Neighbor discovery latency in BLE-like duty-cycled protocols

Neighbor discovery is the procedure using 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.