Maximum throughput of multiple access channels in adversarial environments

Abstract

We consider deterministic distributed broadcasting on multiple access channels in the framework of adversarial queuing. Packets are injected dynamically by an adversary that is constrained by the injection rate and the number of packets that may be injected simultaneously; the latter we call burstiness. A protocol is stable when the number of packets in queues at the stations stays bounded. The maximum injection rate that a protocol can handle in a stable manner is called the throughput of the protocol. We consider adversaries of injection rate 1, that is, of one packet per round, to address the question if the maximum throughput 1 can be achieved, and if so then with what quality of service. We develop a protocol that achieves throughput 1 for any number of stations against leaky-bucket adversaries.The results of this paper appeared in a preliminary form in 'Stability of multiple access channels under maximum broadcast loads' in The protocol has O(n 2 + burstiness) packets queued simultaneously at any time, where n is the number of stations; this upper bound is proved to be best possible. A protocol is called fair when each packet is eventually broadcast. We show that no protocol can be both stable and fair for a system of at least two stations against leaky-bucket adversaries. We study in detail small systems of exactly two and three stations against window adversaries to exhibit differences in quality of broadcast among classes of protocols. A protocol is said to have fair latency if the waiting time of packets is O(burstiness). For two stations, we show that fair latency can be achieved by a full sensing protocol, while there is no stable acknowledgment based protocol. For three stations, we show that fair latency can be achieved by a general protocol, while no full sensing protocol can be stable. Finally, we show that protocols that either are fair or do not have the queue sizes affect the order of transmissions cannot be stable in systems of at least four stations against window adversaries.

Dynamic multiple-message broadcast

“…We evaluate the ratio of the performance of a distributed online algorithm ALG against an optimal algorithm OPT. For one hop networks it is known [10] that no protocol is both stable (i.e., bounded number of packets in the system at any time) and fair (i.e., every packet is eventually delivered). For multihop networks the same result holds as a natural extension of the single hop model.…”

“…Define a Move-big-to-front (MBTF) list [10] of source nodes, initially in any order. According to this list, source nodes circulate a token.…”

“…Chlebus et al [10] gave various deterministic and randomized algorithms for group communication, all of them being only a small polylogarithm away of the corresponding lower bounds on time complexity.…”

“…Anantharamu et al [3] studied packet latency of deterministic dynamic broadcast protocols for arrival rates smaller than 1. Stability, understood as bounded queues, of dynamic deterministic broadcast on multiple access channels against adversaries bounded by arrival rate 1 was studied by Chlebus et al [10], and for arrival rates smaller than 1 by Chlebus et al [11]. In particular, in [10] a protocol Move-big-to-front (MBTF) was designed, achieving stability but not fairness (as both these properties are impossible to achieve simultaneously); we use this algorithm as a subroutine in our dynamic Multiple-Message Broadcast protocol.…”

The Distributed Wireless Gathering Problem

“…Each internal state stipulates whether the pending packet is to be transmitted towards the sink in the current round. Our other assumption is that the protocol is acknowledgment-based [9]. This means that the state of every node depends only on: (1) the number of nodes in the network; (2) the identity of the node; (3) the number of rounds elapsed since the currently processed packet became the first in the FIFO buffer at the node.…”