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#### References

- 1. B. Ata and S. Kumar.
Heavy traffic analysis of open processing networks with complete resource
pooling: asymptotic optimality of discrete review policies.
*Annals of Applied Probability*,**15**(2005), 331-391. Math. Review MR2115046 - 2. S. L. Bell.
*Dynamic Scheduling of a Parallel Server System in Heavy Traffic with Complete Resource Pooling: Asymptotic Optimality of a Threshold Policy.*Ph.D. dissertation, Department of Mathematics, University of California, San Diego, 2003. Math. Review number not available. -
3. 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.
*Annals of Applied Probability*,**11**(2001), 608-649. Math. Review MR1865018 -
4. P. Billingsley.
*Convergence of Probability Measures.*John Wiley and Sons, New York, 1968. Math. Review MR0233396 -
5. M. Bramson. State space collapse with applications to heavy
traffic limits for multiclass queueing networks.
*Queueing Systems*,**30**(1998), 89-148. Math. Review MR1663763 -
6. M. Bramson and R. J. Williams.
Two workload properties for Brownian networks.
*Queueing Systems*,**45**(2003), 191-221. Math. Review MR2024178 - 7. A. Budhiraja and A. P. Ghosh,
A large deviations approach to asymptotically optimal control of
crisscross network in heavy traffic.
*Annals of Applied Probability,***15**(2005), 1887-1935. Math. Review number not available. - 8. P. B. Chevalier and L. Wein. Scheduling networks
of queues: heavy traffic analysis of a multistation closed network.
*Operations Research,***41**(1993), 743-758. Math. Review number not available. - 9. K. L. Chung and R. J. Williams.
*Introduction to Stochastic Integration*. 2nd edition, Birkhäuser, Boston, 1990. Math. Review of 1st Edition MR0711774 -
10. S. N. Ethier and T. G. Kurtz.
*Markov Processes: Characterization and Convergence.*Wiley, New York, 1986. Math. Review MR0838085 -
11. J. M. Harrison.
*Brownian Motion and Stochastic Flow Systems.*John Wiley and Sons, New York, 1985. Math. Review MR0798279 -
12. J. M. Harrison. Brownian models of queueing networks with
heterogeneous customer populations. In
*Stochastic Differential Systems, Stochastic Control Theory and Their Applications, IMA Volume 10*, W. Fleming and P. L. Lions (eds.), Springer Verlag, New York, 1988, pp. 147-186. Math. Review MR0934722 - 13. J. M. Harrison.
Balanced fluid models of multiclass queueing networks: a
heavy traffic conjecture.
In
*Stochastic Networks*, F. P. Kelly and R. J. Williams (eds.), Springer-Verlag, 1995, pp. 1-20. Math. Review MR1381003 - 14. J. M. Harrison. The BIGSTEP approach to flow management in
stochastic processing networks. In
*Stochastic Networks: Theory and Applications,*F. P. Kelly, S. Zachary and I. Ziedins (eds.), Oxford University Press, 1996, pp. 57-90. Math. Review number not available. -
15. J. M. Harrison. Heavy traffic analysis of a system with parallel servers:
asymptotic optimality of discrete-review policies.
*Annals of Applied Probability*,**8**(1998), 822-848. Math. Review MR1627791 -
16. J. M. Harrison.
Brownian models of open processing networks:
canonical representation of workload.
*Annals of Applied Probability*,**10**(2000), 75-103. Correction:**13**(2003), 390-393. Math. Review MR1765204 - 17. J. M. Harrison. A broader view of Brownian networks.
*Annals of Applied Probability*,**13**(2003), 1119-1150. Math. Review MR1994047 -
18. J. M. Harrison and M. J. López. Heavy traffic resource pooling
in parallel-server systems.
*Queueing Systems,***33**(1999), 339-368. Math. Review MR1742575 -
19. J. M. Harrison and J. A. Van Mieghem. Dynamic control of Brownian
networks: state space collapse and equivalent workload formulations.
*Annals of Applied Probability,***7**(1997), 747-771. Math. Review MR1459269 - 20. J. M. Harrison and L. Wein. Scheduling networks of queues:
heavy traffic analysis of a simple open network.
*Queueing Systems,***5**(1989), 265-280. Math. Review MR1030470 - 21. J. M. Harrison and L. Wein. Scheduling networks of queues:
heavy traffic analysis of a two-station closed network.
