Skip to main content
SpringerLink
Log in

The design of novel distributed protocols from differential equations

  • Published:
Distributed Computing Aims and scope Submit manuscript

Abstract

This paper proposes a framework to translate certain subclasses of differential equation systems into practical protocols for distributed systems. The generated protocols are intended for large-scale distributed systems that contain several hundreds to thousands of processes. The synthesized protocols are state machines containing probabilistic transitions and actions, and they are proved to show equivalent stochastic behavior to the original equations. The protocols are probabilistically scalable and reliable, and have practical applications in large-scale distributed systems, e.g., peer to peer systems. In order to illustrate the usefulness of the framework, it is used to generate new solutions for the problems of (a) responsibility migration (giving rise to a novel model of dynamic replication), and (b) majority selection. We present mathematical analysis of these two protocols, and experimental results from our implementations. These two protocols are derived from natural analogies that are represented as differential equations—endemics and the Lotka–Volterra model of competition, respectively. We believe the design framework could be effectively used in transforming, in a very systematic manner, well-known natural phenomena into protocols for distributed systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Achlioptas D. (2001). Lower bounds for random 3-SAT via differential equations. Theor. Comp. Sci. 265(1–2): 159–185

    Article  MATH  Google Scholar 

  2. Ambrosio, J.: Tools for the code generation. ADTmag.com, http://www.adtmag.com/article.asp?id=7850 (2004)

  3. Anderson, R.J.: The Eternity Service. In: Proc. Pragocrypt (1996)

  4. Bailey N.T.J. (1975). Epidemic theory of infectious diseases and its applications, 2nd edn . Hafner, New York

    Google Scholar 

  5. Bhagwan, R., Savage, S., Voelker, G.M.: Understanding availability. Proc. Int. Symp. Peer Peer Syst. 135–140 (2003)

  6. Bhagwan, R., et al.: Total Recall: system support for automated availability management. Proc. Usenix Netw. Sys. Des. Implement. 337–350 (2004)

  7. Cohen, E., Shenker, S.: Replication strategies in unstructured peer-to-peer networks. Proc. ACM SIGCOMM 177–190 (2002)

  8. Colouris G., Dollimore J., Kindberg T. (2001). Distributed systems: concepts and design, 3rd edn. Addison-Wesley, USA

    Google Scholar 

  9. Corradi A., Leonardi L., Zambonelli F. (1999). Diffusive load-balancing policies for dynamic applications. IEEE Concurr. 7(1): 22–31

    Article  Google Scholar 

  10. Das, A., Gupta, I., Motivala, A.: SWIM: scalable weakly-consistent infection-style process group membership protocol. Proc. IEEE Dependable Syst. Netw. 303–312 (2002)

  11. Demers, A., et al.: Epidemic algorithms for replicated database maintenance. Proc. ACM Symp. Princ. Dist. Comp. 1–12 (1987)

  12. Fischer M.J., Lynch N.A., Patterson M. (1985). Impossibility of distributed consensus with one faulty process. J. ACM 32(2): 374–382

    Article  MATH  Google Scholar 

  13. Gray, J., et al.: The dangers of replication and a solution. Proc. ACM SIGMOD 173–182 (1996)

  14. Gupta, I.: On the design of distributed protocols from differential equations. Proc. ACM Symp. Princ. Dist. Comp. 216–225 (2004)

  15. Kreyszig, E.: Advanced engineering mathematics, 8th edn. Wiley, NJ (1998)

  16. Kubiatowicz, J., et al.: Oceanstore: an architecture for globalscale persistent store. Proc. ACM Annl. Symp. Prog. Langs. Oper. Syst. 190–201 (2000)

  17. Kurtz, T.G.: Approximation of population processes. Regional conference series in applied mathematics, SIAM, 1981, ISBN 0-89871-169-X

  18. Maniatis, P. et al.: Preserving peer replicas by rate-limited sampled voting. Proc. ACM Symp. Oper. Syst. Princ. 44–59 (2003)

  19. Merritt, M., Taubenfeld, G.: Computing with infinitely many processes. Proc. Dist. Comp. Springer LNCS 1914, 164–178 (2000)

  20. Mitzenmacher M. (2001). The power of two choices in randomized load balancing. IEEE Trans. Parallel Dist. Syst. 12(10): 1094–1104

    Article  Google Scholar 

  21. Putman R.J., Wratten S.D. (1984). Principles of ecology. Croom Helm, London

    Google Scholar 

  22. Rabin, M.O.: Randomized byzantine generals. Proc. Found. Comp. Sci. 403–409 (1983)

  23. Rowstron, A., Druschel, P.: Storage management and caching in PAST, a large-scale, persistent peer-to-peer storage utility. Proc. ACM Symp. Oper. Syst. Princ. 188–201 (2001)

  24. Saito, Y., et al.: Taming aggressive replication in the Pangaea file system. ACM SIGOPS Oper. Sys. Rev. 15–30 (2001)

  25. Schroeder M.D., Birrell A.D., Needham R.M. (1984). Experience with Grapevine: the growth of a distributed system. ACM Trans. Comp. Syst. 2(1): 3–23

    Article  Google Scholar 

  26. Strogatz S.H. (2001). Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering, 1st edn. Perseus, New York

    Google Scholar 

  27. Weisstein, E.W.: Heat conduction equation. MathWorld–A Wolfram Web Resource, 2004, http://www.mathworld.wolfram.com/HeatConductionEquation.html

  28. Wormald N.C. (1995). Differential equations for random processes and random graphs. Ann. Appl. Prob. 5(4): 1217–1235

    MATH  Google Scholar 

  29. Wu S.-H. et al. (1997). Composition and behaviors of probabilistic I/O automata. Theor. Comp. Sci. 176(1–2): 1–38

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, 201 N. Goodwin Ave., Urbana, IL, 61801, USA

    Indranil Gupta

  2. Wolverine Asset Management, 3555 Scottsdale Circle, Naperville, IL, 60564, USA

    Mahvesh Nagda

  3. Microsoft Corporation, 2400 Elliott Ave, 214, Seattle, WA, 98121, USA

    Christo Frank Devaraj

Authors
  1. Indranil Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mahvesh Nagda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christo Frank Devaraj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Indranil Gupta.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gupta, I., Nagda, M. & Devaraj, C.F. The design of novel distributed protocols from differential equations. Distrib. Comput. 20, 95–114 (2007). https://doi.org/10.1007/s00446-007-0024-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00446-007-0024-2

Keywords

Search

Navigation