Heavy traffic analysis of a system with parallel servers: Asymptotic optimality of discrete-review policies

Annals of Applied Probability

Volumn 8, Issue 3, 1998, Pages 822-848

  Harrison, J Michael ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

BIGSTEP method; Heavy traffic; Queueing theory; Resource pooling

Indexed keywords

EID: 0032147993     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1028903452     Document Type: Article

References (18)

1. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
2. CHEVALIER, P. B. and WEIN, L. M. (1993). Scheduling networks of queues: heavy traffic analysis of a multistation closed network. Oper. Res. 41 743-758.
3. FOSCHINI, G. J. (1977). On heavy traffic diffusion analysis and dynamic routing in packet switched networks. In Computer Performance (K. M. Chandy and M. Reiser, eds.) 499-514. North-Holland, Amsterdam.
4. FOSCHINI, G. J. and SALZ, J. (1978). A basic dynamic routing problem and diffusion. IEEE Trans. Comm. COM-26 320-327.
5. HARRISON, J. M. (1977). The supremum distribution of a Levy process with no negative jumps. Adv. in Appl. Probab. 9 417-422.
6. HARRISON, J. M. (1985). Brownian Motion and Stochastic Flow Systems. Wiley, New York.
7. HARRISON, J. M. (1988). Brownian models of queueing networks with heterogeneous customer populations. In Stochastic Differential Systems, Stochastic Control Theory and Applications (W. Fleming and P.-L. Lions, eds.) 147-186. Springer, New York.
8. HARRISON, J. M. (1996). 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.) 57-90. Oxford Univ. Press.
9. HARRISON, J. M. and WEIN, L. M. (1989). Scheduling networks of queues: heavy traffic analysis of a simple open network. Queueing Systems Theory Appl. 5 265-280.
10. HARRISON, J. M. and WEIN, L. M. (1990). Scheduling networks of queues: heavy traffic analysis of a two-station closed network. Oper. Res. 38 1052-1064.
11. HARRISON, J. M. and VAN MIEGHEM, J. A. (1997). Dynamic control of Brownian networks: state space collapse and equivalent workload formulations. Ann. Appl. Probab. 7 744-771.
12. KELLY, F. P. and LAWS, C. N. (1993). Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling. Queueing Systems Theory Appl. 13 47-86.
13. REIMAN, M. I. (1983). Some diffusion approximations with state space collapse. Proceedings of the International Seminar on Modelling and Performance Evaluation Methodology, Lecture Notes in Control and Inform. Sci. 60 209-240. Springer, Berlin.
14. REIMAN, M. I. (1984). Open queueing networks in heavy traffic. Math. Oper. Res. 9 441-458.
15. REIMAN, M. I. and SIMON, B. (1990). A network of priority queues in heavy traffic: one bottleneck station. Queueing Systems Theory Appl. 6 33-58.
16. VAN MIEGHEM, J. (1995). Dynamic scheduling with convex delay costs: the generalized cμ rule. Ann. Appl. Probab. 5 809-833.
17. WEIN, L. M. (1990). Brownian networks with discretionary routing. Oper. Res. 38 1065-1078.
18. WEIN, L. M. (1991). Scheduling networks of queues: heavy traffic analysis of a two-station network with controllable inputs. Oper. Res. 39 322-340.