Abstract
In this paper, we revisit the performance of the α-synchronizer in distributed systems with probabilistic message loss as introduced in Függer et al. [Perf. Eval. 93(2015)]. In sharp contrast to the infinite-state Markov chain resp. the exponential-size finite-state upper bound presented in the original paper, we introduce a polynomial-size finite-state Markov chain for a new synchronizer variant \(\alpha ^{\prime }\), which provides a new upper bound on the performance of the α-synchronizer. Both analytic and simulation results show that our new upper bound is strictly better than the existing one. Moreover, we show that a modified version of the \(\alpha ^{\prime }\)-synchronizer provides a lower bound on the performance of the α-synchronizer. By means of elaborate simulation results, we show that our new lower bound is also strictly better than the lower bound presented in the original paper.
References
Awerbuch B (1985) Complexity of network synchronization. J ACM 32(4):804–823
Bertsekas DP, Tsitsiklis JN (1989) Parallel and distributed computation. Prentice Hall, Englewood Cliffs
Bettstetter C, Hartmann C (2005) Connectivity of wireless multihop networks in a shadow fading environment. Wirel Netw 11(5):571–579. https://doi.org/10.1007/s11276-005-3513-x
Cerpa A, Wong JL, Kuang L, Potkonjak M, Estrin D (2005a) Statistical model of lossy links in wireless sensor networks. In: Proceedings of the 4th International Symposium on Information Processing in Sensor Networks, IPSN ’05. IEEE Press, Piscataway. http://dl.acm.org/citation.cfm?id=1147685.1147701
Cerpa A, Wong JL, Potkonjak M, Estrin D (2005b) Temporal properties of low power wireless links: Modeling and implications on multi-hop routing. In: Proceedings of the 6th ACM International Symposium on Mobile Ad Hoc Networking and Computing, MobiHoc ’05, pp. 414–425. ACM, New York. https://doi.org/10.1145/1062689.1062741
Clementi AEF, Pasquale F, Monti A, Silvestri R (2007) Communication in dynamic radio networks. In: Proceedings of the Twenty-sixth Annual ACM Symposium on Principles of Distributed Computing, PODC ’07, pp. 205–214. ACM, New York. https://doi.org/10.1145/1281100.1281131
Clementi AE, Macci C, Monti A, Pasquale F, Silvestri R (2008) Flooding time in edge-markovian dynamic graphs. In: Proceedings of the Twenty-seventh ACM Symposium on Principles of Distributed Computing, PODC ’08, pp. 213–222. ACM, New York. https://doi.org/10.1145/1400751.1400781, USA
Dousse O, Baccelli F, Thiran P (2005) Impact of interferences on connectivity in ad hoc networks. IEEE/ACM Trans Netw 13(2):425–436. https://doi.org/10.1109/TNET.2005.845546
Függer M, Kößler A, Nowak T, Schmid U, Zeiner M (2015) The effect of forgetting on the performance of a synchronizer. Perform Eval 93, 1–16. https://doi.org/10.1016/j.peva.2015.08.002. http://www.sciencedirect.com/science/article/pii/S0166531615000826
Fussen M, Wattenhofer R, Zollinger A (2005) Interference arises at the receiver. In: 2005 international conference on Wireless networks, communications and mobile computing, vol. 1, pp. 427–432. https://doi.org/10.1109/WIRLES.2005.1549447
Gupta P, Kumar PR (2000) The capacity of wireless networks. IEEE Trans Inf Theory 46(2):388–404. https://doi.org/10.1109/18.825799
Moscibroda T, Wattenhofer R (2006) The complexity of connectivity in wireless networks. In: Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications, pp. 1–13. https://doi.org/10.1109/INFOCOM.2006.23
Nowak T, Függer M, Kößler A (2013) On the performance of a retransmission-based synchronizer. Theor Comput Sci 509, 25–39
Propp JG, Wilson DB (1996) Exact sampling with coupled markov chains and applications to statistical mechanics. Random Struct Algorithm 9(1-2):223–252
Rajsbaum S (1994a) Upper and lower bounds for stochastic marked graphs. Inf Process Lett 49(6):291–295
Rajsbaum S, Sidi M (1994b) On the performance of synchronized programs in distributed networks with random processing times and transmission delays. IEEE Trans Parallel Distrib Syst 5(9):939–950
Schilcher U, Bettstetter C, Brandner G (2012) Temporal correlation of interference in wireless networks with rayleigh block fading. IEEE Trans Mob Comput 11(12):2109–2120
Schilcher U, Toumpis S, Haenggi M, Crismani A, Brandner G, Bettstetter C (2016) Interference functionals in poisson networks. IEEE Trans Inf Theory 62 (1):370–383. https://doi.org/10.1109/TIT.2015.2501799
Ware C, Judge J, Chicharo J, Dutkiewicz E (2000) Unfairness and capture behaviour in 802.11 adhoc networks. In: 2000 IEEE International conference on communications. ICC 2000. Global convergence through communications
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Zeiner, M., Schmid, U. Upper and Lower Bounds for the Synchronizer Performance in Systems with Probabilistic Message Loss. Methodol Comput Appl Probab 23, 1023–1056 (2021). https://doi.org/10.1007/s11009-020-09792-z
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DOI: https://doi.org/10.1007/s11009-020-09792-z
Keywords
- Distributed systems
- Synchronizer
- Performance analysis
- Probabilistic message loss
- Markov chain
Mathematics Subject Classification (2010)
- 60J20
- 60J10
- 68Q87
- 68W15