research-article

The age of gossip: spatial mean field regime

Authors:

Augustin Chaintreau,

Jean-Yves Le Boudec,

Nikodin RistanovicAuthors Info & Claims

SIGMETRICS '09: Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems

Pages 109 - 120

https://doi.org/10.1145/1555349.1555363

Published: 15 June 2009 Publication History

Abstract

Disseminating a piece of information, or updates for a piece of information, has been shown to benefit greatly from simple randomized procedures, sometimes referred to as gossiping, or epidemic algorithms. Similarly, in a network where mobile nodes occasionally receive updated content from a base station, gossiping using opportunistic contacts allows for recent updates to be efficiently maintained, for a large number of nodes. In this case, however, gossiping depends on node mobility. For this reason, we introduce a new gossip model, with mobile nodes moving between different classes that can represent locations or states, which determine gossiping behavior of the nodes. Here we prove that, when the number of mobile nodes becomes large, the age of the latest updates received by mobile nodes approaches a deterministic mean-field regime. More precisely, we show that the occupancy measure of the process constructed, with the ages defined above, converges to a deterministic limit that can be entirely characterized by differential equations. This major simplification allows us to characterize how mobility, source inputs and gossiping influence the age distribution for low and high ages. It also leads to a scalable numerical evaluation of the performance of mobile update systems, which we validate (using a trace of 500 taxicabs) and use to propose infrastructure deployment.

References

[1]

http://cabspotting.org/.

[2]

E. Altman, P. Nain, and J. Bermond. Distributed storage management of evolving files in delay tolerant ad hoc networks. In Proc. of IEEE INFOCOM, 2009.

[3]

N. Banerjee, M. D. Corner, D. Towsley, and B. N. Levine. Relays, base stations, and meshes: enhancing mobile networks with infrastructure. In Proc. of ACM MobiCom, 2008.

Digital Library

[4]

C. Bordenave, D. McDonald, and A. Proutiere. A particle system in interaction with a rapidly varying environment: Mean field limits and applications. arXiv:math/0701363v2.

[5]

J. Burgess, B. Gallagher, D. Jensen, and B. N. Levine. MaxProp: Routing for Vehicle-Based Disruption Tolerant Networking. In Proceedings of IEEE Infocom 2006, Barcelona, Spain, 2006.

[6]

A. Chaintreau, J.-Y. Le Boudec, and N. Ristanovic. The age of gossip: spatial mean field regime. Technical report LCA-REPORT-2009-003, EPFL, 2009.

[7]

N. Champagnat, R. Ferrière, and S. Méléard. Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theoretical Population Biology, 69:297--321, 2006.

[8]

A. Demers, D. Greene, C. Hauser, W. Irish, J. Larson, S. Shenker, H. Sturgis, D. Swinehart, and D. Terry. Epidemic algorithms for replicated database maintenance. In Proc. of ACM PODC, 1987.

Digital Library

[9]

A. Federgruen and H. Groenevelt. The greedy procedure for resource allocation problems: Necessary and sufficient conditions for optimality. Oper. Res., 34(6):909--918, 1986.

Digital Library

[10]

A. Ganesh, L. Massoulie, and D. Towsley. The effect of network topology on the spread of epidemics. In Proc. of IEEE INFOCOM, 2005.

[11]

IEEE1609.1. IEEE trial-use standard for wireless access in vehicular environments (wave)-- resource manager, 2006.

[12]

S. Ioannidis, A. Chaintreau, and L. Massoulié. Optimal and Scalable Distribution of Content Updates over a Mobile Social Network. In Proc. of IEEE INFOCOM, 2009.

[13]

T. G. Kurtz. Approximation of Population Processes. SIAM, 1981.

[14]

D. McDonald. Lecture Notes on Mean Field Convergence, 2007.

[15]

R. Rudnicki and R. Wieczorek. Fragmentation & coagulation models of phytoplankton. Bull. Pol. Acad. Sci. Math., 54:175--191, 2006.

[16]

E. Seneta. Nonnegative Matrices and Markov Chains. 2nd edition, Springer, 1981.

[17]

A. Vahdat and D. Becker. Epidemic routing for partially-connected ad hoc networks. Technical Report CS-2000-06, UCSD, 2000.

[18]

X. Zhang, G. Neglia, J. Kurose, and D. Towsley. Performance modeling of epidemic routing. Computer Networks, 51(10):2867--2891, 2007.

