Optimal load balancing on distributed homogeneous unreliable processors

Operations Research

Volumn 46, Issue 4, 1998, Pages 563-573

  Liu, Zhen ^a   Righter, Rhonda ^b  

^a INRIA   (France)

^b SANTA CLARA UNIVERSITY   (United States)

Author keywords

Dynamic programming optimal control, semi Markow; Probability, stochastic model applications: distributed routing; Queues, cyclic: optimality of round robin routing

Indexed keywords

DISTRIBUTED PARAMETER CONTROL SYSTEMS; DYNAMIC PROGRAMMING; MARKOV PROCESSES; MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS; PROBABILITY; QUEUEING THEORY;

DISTRIBUTED ROUTING;

PROGRAM PROCESSORS;

EID: 0032117493     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.46.4.563     Document Type: Article

References (35)

1. BOEL, R. K. AND J. H. VAN SCHUPPEN. 1989. Distributed Routing for Load Balancing. Proc. IEEE. 77, 210-221.
2. CHANG, C. S. 1992. A New Ordering for Stochastic Majorization: Theory and Applications. Advances in Applied Probability, 24, 604-634.
3. CHANG, C. S., X. L. CHAO, AND M. PINEDO. 1990. A Note on Queues with Bernoulli Routing. Proc. 29th Conf. on Decision and Control, 897-902.
4. COMBE, M. B. AND O. J. BOXMA. 1994. Optimization of Static Traffic Allocation Policies. Theoretical Computer Science A, 125, 17-43.
5. DALEY, D. J. 1987. Certain Optimality Properties of the First Come First Served Discipline for G/G/s Queues. Stochastic Processes and Their Applications, 25, 301-308.
6. EPHREMIDES, A., P. VARAIYA, AND J. WALRAND. 1980. A simple dynamic routing problem. IEEE Trans. on Auto. Control, AC-25, 690-693.
7. FOSS, S. C. 1980. Approximation of Multichannel Queueing Systems (in Russian). Sibirski Mat. Zh. 21, 132-140.
8. (Transl.: Siberian Math. J. 21, 851-857.)
9. FOSS, S. G. 1981. Comparison of Servicing Strategies in Multichannel Queueing Systems (in Russian). Sibirski Math. Zh. 22, 190-197.
10. (Transl.: Siberian Math. J. 22, 142-147.)
11. GELENBE, E. 1989. Multiprocessor Performance. John Wiley and Sons, New York.
12. GELENBE, E. AND F. PEKERGIN. 1993. Load Balancing Pragmatics. Technical Report, EHEI Université René Descartes.
13. GÜN, L. AND A. JEAN-MARIE. 1993. Parallel Queues with Resequencing. J. ACM. 40, 1188-1208.
14. HAJEK, B. 1983. The Proof of a Folk Theorem on Queueing Delay with Applications to Routing in Networks. J. Assoc. Comp. Mach. 30, 834-851.
15. HAJEK, B. 1985. Extremal Splittings of Point Processes. Math. O. R. 10, 543-556.
16. HORDIJK, A. AND G. KOOLE. 1990. On the Optimality of the Generalized Shortest Queue Policy. Prob. in the Engin. and Info. Sci. 4, 477-487.
17. JEAN-MARIE, A. AND Z. LIU. 1992. Stochastic Comparisons for Queueing Models via Random Sums and Intervals. Adv. Appl. Prob. 24, 960-985.
18. KOOLE, G. 1996. On the Pathwise Optimal Bernoulli Routing Policy for Homogeneous Parallel Servers. Math. Oper. Res. 21, 469-476.
19. LIU, Z. AND D. TOWSLEY. 1994a. Optimality of the Round-Robin Routing Policy. J. Appl. Prob. 31, 466-478.
20. LIU, Z. AND D. TOWSLEY. 1994b. Effects of Service Disciplines in G/G/s Queueing Systems. Ann. O. R. 48, Special Issue on Queueing Networks, 401-429.
21. LIU, Z. AND D. TOWSLEY. 1994c. Stochastic Scheduling in In-Forest Networks. Adv. Appl. Prob. 26, 222-241.
22. MARSHALL, A. W. AND I. OLKIN. 1979. Inequalities: Theory of Majorization and Its Applications. Academic Press, Orlando.
23. MENICH, R. 1987. Optimality of Shortest Queue Routing for Dependent Service Stations. Proc. 26th Conf. on Decision and Control, 1069-1072.
24. SPARAGGIS, P. D., D. TOWSLEY, AND C. G. CASSANDRAS. 1993. Extremal Properties of the SNQ and the LNQ Policies in Finite Capacity Systems with State-dependent Service Rates. J. Appl. Prob. 30, 223-236.
25. STAMOULIS, G. D. AND J. N. TSITSIKLIS. 1991. Optimal Distributed Policies for Choosing Among Multiple Servers. Proc. Conf. Dec. Cont. 815-820.
26. STOYAN, D. 1983. Comparison Methods for Queues and Other Stochastic Models. English translation, D. J. Daley (ed.), John Wiley and Sons, New York.
27. TOWSLEY, D., P. D. SPARAGGIS, AND C. G. CASSANDRAS. 1993. Optimal Routing and Buffer Allocation for a Class of Finite Capacity Queueing Systems. IEEE Trans. Autom. Control. 37, 1446-1451.
28. VASICEK, O. A. 1997. An Inequality for the Variance of Waiting Time Under a General Queueing Discipline. Opns. Res. 25, 879-884.
29. WALRAND, J. 1988. An Introduction to Queueing Networks. Prenctice Hall, Englewood Cliffs, NJ.
30. WANG, Y.-T. AND R. J. T. MORRIS. 1985. Load Sharing in Distributed Systems. IEEE Trans. Comp. C-34, 204-217.
31. WEBER, R. R. 1978. On the Optimal Assignment of Customers to Parallel Queues. J. Appl. Prob. 15, 406-413.
32. WHITT, W. 1986. Deciding Which Queue to Join: Some Counterexamples. Opns. Res. 34, 55-62.
33. WINSTON, W. 1977. Optimality of the Shortest Line Discipline. J. Appl. Prob. 14, 181-189.
34. WOLFF, R. W. 1977. An Upper Bound for Multi-Channel Queues, J. Appl. Prob. 14, 884-888.
35. WOLFF, R. W. 1987. Upper Bounds on Work in Systems for Multichannel Queues. J. Appl. Prob. 24, 547-551.