Abstract
This paper presents and proves correct two self-stabilizing deterministic algorithms solving the mutual exclusion and the group mutual exclusion problems in the model of population protocols with covering. In this variant of the population protocol model, a local fairness is used and bounded state anonymous mobile agents interact in pairs according to constraints expressed in terms of their cover times. The cover time is an indicator of the “time” for an agent to communicate with all the other agents. This indicator is expressed in the number of the pairwise communications (events) and is unknown to agents. In the model, we also assume the existence of a particular agent, the base station. In contrast with the other agents, it has a memory size proportional to the number of agents. We prove that without this kind of assumption, the mutual exclusion problem has no solution.
The algorithms in the paper use a phase clock tool. This is a synchronization tool that was recently proposed in the model we use. For our needs, we extend the functionality of this tool to support also phases with unbounded (but finite) duration. This extension seems to be useful also in the future works.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
The Dartmouth wireless trace archive - Dartmouth College (2007), http://crawdad.cs.dartmouth.edu/
Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. DC 18(4), 235–253 (2006)
Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. TAAS 3(4) (2008)
Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: A time-optimal selfstabilizing synchronizer using a phase clock. IEEE TDSC 4(3), 180–190 (2007)
Awerbuch, B., Varghese, G.: Distributed program checking: a paradigm for building self-stabilizing distributed protocols (extended abstract). In: FOCS, pp. 258–267 (1991)
Beauquier, J., Burman, J.: Self-Stabilizing Synchronization in Mobile Sensor Networks with Covering. In: Rajaraman, R., Moscibroda, T., Dunkels, A., Scaglione, A. (eds.) DCOSS 2010. LNCS, vol. 6131, pp. 362–378. Springer, Heidelberg (2010)
Beauquier, J., Burman, J.: Self-stabilizing mutual exclusion and group mutual exclusion for population protocols with covering (extended version). Technical Report inria-00625838, INRIA (2011), http://hal.inria.fr/inria-00625838/en/
Beauquier, J., Burman, J., Clement, J., Kutten, S.: On utilizing speed in networks of mobile agents. In: PODC, pp. 305–314 (2010)
Beauquier, J., Burman, J., Kutten, S.: A self-stabilizing transformer for population protocols with covering. Theor. Comput. Sci. 412(33), 4247–4259 (2011)
Beauquier, J., Clement, J., Messika, S., Rosaz, L., Rozoy, B.: Self-Stabilizing Counting in Mobile Sensor Networks with a Base Station. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 63–76. Springer, Heidelberg (2007)
Cai, H., Eun, D.Y.: Crossing over the bounded domain: from exponential to power-law inter-meeting time in MANET. In: MOBICOM, pp. 159–170 (2007)
Canepa, D., Gradinariu Potop-Butucaru, M.: Self-stabilizing tiny interaction protocols. In: WRAS, pp. 10:1–10:6 (2010)
Couvreur, J.-M., Francez, N., Gouda, M.G.: Asynchronous unison (extended abstract). In: ICDCS, pp. 486–493 (1992)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. of the ACM 17(11), 643–644 (1974)
Dolev, S.: Self-Stabilization. The MIT Press (2000)
Dwork, C., Lynch, N.A., Stockmeyer, L.J.: Consensus in the presence of partial synchrony. J. ACM 35(2), 288–323 (1988)
Fischer, M., Jiang, H.: Self-Stabilizing Leader Election in Networks of Finite-State Anonymous Agents. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 395–409. Springer, Heidelberg (2006)
Hadzilacos, V.: A note on group mutual exclusion. In: PODC, pp. 100–106 (2001)
Herman, T.: Adaptivity through Distributed Convergence (Ph.D. Thesis). University of Texas at Austin (1991)
Hong, S., Rhee, I., Joon Kim, S., Lee, K., Chong, S.: Routing performance analysis of human-driven delay tolerant networks using the truncated levy walk model. In: MobilityModels, pp. 25–32 (2008)
Peterson, J.L., Silberschatz, A.: Operating system concepts. Addison-Wesley (1985)
Joung, Y.-J.: Asynchronous group mutual exclusion. Distributed Computing 13(4), 189–206 (2000)
Karagiannis, T., Le Boudec, J., Vojnovic, M.: Power law and exponential decay of inter contact times between mobile devices. In: MOBICOM, pp. 183–194 (2007)
McNett, M., Voelker, G.M.: Access and mobility of wireless PDA users, vol. 9, pp. 40–55 (2005)
Rhee, I., Shin, M., Hong, S., Lee, K., Chong, S.: On the levy-walk nature of human mobility. In: INFOCOM, pp. 924–932 (2008)
Tel, G.: Introduction to Distributed Algorithms, 2nd edn. Cambridge University Press (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Beauquier, J., Burman, J. (2011). Self-stabilizing Mutual Exclusion and Group Mutual Exclusion for Population Protocols with Covering. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-25873-2_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25872-5
Online ISBN: 978-3-642-25873-2
eBook Packages: Computer ScienceComputer Science (R0)