Deterministic Contention Resolution without Collision Detection: Throughput vs Energy

Abstract

This paper studies the Contention resolution problem on a shared channel (also known as a multiple access channel). A set of $n$ stations are connected to a common device and are able to communicate by transmitting and listening. Each station may have a message to broadcast. At any round, a transmission is successful if and only if exactly one station is transmitting at that round. Simultaneous transmissions interfere one another and, as a result, the respective messages are lost. The Contention resolution is the fundamental problem of scheduling the transmissions into rounds in such a way that any station delivers successfully its message on the channel. We consider a general dynamic distributed setting. We assume that the stations can join (or be activated on) the channel at arbitrary times (dynamic scenario). This has to be contrasted with the simplified static scenario, in which all stations are assumed to be activated simultaneously. We also assume that the stations are not able to detect whether a collision among simultaneous transmissions occurred (model without collision detection). Finally, there is no global clock in the system: each station measures the time using its own local clock which starts when the station is activated and is possibly out of sync with respect to the other stations. We study non-adaptive deterministic distributed algorithms for the contention resolution problem and assess their efficiency both in terms of channel utilization (also called throughput) and energy consumption. While this topic has been quite extensively examined for randomized algorithms, this is, to the best of our knowledge, the first paper to discuss to which extent deterministic contention resolution algorithms can be efficient in terms of both channel utilization and energy consumption. Our results imply an exponential separation gap between static and dynamic setting with respect to channel utilization. We also show that the knowledge of the number of participating stations k (or an upper bound on it) has a substantial impact on the energy consumption.