*Operations Research,***38**(1990), 1052-1064. Math. Review MR1095959 -
22. D. L. Iglehart and W. Whitt.
The equivalence of functional central limit theorems for
counting processes and associated partial sums.
*Ann. Math. Statist.,***42**(1971), 1372-1378. Math. Review MR0310941 -
23. W. C. Jordan and C. Graves. Principles on the benefits of manufacturing
process flexibility.
*Management Science,***41**(1995), 577-594. Math. Review number not available. - 24. 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. Math. Review MR1218844 - 25. H. J. Kushner and Y. N. Chen. Optimal
control of assignment of jobs to processors
under heavy traffic.
*Stochastics and Stochastics Rep.,*(2000), no. 3-4, pp. 177-228. Math. Review MR1746180**68** - 26. H. J. Kushner and P. Dupuis.
*Numerical Methods for Stochastic Control Problems in Continuous Time.*Springer-Verlag, New York, 1992. Math. Review MR1217486 - 27. H. J. Kushner and L. F. Martins.
Numerical methods
for stochastic singular control problems.
*SIAM J. Control and Optimization***29**(1991), 1443-1475. Math. Review MR1132190 - 28. C. N. Laws.
*Dynamic Routing in Queueing Networks.*Ph.D. dissertation, Statistical Laboratory, University of Cambridge, U.K., 1990. Math. Review number not available. - 29. C. N. Laws.
Resource pooling in queueing networks with dynamic
routing.
*Advances in Applied Probability,***24**(1992), 699-726. Math. Review MR1174386 - 30. C. N. Laws and G. M. Louth. Dynamic scheduling of a four-station
queueing network.
*Probab. Engrg. Inform. Sci.,***4**(1990), 131-156. Math. Review number not available. -
31. A. Mandelbaum and A. L. Stolyar.
Scheduling flexible servers with convex delay costs:
heavy-traffic optimality of the generalized c-mu-rule.
*Operations Research*,**52**(2004), 836-855. Math. Review MR2104141 -
32. S. P. Meyn. Dynamic safety-stocks for asymptotic optimality in stochastic networks
.
*Queueing Systems,***50**(2005), 255-297. Math. Review number not available. - 33. T. Osogami, M. Harchol-Balter, A. Scheller-Wolf, and L. Zhang.
Exploring threshold-based policies for load sharing.
*Proceedings of 42nd Annual Allerton Conference on Communication, Control and Computing,*University of Illinois, Urbana-Champaign, October 2004. Math. Review number not available. - 34. W. P. Peterson. A heavy traffic limit theorem for networks
of queues with multiple customer types.
*Mathematics of Operations Research,***16**(1991), 90-118. Math. Review MR1106792 - 35. M. Squillante, C. H. Xia, D. Yao, and L. Zhang.
Threshold-based priority policies for parallel-server systems with affinity
scheduling.
*Proc. IEEE American Control Conference*(2001), 2992-2999. Math. Review number not available. -
36. A. L. Stolyar.
Maxweight scheduling in a generalized switch: state space
collapse and workload minimization in heavy traffic.
*Annals of Applied Probability*,**14**(2004), 1-53. Math. Review MR2023015 -
37. Y. C. Teh.
*Threshold Routing Strategies for Queueing Networks.*D. Phil. thesis, University of Oxford, 1999. Math. Review number not available. -
38. Y. C. Teh and A. R. Ward.
Critical thresholds for dynamic routing in queueing networks.
*Queueing Systems*,**42**(2002), 297-316. Math. Review MR1935144 -
39. L. Wein. Scheduling networks of queues: heavy traffic analysis
of a two-station network with controllable inputs.
*Operations Research,***38**(1990), 1065-1078. Math. Review MR1095960 - 40. R. J. Williams.
An invariance principle for semimartingale reflecting Brownian motions
in an orthant.
*Queueing Systems*,**30**(1998), 5-25. Math. Review MR1663755 - 41. R. J. Williams. Diffusion approximations
for open multiclass queueing networks: sufficient conditions
involving state space collapse.
*Queueing Systems*,**30**(1998), 27-88. Math. Review MR1663759 - 42. 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,*D. R. McDonald and S. R. E. Turner (eds.), American Mathematical Society, Providence, RI, 2000, 49-71. Math. Review MR1788708

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