems 24 (1996) 83-99.
13. J.M. Harrison, Brownian models of queueing networks with heterogeneous customer populations, in: Stochastic Differential Systems, Stochastic Control Theory and Their Applications, eds. W. Fleming and P.L. Lions, The IMA Volumes in Mathematics and its Applications, Vol. 10 (Springer, New York, 1988) pp. 147-186.
14. J.M. Harrison, The BIGSTEP approach to flow management in stochastic processing networks, in: Stochastic Networks: Theory and Applications, eds. F.P. Kelly, S. Zachary and I. Ziedins (Oxford Univ. Press, Oxford, 1996) pp. 57-90.
15. J.M. Harrison, Heavy traffic analysis of a system with parallel servers: Asymptotic optimality of discrete-review policies, Ann. Appl. Probab. 8 (1998) 822-848.
16. J.M. Harrison, Brownian models of open processing networks: Canonical representation of workload, Ann. Appl. Probab. 10 (2000) 75-103.
17. J.M. Harrison, Correction - Brownian models of open processing networks: Canonical representation of workload, Ann. Appl. Probab. 13 (2003) 390-393.
18. J.M. Harrison, Stochastic networks and activity analysis, in: Analytic Methods in Applied Probability: In Memory of Fridrih Karpelevic, ed. Y. Suhov (Amer. Math. Soc., Providence, RI, 2002).
19. J.M. Harrison, A broader view of Brownian networks, Ann. Appl. Probab. 13 (2003) 1119-1150.
20. J.M. Harrison and M.J. López, Heavy traffic resource pooling in parallel-server systems, Queueing Systems 33 (1999) 339-368.
21. J.M. Harrison and J.A. Van Mieghem, Dynamic control of Brownian networks: State space collapse and equivalent workload formulations, Ann. Appl. Probab. 7 (1997) 747-771.
22. J.M. Harrison and L. Wein, Scheduling networks of queues: Heavy traffic analysis of a simple open network, Queueing Systems 5 (1989) 265-280.
23. F.P. Kelly and C.N. Laws, Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling, Queueing Systems 13 (1993) 47-86.
24. G.J. Koehler, A.B. Whinston and G.P. Wright, Optimization over Leontief Substitution Systems (North-Holland, Amsterdam, 1975).
25. T.C. Koopmans, Activity Analysis of Production and Allocation (Wiley, New York, 1951).
26. S. Kumar, Scheduling open queueing networks with sufficiently flexible resources, in: Proc. of the 37th Allerton Conf., University of Illinois, September 1999.
27. S. Kumar, Two-server closed networks in heavy traffic: Diffusion limits and asymptotic optimality, Ann. Appl. Probab. 10 (2000) 930-961.
28. H.J. Kushner and Y.N. Chen, Optimal control of assignment of jobs to processors under heavy traffic, Stochastics and Stochastic Rep. 68 (2000) 177-228.
29. H.J. Kushner and L.F. Martins, Heavy traffic analysis of a controlled multiclass queueing network via weak convergence methods, SIAM J. Control Optim. 34 (1996) 1781-1797.
30. C.N. Laws and Y.C. Teh, Alternative routeing in fully-connected queueing networks, Adv. in Appl. Probab. 32 (2000) 962-982.
31. C. Maglaras, Discrete-review policies for scheduling stochastic networks: Trajectory tracking and fluid-scale asymptotic optimality, Ann. Appl. Probab. 10 (2000).
32. C. Maglaras, Continuous-review tracking policies for dynamic control of stochastic networks, Queueing Systems 43 (2003) 43-80.
33. A. Mandelbaum and A.L. Stolyar, Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ-rule, Operations Research, to appear.
34. L.F. Martins, S.E. Shreve and H.M. Soner, Heavy traffic convergence of a controlled, multi-class queueing system, SIAM J. Control Optim. 34 (1996) 2133-2171.
35. S.P. Meyn, Sequencing and routing in multiclass queueing networks. Part I: Feedback regulation, SIAM J. Control Optim. 40 (2001) 741-776.
36. M. Squillante, C.H. Xia, D. Yao and L. Zhang, Threshold based priority policies for parallel server systems, Preprint (2000).
37. A.L. Stolyar, Maxweight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic, Preprint.
38. R.J. Williams, Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse, Queueing Systems 30 (1998) 27-88.
39. R.J. Williams, On dynamic scheduling of a parallel server system with complete resource pooling, in: Analysis of Communication Networks: Call Centres, Traffic and Performance, eds. D.R. McDonald and S.R.E. Turner, Fields Institute Communications, Vol. 28 (Amer. Math. Soc., Providence, RI, 2000) pp. 49-71.
40. D.D. Yao, ed., Stochastic Modeling and Analysis of Manufacturing Systems (Springer, New York, 1994).