Abstract
We investigate deterministic broadcasting on multiple-access channels in the framework of adversarial queuing. A protocol is stable when the number of packets stays bounded, and it is fair when each packet is eventually broadcast. We address the question if stability and fairness can be achieved against the maximum injection rate of one packet per round. We study three natural classes of protocols: acknowledgment based, full sensing and fully adaptive. We show that no adaptive protocol can be both stable and fair for the system of at least two stations against leaky-bucket adversaries, while this is achievable against window adversaries. We study in detail small systems of exactly two and three stations attached to the channel. For two stations, we show that bounded latency can be achieved by a full-sensing protocol, while there is no stable acknowledgment-based protocol. For three stations, we show that bounded latency can be achieved by an adaptive protocol, while there is no stable full-sensing protocol. We develop an adaptive protocol that is stable for any number of stations against leaky-bucket adversaries. The protocol has \({\mathcal O}(n^2)\) packets queued simultaneously, which is proved to be best possible as an upper bound. We show that protocols that do not use queue sizes at stations in an effective way or are greedy by having stations with nonempty queues withhold the channel cannot be stable in systems of at least four stations.
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References
Abramson, N.: Development of the Alohanet. IEEE Transactions on Information Theory 31, 119–123 (1985)
Aiello, W., Kushilevitz, E., Ostrovsky, R., Rosén, A.: Adaptive packet routing for bursty adersarial traffic. Journal of Computer and System Sciences 60, 482–509 (2000)
Alvarez, C., Blesa, M., Serna, M.: A characterization of universal stability in the adversarial queuing model. SIAM Journal on Computing 34, 41–66 (2004)
Andrews, M., Awerbuch, B., Fernández, A., Leighton, T., Liu, Z., Kleinberg, J.: Universal-stability results and performance bounds for greedy contention-resolution protocols. Journal of the ACM 48, 39–69 (2001)
Bender, M.A., Farach-Colton, M., He, S., Kuszmaul, B.C., Leiserson, C.E.: Adversarial contention resolution for simple channels. In: SPAA. Proceedings, 17th ACM Symposium on Parallel Algorithms, pp. 325–332 (2005)
Bhattacharjee, R., Goel, A., Lotker, Z.: Instability of FIFO at arbitrary low rates in the adversarial queuing model. SIAM Journal on Computing 34, 318–332 (2004)
Borodin, A., Kleinberg, J.M., Raghavan, P., Sudan, M., Williamson, D.P.: Adversarial queuing theory. Journal of the ACM 48, 13–38 (2001)
Chlebus, B.S., Kowalski, D.R., Rokicki, M.A.: Adversarial queuing on the multiple-access channel. In: PODC. Proceedings, 25th ACM Symposium on Principles of Distributed Computing, pp. 92–101 (2006)
Gallager, R.G.: A perspective on multiaccess channels. IEEE Transactions on Information Theory 31, 124–142 (1985)
Gamarnik, D.: Stability of adaptive and nonadaptive packet routing policies in adversarial queueing networks. SIAM Journal on Computing 32, 371–385 (2003)
Goldberg, L.A., Jerrum, M., Kannan, S., Paterson, M.: A bound on the capacity of backoff and acknowledgement-based protocols. SIAM Journal on Computing 33, 313–331 (2004)
Goldberg, L.A., MacKenzie, P., Paterson, M., Srinivasan, A.: Contention resolution with constant expected delay. Journal of the ACM 47, 1048–1096 (2000)
Hastad, J., Leighton, T., Rogoff, B.: Analysis of backoff protocols for multiple access channels. SIAM Journal on Computing 25, 740–774 (1996)
Koukopoulos, D., Mavronicolas, M., Nikoletseas, S.E., Spirakis, P.G.: The impact of network structure on the stability of greedy protocols. Theory of Computing Systems 38, 425–460 (2005)
Lotker, Z., Patt-Shamir, B., Rosén, A.: New stability results for adversarial queuing. SIAM Journal on Computing 33, 286–303 (2004)
Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)
Metcalfe, R.M., Boggs, D.R.: Ethernet: distributed packet switching for local computer networks. Communications of the ACM 19, 395–404 (1976)
Raghavan, P., Upfal, E.: Stochastic contention resolution with short delays. SIAM Journal on Computing 28, 709–719 (1998)
Rosén, A.: A note on models for non-probabilistic analysis of packet switching networks. Information Processing Letters 84, 237–240 (2002)
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Chlebus, B.S., Kowalski, D.R., Rokicki, M.A. (2007). Stability of the Multiple-Access Channel Under Maximum Broadcast Loads. In: Masuzawa, T., Tixeuil, S. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2007. Lecture Notes in Computer Science, vol 4838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76627-8_12
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DOI: https://doi.org/10.1007/978-3-540-76627-8_12
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