On the Design of an Intelligent Speed Advisory System for Cyclists

Traffic-related pollution is becoming a major societal problem globally. Cyclists are particularly exposed to this form of pollution due to their proximity to vehicles' tailpipes. In a number of recent studies, it is been shown that exposure to this form of pollution eventually outweighs the cardio-vascular benefits associated with cycling. Hence during cycling there are conflicting effects that affect the cyclist. On the one hand, cycling effort gives rise to health benefits, whereas exposure to pollution clearly does not. Mathematically speaking, these conflicting effects give rise to convex utility functions that describe the health threats accrued to cyclists. More particularly, and roughly speaking, for a given level of background pollution, there is an optimal length of journey time that minimises the health risks to a cyclist. In this paper, we consider a group of cyclists that share a common route. This may be recreational cyclists, or cyclists that travel together from an origin to destination. Given this context, we ask the following question. What is the common speed at which the cyclists should travel, so that the overall health risks can be minimised? We formulate this as an optimisation problem with consensus constraints. More specifically, we design an intelligent speed advisory system that recommends a common speed to a group of cyclists taking into account different levels of fitness of the cycling group, or different levels of electric assist in the case that some or all cyclists use e-bikes (electric bikes). To do this, we extend a recently derived consensus result to the case of quasi-convex utility functions. Simulation studies in different scenarios demonstrate the efficacy of our proposed system.