Abstract
A distributed system is scalable if the rate at which it completes its computation and communication tasks does not depend on its size. As an example, the scalability of a peer-to-peer application that transmits data among a large group depends on the topology and the synchronization implemented between the peers. This work describes a model designed to shed light on the conditions that enable scalability. Formally, we model here a collection of tasks, each requiring a random amount of time, which are related by precedence constraints. We assume that the tasks are organized along an euclidean lattice of dimension d. Our main assumption is that the precedence relation between these tasks is invariant by translation along any of these dimensions, so that the evolution of the system follows Uniform Recurrence Equations (UREs). Our main result is that scalability may be shown under two general conditions: (1) a criterion called “sharpness” satisfied by the precedence relation and (2) a condition on the distribution of each task completion time, which only depends on the dimension d. These conditions are shown to be tight. This result offers a universal technique to prove scalability which can be useful to design new systems deployed among an unlimited number of collaborative nodes.
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References
Martin, J.: Large tandem queuing networks with blocking. Queuing Systems, Theory and Applications 41, 45–72 (2002)
Baccelli, F., Chaintreau, A., Liu, Z., Riabov, A.: The one-to-many TCP overlay: A scalable and reliable multicast architecture. In: Proceedings of IEEE INFOCOM, vol. 3, pp. 1629–1640 (2005)
He, J., Chaintreau, A.: BRADO: scalable streaming through reconfigurable trees (extended abstract). In: Proceedings of ACM Sigmetrics, pp. 377–378 (2007)
Chaintreau, A.: Processes of Interaction in Data Networks. PhD thesis, INRIA-ENS (2006), http://www.di.ens.fr/~chaintre/research/AugustinChaintreauPhD.pdf
Jelenkovic, P., Momcilovic, P., Squillante, M.S.: Buffer scalability of wireless networks. In: Proceedings of IEEE INFOCOM, pp. 1–12 (2006)
Xia, C., Liu, Z., Towsley, D., Lelarge, M.: Scalability of fork/join queueing networks with blocking. In: Proceedings of ACM Sigmetrics, pp. 133–144 (2007)
Chen, L., Reddy, K., Agrawal, G.: Gates: A grid-based middleware for processing distributed data streams. In: HPDC 2004. Proceedings of the 13th IEEE International Symposium on High Performance Distributed Computing, pp. 192–201 (2004)
Kingman, J.: Subadditive ergodic theory. Annals of Probability 1(6), 883–909 (1973)
Karp, R.M., Miller, R.E., Winograd, S.: The organization of computations for uniform recurrence equations. J. ACM 14(3), 563–590 (1967)
Gandolfi, A., Kesten, H.: Greedy lattice animals II: linear growth. Annals Appl. Prob. 1(4), 76–107 (1994)
Martin, J.: Linear growth for greedy lattice animals. Stochastic Processes and their Applications 98(1), 43–66 (2002)
Chaintreau, A.: Sharpness: a tight condition for scalability. Technical Report CR-PRL-2008-04-0001, Thomson (2008)
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Chaintreau, A. (2008). Sharpness: A Tight Condition for Scalability. In: Shvartsman, A.A., Felber, P. (eds) Structural Information and Communication Complexity. SIROCCO 2008. Lecture Notes in Computer Science, vol 5058. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69355-0_8
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DOI: https://doi.org/10.1007/978-3-540-69355-0_8
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