Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cμ-rule

Operations Research

Volumn 52, Issue 6, 2004, Pages 836-855

  Mandelbaum, Avishai ^a   Stolyar, Alexander L ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

Networks: stochastic; Production scheduling: sequencing stochastic; Queues: diffusion models, networks, optimization

Indexed keywords

DIFFUSION MODELS; NETWORKS; PRODUCTION/SCHEDULING: SEQUENCING/STOCHASTIC; QUEUES;

COSTS; CUSTOMER SATISFACTION; FUNCTIONS; OPTIMIZATION; QUEUEING THEORY; RANDOM PROCESSES; SERVERS; SET THEORY;

SCHEDULING;

EID: 12344326034     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.1040.0152     Document Type: Article

References (26)

1. Andrews, M., K. Kumaran, K. Ramanan, A. L. Stolyar, R. Vijayakumar, P. Whiting. 2004. Scheduling in a queueing system with asynchronously varying service rates. Probab. Engrg. Inform. Sci. 18 191-217.
2. Armony, M., N. Bambos. 1999. Queueing networks with interacting service resources. Proc. 37th Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, 42-51.
3. Bell, S. L., R. J. Williams. 2001. Dynamic scheduling of a system with two parallel servers in heavy traffic with complete resource pooling: Asymptotic optimality of a continuous review threshold policy. Ann. Probab. 11 608-649.
4. Bramson, M. 1998. State space collapse with applications to heavy traffic limits for multiclass queueing networks. Queueing Systems 30 89-148.
5. Chen, H., A. Mandelbaum. 1991a. Stochastic discrete flow networks: Diffusion approximations and bottlenecks. Ann. Probab. 19 1463-1519.
6. Chen, H., A. Mandelbaum. 1991b. Leontief systems, RBV's and RBM's. M. H. A. Davis, R. J. Elliott, eds. Applied Stochastic Analysis. Gordon and Breach Science Publishers, New York, 1-43.
7. Cox, D. R., W. L. Smith. 1961. Queues. Methuen, London, U.K., and Wiley, New York.
8. Dai, J. G., B. Prabhakar. 2000. The throughput of data switches with and without speedup. Proc. INFOCOM'2000, 556-564.
9. Ethier, S. N., T. G. Kurtz. 1986. Markov Process: Characterization and Convergence. John Wiley and Sons, New York.
10. Glazebrook, K. D., J. Nino-Mora. 2001. Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance. Oper. Res. 49 609-623.
11. Harrison, J. M. 1998. Heavy traffic analysis of a system with parallel servers: Asymptotic optimality of discrete review policies. Ann. Appl. Probab. 8 822-848.
12. Harrison, J. M., M. J. Lopez. 1999. Heavy traffic resource pooling in parallel-server systems. Queueing Systems 33 339-368.
13. Harrison, J. M., J. A. Van Mieghem. 1997. Dynamic control of Brownian networks: State space collapse and equivalent workload formulations. Ann. Appl. Probab. 7 747-771.
14. Klimov, G. P. 1974. Time sharing systems 1. Theory Probab. Appl. 19 532-551.
15. Klimov, G. P. 1978. Time sharing systems II. Theory Probab. Appl. 23 314-321.
16. McKeown, N., V. Anantharam, J. Walrand. 1996. Achieving 100% throughput in an input-queued switch. Proc. INFOCOM'96, 296-302.
17. Reiman, M. I. 1984. Some diffusion approximations with state space collapse. Proc. Internat. Seminar Modeling Performance Evaluation Methodology. Lecture Notes in Control and Information Sciences. Springer, New York, 209-240.
18. Reiman, M. I. 1988. A multiclass feedback queue in heavy traffic. Adv. Appl. Probab. 20 179-207.
19. Stolyar, A. L. 2004. MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic. Ann. Appl. Probab. 14 1-53.
20. Tassiulas, L., A. Ephremides. 1992. Stability properties of constrainted queueing systems and scheduling policies for maximum through-put in multishop radio network. IEEE Trans. Automatic Control 37 1936-1948.
21. Van Mieghem, J. A. 1995. Dynamic scheduling with convex delay costs: The generalized cμ rule. Ann. Appl. Probab. 5 809-833.
22. Whitt, W. 1999. Improving service by informing customers about anticipated delays. Management Sci. 45 192-207.
23. Williams, R. J. 1998a. An invariance principle for semimartingale reflecting Brownian motions in an orthant. Queueing Systems 30 5-25.
24. Williams, R. J. 1998b. Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse. Queueing Systems 30 27-88.
25. Williams, R. J. 2000. On dynamic scheduling of a parallel server system with complete resource pooling. Fields Institute Communications 28 49-71.
26. Zohar, E., A. Mandelbaum, N. Shimkin. 2002. Adaptive behavior of impatient customers in tele-queues: Theory and empirical support. Management Sci. 48 566-583.