I have a polyline and a point layer. The polyline layer contains different roads. The point layer contains points along these roads with random distances between the points. The points are also listed randomly and not in order along these roads.

I want to connect with polylines the points along the roads which are close each other at a maximum (e.g. 35.0 m) or smaller distance.

The roads turn even to 180o at some points (as shown in the attached figure) and the distance between the roads can be smaller than 35.0 m.

My ultimate purpose is to get the road segments where the points are distant in maximum 35m.

Any suggestion how to work these out?

I use ArcGIS 10.4.1 for Desktop