You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Neighbor discovery is the procedure in which two wireless devices initiate a first contact. In low power ad-hoc networks, radios are duty-cycled and the latency until a packet meets a reception phase of another device is determined by a random process. Most research considers slotted protocols, in which the points in time for reception are temporally coupled to beacon transmissions. In contrast, many recent protocols, such as ANT ANT+ and Bluetooth Low Energy (BLE) use a slotless, periodic-interval based scheme for neighbor discovery. Here, one device periodically broadcasts packets, whereas the other device periodically listens to the channel. Both periods are independent from each other and drawn over continuous time. Such protocols provide 3 degrees of freedom (viz., the intervals for advertising and scanning and the duration of each scan phase). Though billions of existing BLE devices rely on these protocols, neither their expected latencies nor beneficial configurations with good latency-duty-cycle relations are known. Parametrizations for the participating devices are usually determined based on a “good guess”. In this paper, we, for the first time, present a mathematical theory which can compute the neighbor discovery latencies for all possible parametrizations. Further, our theory shows that upper bounds on the latency can be guaranteed for all parametrizations, except for a finite number of singularities. Therefore, slotless, periodic interval-based protocols can be used in applications with deterministic latency demands, which have been reserved for slotted protocols until now. Our proposed theory can be used for analyzing the neighbor discovery latencies, for tweaking protocol parameters and for developing new protocols.

Cited Abstract(s):
[1]: Vehicles today employ many different sensors to provide information such as tire pressure, proximity to objects and so on to Electronic Control Units for state maintenance and actuation functions. This has resulted in an increase in the number, weight and complexity of wiring as well as wiring harness for in-vehicle communication networks. Reducing the amount of cables will improve fuel efficiency; reduce cost of manufacturing and maintenance of vehicles greatly. Bluetooth Low Energy (BLE) is a great candidate for cable replacement given its supported data rates and widespread adoption in many markets. BLE device discovery is required to establish the presence of nodes within each other's communication range and begin reliable exchange of data. In our system, the nodes are the sensors and actuators. The fundamental problem in such device discovery is that energy consumption and discovery latency are inversely related. Therefore an efficient trade-off BLE connection setup that reduces energy-consumption while being able to provide worst-case discovery latency guarantees is critical especially in the automotive industry. We propose a mechanism that exploits Chinese Remainder Theorem (CRT) to provide worst-case latency guarantees during the connection setup phase of BLE devices. We provide the required modifications in BLE as well as provide evaluation results to show the improved performance. To the best of our knowledge this is the first work that considers providing bounded-latency connection setup for BLE devices using CRT and its application for automotive cable replacement.
Usually, PI-based protocols are considered to be non-deterministic, since no upper bound could be determined until now. To overcome the lack of determinism, it has been proposed to configure the BLE protocol such that the parameter values fulfill the CRT [1] . However, such configurations restrict the range of possible valuations unnecessarily. In summary, to the best of our knowledge, no valid model for PI-based protocols for the general case ( @math ) has been presented until now.