Article

Free access

Analyses of load stealing models based on differential equations

Author:

Michael MitzenmacherAuthors Info & Claims

SPAA '98: Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures

Pages 212 - 221

https://doi.org/10.1145/277651.277687

Published: 01 June 1998 Publication History

PDF eReader

References

[1]

D. Achlioptas and M. Molloy. The analysis of a listcoloring algorithm on a random graph. In Proceedings of the 38th IEEE Symposium on Foundations of Computer Science, pages 204-212, 1997.

Digital Library

Google Scholar

[2]

M. Alanyali and B. Hajek. Analysis of simple algorithms for dynamic load balancing. In INFOCOM 95, 1995.

Digital Library

Google Scholar

[3]

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. In Proceedings of the 26th A CM Symposium on the Theory of Computing, pages 593-602, 1994.

Digital Library

Google Scholar

[4]

R. Blumofe. Executing Multithreaded Program E#- ciently. PhD thesis, Massachusetts Institute of Technology, September 1995.

Digital Library

Google Scholar

[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 A CM Syposium on Parallel Algorithms and Architectures, 1996.

Digital Library

Google Scholar

[6]

R. Blumofe, C. Joerg, B. Kuszmaul, C. Leiserson, K. Randall, and Y. Zhou. Cilk: An efficient multithreaded runtime system. In Proceedings of the 5th A CM SIGPLAN Symposium on Principles and Practice of Parallel Programming, 1995.

Digital Library

Google Scholar

[7]

R. Blumofe and C. Leiserson. Space-efficient scheduling of multithreaded computations. In Proceedings of the 25th Annual A CM Symposium on Theory of Computing, pages 362-371, 1993.

Digital Library

Google Scholar

[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, 1994.

Digital Library

Google Scholar

[9]

D. L. Eager, E. D. Lazokwska, and J. Zahorjan. A comparison of receiver-initiated and sender-initiated adaptive load sharing. Performance Evaluation Review, 16:53-68, March 1986.

Digital Library

Google Scholar

[10]

S. N. Ethier and T. G. Kurtz. Markov Processes: Characterization and Convergence. John Wiley and Sons, 1986.

Google Scholar

[11]

B. Hajek. Asymptotic analysis of an assignment problem arising in a distributed communications protocol. In Proceedings of the 2Tth Conference on Decision and Control, pages 1455-1459, 1988.

Crossref

Google Scholar

[12]

M. Harchol-Balter and D. Wolfe. Bounding delays in packet-routing networks. In Proceedings of the Twenty- Seventh Annual A CM Symposium on the Theory of Computing, pages 248-257, 1995.

Digital Library

Google Scholar

[13]

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.

Digital Library

Google Scholar

[14]

R. M. Karp, U. V. Vazirani, and V. V. Vazirani. An optimal algorithm for on-line bipartite matching. In Proceedings of the #2nd A CM Symposium on the Theory of Computing, pages 352-358, 1990.

Digital Library

Google Scholar

[15]

R. M. Karp and Y. Zhang. A randomized parallel branch-and-bound procedure. In Proceedings of the 20th A CM Symposium on the Theory of Computing, pages 290-300, 1988.

Digital Library

Google Scholar

[16]

L. Kleinrock. Queueing Systems, Volume i: Theory. John Wiley and Sons, 1976.

Google Scholar

[17]

T. G. Kurtz. Solutions of ordinary differential equations as limits of pure jump Markov processes. Journal of Applied Probability, 7:49-58, 1970.

Crossref

Google Scholar

[18]

T. G. Kurtz. Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. Journal of Applied Probability, 8:344-356, 1971.

Crossref

Google Scholar

[19]

T. G. Kurtz. Strong approximation theorems for density dependent Markov chains. Stochastic Processes and Applications, 6:223-240, 1978.

Crossref

Google Scholar

[20]

T. G. Kurtz. Approximation of Population Processes. CBMS-NSF Regional Conf. Series in Applied Math. SIAM, 1981.

Crossref

Google Scholar

[21]

M. Luby, M. Mitzenmacher, M. A. Shokrollahi, D. Spielman, and V. Stemann. Practical loss-resilient codes. In Proceedings of the 29th A CM Symposium on the Theory of Computing, pages 150-159, 1997.

Digital Library

Google Scholar

[22]

J. Martin and Y. M. Suhov. Fast jackson networks. available at uw#.statslab, cam. ac.uk/~jmb, January 1998.

Google Scholar

[23]

A. N. Michel and R. K. Miller. Qualitative Analysis of Large Scale Dynamical Systems. Academic Press, Inc., 1977.

Google Scholar

[24]

R. Mirchandaney, D. Towsley, and J. A. Stankovic. Analysis of the effects of delays on load sharing. Journal of Parallel and Distributed Systems, 1513-1525:331- 346, November 1989.

Google Scholar

[25]

R. Mirchandaney, D. Towsley, and J. A. Stankovic. Adaptive load sharing in heterogeneous systems. Journal of Parallel and Distributed Systems, 9:331-346, 1990.

Digital Library

Google Scholar

[26]

M. Mitzenmacher. Bounds on the greedy routing algorithm for array networks. In Proceedings of the Sixth Annual A CM Symposium on Parallel Algorithms and Architectures, pages 248-259, 1994. To appear in the Journal of Computer Systems and Science.

Digital Library

Google Scholar

[27]

M. Mitzenmacher. Constant time per edge is optimal on rooted tree networks. In Proceedings of the Eighth Annual A CM Symposium on Parallel Algorithms and Architectures, pages 162-169, 1996.

Digital Library

Google Scholar

[28]

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.

Digital Library

Google Scholar

[29]

M. Mitzenmacher. The Power of Two Choices in Randomized Load Balancing. PhD thesis, University of California at Berkeley, September 1996.

Digital Library

Google Scholar

[30]

M. Mitzenmacher. On the analysis of randomized load balancing schemes. In Proceedings of the 9th Annual Symposium on Parallel Algorithms and Architectures, pages 292-301, 1997.

Digital Library

Google Scholar

[31]

M. Mitzenmacher. Tight thresholds for the pure literal rule. Technical Report Technical Note 1997-011, Digital Systems Research Center, June 1997.

Google Scholar

[32]

B. Pittel, J. Spencer, and N. Wormald. Sudden emergence of a giant k-core in a random graph. Journal of Combinatorial Series B, 67:111-151, 1996.

Digital Library

Google Scholar

[33]

R. Righter. and J. Shanthikumar. Extremal properties of the FIFO discipline in queueing networks. Journal of Applied Probability, 29:967-978, November 1992.

Crossref

Google Scholar

[34]

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 A CM Syposium on Parallel Algorithms and Architectures, pages 237-245, 1991.

Digital Library

Google Scholar

[35]

A. Shwartz and A. Weiss. Large Deviations for Performance Analysis. Chapman & Hall, 1995.

Google Scholar

[36]

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 A CM Symposium on Parallel Algorithms and Architectures, p. 248-259, 1991.

Digital Library

Google Scholar

[37]

N. D. Vvedensl#ya, 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.

Google Scholar

[38]

N. D. Vvedenskaya and Y. M. Suhov. Dobrushin's mean-field approximation for a queue with dynamic routing. Technical Report 3328, INRIA, December 1997.

Google Scholar

[39]

N. C. Wormald. Differential equations for random processes and random graphs. Annals of A ppl. Prob., 5:1217-1235, 1995.

Google Scholar

Cited By

View all

Nissim RSchwartz O(2023)Stragglers in Distributed Matrix MultiplicationJob Scheduling Strategies for Parallel Processing10.1007/978-3-031-43943-8_4(74-96)Online publication date: 15-Sep-2023
https://doi.org/10.1007/978-3-031-43943-8_4
Aksenova ELazutina ASokolov A(2021)About Optimal Management of Work-Stealing Deques in Two-Level MemoryLobachevskii Journal of Mathematics10.1134/S199508022107002742:7(1475-1482)Online publication date: 9-Aug-2021
https://doi.org/10.1134/S1995080221070027
Барковский ЕЛазутина АСоколов А(2019)The Optimal Control of Two Work-Stealing Deques, Moving One After Another in a Shared MemoryProgram Systems: Theory and ApplicationsПрограммные системы: теория и приложения10.25209/2079-3316-2019-10-1-3-1710:1(3-17)Online publication date: 2019
https://doi.org/10.25209/2079-3316-2019-10-1-3-17
Show More Cited By

Index Terms

Analyses of load stealing models based on differential equations
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
2. Theory of computation
  1. Models of computation
    1. Abstract machines

Recommendations

Two-dimensional differential transform for partial differential equations

The differential transform is a numerical method for solving differential equations. In this paper, we present the definition and operation of the two-dimensional differential transform. A distinctive feature of the differential transform is its ability ...
Numerical solution of distributed order fractional differential equations

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. ...
Solving systems of fractional differential equations using differential transform method

This paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method,...

