TY - GEN
T1 - Stability of the multiple-access channel under maximum broadcast loads
AU - Chlebus, Bogdan S.
AU - Kowalski, Dariusz R.
AU - Rokicki, Mariusz A.
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2007
Y1 - 2007
N2 - 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 Ο(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.
AB - 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 Ο(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.
KW - Adversarial queuing
KW - Deterministic broadcast
KW - Fairness
KW - Latency
KW - Multiple-access channel
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=38349010901&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38349010901&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-76627-8_12
DO - 10.1007/978-3-540-76627-8_12
M3 - Conference contribution
AN - SCOPUS:38349010901
SN - 9783540766261
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 124
EP - 138
BT - Stabilization, Safety, and Security of Distributed Systems - 9th International Symposium, SSS 2007, Proceedings
PB - Springer Verlag
T2 - 9th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2007
Y2 - 14 November 2007 through 16 November 2007
ER -