Theory Comput Syst (2017) 61:820–850
Adversarial Multiple Access Channels with Individual
· Bogdan S. Chlebus
Mariusz A. Rokicki
Published online: 28 November 2016
© Springer Science+Business Media New York 2016
Abstract We study deterministic distributed broadcasting in synchronous multiple-
access channels. Packets are injected into n nodes by a window-type adversary that
is constrained by a window w and injection rates individually assigned to all nodes.
We investigate what queue size and packet latency can be achieved with the maxi-
mum aggregate injection rate of one packet per round, depending on properties of
channels and algorithms. We give a non-adaptive algorithm for channels with col-
lision detection and an adaptive algorithm for channels without collision detection
(min(n + w, w log n)) packet latency. We show that packet latency
has to be either (w max(1, log
n)),whenw ≤ n,or(w + n),whenw>n,
as a matching lower bound to these algorithms. We develop a non-adaptive algo-
rithm for channels without collision detection that achieves
(n + w) queue size and
(nw) packet latency. This is in contrast with the adversarial model of global injec-
tion rates, in which non-adaptive algorithms with bounded packet latency do not exist
The results of this paper were presented in a preliminary form in .
The work of the first author was supported by NSF Grant 1016847.
The work of the second author was supported in part by NSF Grants 0310503 and 1016847,
and by the Engineering and Physical Sciences Research Council under [grant number
The work of the third author was partly done when he was with the University of Colorado Denver,
and it was supported by NSF Grant 0310503 and by the Engineering and Physical Sciences Research
Council under [grant number EP/G023018/1].
Bogdan S. Chlebus
Department of Computer Science and Engineering, University of Colorado Denver, Denver,
Colorado 80217, USA
Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK