Analyses of load stealing models based on families of differential equations

Theory of Computing Systems

Volumn 34, Issue 1, 2000, Pages 77-98

  Mitzenmacher, M ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SCIENCE; MATHEMATICAL TECHNIQUES;

DYNAMIC SETTINGS; LIMITING BEHAVIOR; NUMERICAL APPROXIMATIONS; SYSTEM BEHAVIORS; WORK-STEALING;

DIFFERENTIAL EQUATIONS;

EID: 0035586976     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s002240010010     Document Type: Article

References (47)

1. D. Achlioptas and M. Molloy. The analysis of a list-coloring algorithm on a random graph. In Proceedings of the 38th IEEE Symposium on Foundations of Computer Science, pages 204-212, 1997.
2. M. Alanyali and B. Hajek. Analysis of simple algorithms for dynamic load balancing. In INFOCOM 95, vol. 1, pages 230-238, 1995.
3. Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. In Proceedings of the 26th ACM Symposium on the Theory of Computing, pages 593-602, 1994.
4. R. Blumofe. Executing Multithreaded Program Efficiently. Ph.D. thesis, Massachusetts Institute of Technology, September 1995.
5. R. Blumofe, M. Frigo, C. Joerg, C. Leiserson, and K. Randall. An analysis of dag-consistent distributed shared-memory algorithms. In Proceedings of the 8th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 297-308, 1996.
6. R. Blumofe, C. Joerg, B. Kuszmaul, C. Leiserson, K. Randall, and Y. Zhou. Cilk: an efficient multithreaded runtime system. Journal of Parallel and Distributed Computing, 37(1):55-69, 1996.
7. R. Blumofe and C. Leiserson. Space-efficient scheduling of multithreaded computations. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pages 362-371, 1993.
8. R. Blumofe and C. Leiserson. Scheduling multithreaded computations by work stealing. In Proceedings of the 35th Annual IEEE Conference on Foundations of Computer Science, pages 356-368, 1994.
9. The Cilk Project. Available at http://theory.lcs.mit.edu/~cilk/home/intro.html.
10. M. Dahlin. Interpreting stale load information. In Proceedings of the 19th IEEE International Conference on Distributed Computing Systems (ICDCS), pages 285-296, May 1999. Also available as TR98-20, Department of Computer Sciences, University of Texas at Austin.
11. D. L. Eager, E. D. Lazowska, and J. Zahorjan. A comparison of receiver-initiated and sender-initiated adaptive load sharing. Performance Evaluation Review, 16:53-68, March 1986.
12. S. N. Ethier and T. G. Kurtz. Markov Processes: Characterization and Convergence. Wiley, New York 1986.
13. R. J. Gibbens, P. J. Hunt, and F. P. Kelly. Bistability in communication networks. In Disorder in Physical Systems (G. R. Grimmett and D. J. A. Welsh, eds.), pages 113-128. Oxford University Press, Oxford, 1990.
14. B. Hajek. Asymptotic analysis of an assignment problem arising in a distributed communications protocol. In Proceedings of the 27th Conference on Decision and Control, pages 1455-1459, 1988.
15. M. Harchol-Balter and D. Wolfe. Bounding delays in packet-routing networks. In Proceedings of the Twenty-Seventh Annual ACM Symposium on the Theory of Computing, pages 248-257, 1995.
16. R. M. Karp and M. Sipser. Maximum matchings in sparse random graphs. In Proceedings of the 22nd IEEE Symposium on Foundations of Computer Science, pages 364-375, 1981.
17. R. M. Karp, U. V. Vazirani, and V. V. Vazirani. An optimal algorithm for on-line bipartite matching. In Proceedings of the 22nd ACM Symposium on the Theory of Computing, pages 352-358, 1990.
18. R. M. Karp and Y. Zhang. A randomized parallel branch-and-bound procedure. In Proceedings of the 20th ACM Symposium on the Theory of Computing, pages 290-300, 1988.
19. F. P. Kelly. Reversibility and Stochastic Networks. Wiley, New York, 1979.
20. L. Kleinrock. Queueing Systems, Volume I. Wiley, New York, 1976.
21. T. G. Kurtz. Solutions of ordinary differential equations as limits of pure jump Markov processes. Journal of Applied Probability, 7:49-58, 1970.
22. T. G. Kurtz. Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. Journal of Applied Probability, 8:344-356, 1971.
23. T. G. Kurtz. Strong approximation theorems for density dependent Markov chains. Stochastic Processes and Applications, 6:223-240, 1978.
24. T. G. Kurtz. Approximation of Population Processes. CBMS-NSF Regional Conference Series in Applied Mathematics SIAM, Philadelphia, PA, 1981.