Digital Library

Cited By

Rashidi LTowsley DMohseni-Kabir AMovaghar A(2023)On the Performance Analysis of Epidemic Routing in Non-Sparse Delay Tolerant NetworksIEEE Transactions on Mobile Computing10.1109/TMC.2022.314468322:7(4134-4149)Online publication date: 1-Jul-2023
https://doi.org/10.1109/TMC.2022.3144683
Rashidi LDalili-Yazdi AEntezari-Maleki RSousa LMovaghar A(2021)Modeling Epidemic Routing: Capturing Frequently Visited Locations While Preserving ScalabilityIEEE Transactions on Vehicular Technology10.1109/TVT.2021.305754170:3(2713-2727)Online publication date: Mar-2021
https://doi.org/10.1109/TVT.2021.3057541
Rizzo GPalma NMarsan MMancuso V(2020)A Walk Down Memory Lane: On Storage Capacity in Opportunistic Content Sharing Systems2020 IEEE 21st International Symposium on "A World of Wireless, Mobile and Multimedia Networks" (WoWMoM)10.1109/WoWMoM49955.2020.00022(50-59)Online publication date: Aug-2020
https://doi.org/10.1109/WoWMoM49955.2020.00022
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Index Terms

The age of gossip: spatial mean field regime
1. Computing methodologies
  1. Modeling and simulation
    1. Model development and analysis
      1. Modeling methodologies
2. Networks
  1. Network types
    1. Mobile networks
    2. Wireless access networks

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Published In

cover image ACM Conferences

SIGMETRICS '09: Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems

June 2009

336 pages

ISBN:9781605585116

DOI:10.1145/1555349

General Chairs:
John Douceur
Microsoft Research, USA
,
Albert Greenberg
Microsoft Research, USA
,
Program Chairs:
Thomas Bonald
Orange Labs, France
,
Jason Nieh
Columbia University, USA

ACM SIGMETRICS Performance Evaluation Review Volume 37, Issue 1
SIGMETRICS '09
June 2009
320 pages
ISSN:0163-5999
DOI:10.1145/2492101
Issue’s Table of Contents

Copyright © 2009 ACM.

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]

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Published: 15 June 2009

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SIGMETRICS09: ACM SIGMETRICS/PERFORMANCE Joint International Conference on Measurement and Modeling of Computer Systems

June 15 - 19, 2009

WA, Seattle, USA

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Overall Acceptance Rate 459 of 2,691 submissions, 17%

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Cited By

Rashidi LTowsley DMohseni-Kabir AMovaghar A(2023)On the Performance Analysis of Epidemic Routing in Non-Sparse Delay Tolerant NetworksIEEE Transactions on Mobile Computing10.1109/TMC.2022.314468322:7(4134-4149)Online publication date: 1-Jul-2023
https://doi.org/10.1109/TMC.2022.3144683
Rashidi LDalili-Yazdi AEntezari-Maleki RSousa LMovaghar A(2021)Modeling Epidemic Routing: Capturing Frequently Visited Locations While Preserving ScalabilityIEEE Transactions on Vehicular Technology10.1109/TVT.2021.305754170:3(2713-2727)Online publication date: Mar-2021
https://doi.org/10.1109/TVT.2021.3057541
Rizzo GPalma NMarsan MMancuso V(2020)A Walk Down Memory Lane: On Storage Capacity in Opportunistic Content Sharing Systems2020 IEEE 21st International Symposium on "A World of Wireless, Mobile and Multimedia Networks" (WoWMoM)10.1109/WoWMoM49955.2020.00022(50-59)Online publication date: Aug-2020
https://doi.org/10.1109/WoWMoM49955.2020.00022
Altman EEl-Azouzi RMenasche DXu Y(2019)Forever YoungProceedings of the Twentieth ACM International Symposium on Mobile Ad Hoc Networking and Computing10.1145/3323679.3326507(91-100)Online publication date: 2-Jul-2019
https://dl.acm.org/doi/10.1145/3323679.3326507
Rashidi LEntezari-Maleki RChatzopoulos DHui PTrivedi KMovaghar A(2019)Performance Evaluation of Epidemic Content Retrieval in DTNs With Restricted MobilityIEEE Transactions on Network and Service Management10.1109/TNSM.2019.290910816:2(701-714)Online publication date: Jun-2019
https://doi.org/10.1109/TNSM.2019.2909108
Rashidi LDalili-Yazdi AEntezari-Maleki RSousa LMovaghar A(2019)Scalable Performance Analysis of Epidemic Routing Considering Skewed Location Visiting Preferences2019 IEEE 27th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS)10.1109/MASCOTS.2019.00029(201-213)Online publication date: Oct-2019
https://doi.org/10.1109/MASCOTS.2019.00029
Hargreaves EMenasche DNeglia G(2019)How Often Should I Access My Online Social Networks?2019 IEEE 27th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS)10.1109/MASCOTS.2019.00028(189-200)Online publication date: Oct-2019
https://doi.org/10.1109/MASCOTS.2019.00028
Francesco D(2019)Delay‐Tolerant NetworksWiley Encyclopedia of Electrical and Electronics Engineering10.1002/047134608X.W8390(1-7)Online publication date: 21-Feb-2019
https://doi.org/10.1002/047134608X.W8390
Cecchi FBorst Svan Leeuwaarden JWhiting P(2018)Spatial Mean-Field Limits for Ultra-Dense Random-Access NetworksACM SIGMETRICS Performance Evaluation Review10.1145/3199524.319954545:3(123-136)Online publication date: 20-Mar-2018
https://dl.acm.org/doi/10.1145/3199524.3199545
Gast N(2017)Expected Values Estimated via Mean-Field Approximation are 1/N-AccurateProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/30844541:1(1-26)Online publication date: 13-Jun-2017
https://dl.acm.org/doi/10.1145/3084454
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