Comments

Information & Contributors

Information

Published In

SPAA '98: Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures

June 1998

312 pages

ISBN:0897919890

DOI:10.1145/277651

Chairmen:
Gary Miller
Carnegie Mellon Univ., Pittsburgh, PA
,
Phillip B. Gibbons
Bell Labs

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1998

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

SPAA/PODC98

Sponsor:

SPAA/PODC98: 10th Annual ACM Symposium on Parallel Algorithms and Architectures/Symposium on Principles of Distributed Computing

June 28 - July 2, 1998

Puerto Vallarta, Mexico

Acceptance Rates

SPAA '98 Paper Acceptance Rate 30 of 84 submissions, 36%;

Overall Acceptance Rate 447 of 1,461 submissions, 31%

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

32
Total Citations
View Citations
435
Total Downloads

Downloads (Last 12 months)21
Downloads (Last 6 weeks)3

Reflects downloads up to 09 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Nissim RSchwartz O(2023)Stragglers in Distributed Matrix MultiplicationJob Scheduling Strategies for Parallel Processing10.1007/978-3-031-43943-8_4(74-96)Online publication date: 15-Sep-2023
https://doi.org/10.1007/978-3-031-43943-8_4
Aksenova ELazutina ASokolov A(2021)About Optimal Management of Work-Stealing Deques in Two-Level MemoryLobachevskii Journal of Mathematics10.1134/S199508022107002742:7(1475-1482)Online publication date: 9-Aug-2021
https://doi.org/10.1134/S1995080221070027
Барковский ЕЛазутина АСоколов А(2019)The Optimal Control of Two Work-Stealing Deques, Moving One After Another in a Shared MemoryProgram Systems: Theory and ApplicationsПрограммные системы: теория и приложения10.25209/2079-3316-2019-10-1-3-1710:1(3-17)Online publication date: 2019
https://doi.org/10.25209/2079-3316-2019-10-1-3-17
Yang JHe Q(2018)Scheduling Parallel Computations by Work StealingInternational Journal of Parallel Programming10.1007/s10766-016-0484-846:2(173-197)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1007/s10766-016-0484-8
Kuchumov RSokolov AKorkhov V(2018)Staccato: Cache-Aware Work-Stealing Task Scheduler for Shared-Memory SystemsComputational Science and Its Applications – ICCSA 201810.1007/978-3-319-95171-3_8(91-102)Online publication date: 4-Jul-2018
https://doi.org/10.1007/978-3-319-95171-3_8
Aksenova ESokolov A(2017)Modeling of the Memory Management Process for Dynamic Work-Stealing Schedulers2017 Ivannikov ISPRAS Open Conference (ISPRAS)10.1109/ISPRAS.2017.00009(12-15)Online publication date: Nov-2017
https://doi.org/10.1109/ISPRAS.2017.00009
Li CLiao XJin H(2017)Enhancing application performance via DAG-driven scheduling in task parallelism for cloud centerPeer-to-Peer Networking and Applications10.1007/s12083-017-0576-2Online publication date: 16-Jun-2017
https://doi.org/10.1007/s12083-017-0576-2
Li QYang F(2015)Mean-Field Analysis for Heterogeneous Work Stealing ModelsInformation Technologies and Mathematical Modelling - Queueing Theory and Applications10.1007/978-3-319-25861-4_3(28-40)Online publication date: 9-Dec-2015
https://doi.org/10.1007/978-3-319-25861-4_3
Sokolov ABarkovsky E(2015)The Mathematical Model and the Problem of Optimal Partitioning of Shared Memory for Work-Stealing DequesProceedings of the 13th International Conference on Parallel Computing Technologies - Volume 925110.1007/978-3-319-21909-7_11(102-106)Online publication date: 31-Aug-2015
https://dl.acm.org/doi/10.1007/978-3-319-21909-7_11
Kumar VBlackburn SGrove D(2014)Friendly barriersACM SIGPLAN Notices10.1145/2674025.257620749:7(165-176)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1145/2674025.2576207
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

Two-dimensional differential transform for partial differential equations

Numerical solution of distributed order fractional differential equations

Solving systems of fractional differential equations using differential transform method