25. M. Luby, M. Mitzenmacher, M. A. Shokrollahi, D. Spielman, and V. Stemann. Practical loss-resilient codes. In Proceedings of the 29th ACM Symposium on the Theory of Computing, pages 150-159, 1997.
26. J. Martin and Y. M. Suhov. Fast Jackson networks. Annals of Applied Probability, 9(3):854-870, 1999.
27. A. N. Michel and R. K. Miller. Qualitative Analysis of Large Scale Dynamical Systems. Academic Press, New York, 1977.
28. R. Mirchandaney, D. Towsley, and J. A. Stankovic. Analysis of the effects of delays on load sharing. IEEE Transactions on Computing, 38:1513-1525, 1989.
29. R. Mirchandaney, D. Towsley, and J. A. Stankovic. Adaptive load sharing in heterogeneous systems. Journal of Parallel and Distributed Systems, 9:331-346, 1990.
30. M. Mitzenmacher. Bounds on the greedy routing algorithm for array networks. In Proceedings of the Sixth Annual ACM Symposium on Parallel Algorithms and Architectures, pages 248-259, 1994. To appear in the Journal of Computer Systems and Science.
31. M. Mitzenmacher. Constant time per edge is optimal on rooted tree networks. In Proceedings of the Eighth Annual ACM Symposium on Parallel Algorithms and Architectures, pages 162-169, 1996.
32. M. Mitzenmacher. Load balancing and density dependent jump Markov processes. In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science, pages 213-222, 1996.
33. M. Mitzenmacher. The Power of Two Choices in Randomized Load Balancing. Ph.D. thesis, University of California at Berkeley, September 1996.
34. M. Mitzenmacher. How useful is old information? In Proceedings of the 16th ACM Symposium on Principles of Distributed Computing, 1997, pages 83-91. Journal version to appear in IEEE Transactions on Parallel and Distributed Systems.
35. M. Mitzenmacher. On the analysis of randomized load balancing schemes. In Proceedings of the 9th ACM Symposium on Parallel Algorithms and Architectures, pages 292-301, 1997. Journal version in Theory of Computing Systems, 32:361-386, 1999.
36. M. Mitzenmacher. On the analysis of randomized load balancing schemes. In Proceedings of the 9th ACM Symposium on Parallel Algorithms and Architectures, pages 292-301, 1997. Journal version in Theory of Computing Systems, 32:361-386, 1999.
37. M. Mitzenmacher. Tight Thresholds for the Pure Literal Rule. Technical Note 1997-011, Digital Systems Research Center, Palo Alto, CA, June 1997.
38. B. Pittel, J. Spencer, and N. Wormald. Sudden emergence of a giant k-core in a random graph. Journal of Combinatorial Theory, Series B, 67:111-151, 1996.
39. R. Righter and J. Shanthikumar. Extremal properties of the FIFO discipline in queueing networks. Journal of Applied Probability, 29:967-978, November 1992.
40. L. Rudolph, M. Slivkin-Allalouf, and E. Upfal. A simple load balancing scheme for task allocation in parallel machines. In Proceedings of the 3rd Annual ACM Symposium on Parallel Algorithms and Architectures, pages 237-245, 1991.
41. A. Shwartz and A. Weiss. Large Deviations for Performance Analysis. Chapman & Hall, London, 1995.
42. G. D. Stamoulis and J. N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. IEEE Transactions on Communications, 42(11):3051-3061, November 1994. An early version appeared in the Proceedings of the Second Annual ACM Symposium on Parallel Algorithms and Architectures, pages 248-259, 1991.
43. G. D. Stamoulis and J. N. Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies. IEEE Transactions on Communications, 42(11):3051-3061, November 1994. An early version appeared in the Proceedings of the Second Annual ACM Symposium on Parallel Algorithms and Architectures, pages 248-259, 1991.
44. N. D. Vvedenskaya, R. L. Dobrushin, and F. I. Karpelevich. Queueing system with selection of the shortest of two queues: an asymptotic approach. Problems of Information Transmission, 32:15-27, 1996.
45. N. D. Vvedenskaya and Y. M. Suhov. Dobrushin's mean-field approximation for a queue with dynamic routing. Markov Processes and Related Fields, 3(4):493-527, 1997. Also available as Technical Report 3328, INRIA, December 1997.
46. N. C. Wormald. Differential equations for random processes and random graphs. Annals of Applied Probability, 5:1217-1235, 1995.
47. T. Yoskizawa. Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions. Springer-Verlag, New York, 1975.