How to draw lines to nearest vertices?

[RichThomas2]

I have two input feature layers: 1. Points, 2. Polylines.  I would like to generate a new feature layer of polylines, one for each point, that starts at each point and ends at the closest vertex in the closest polyline. Sounds a lot like the Generate Near Table, right? But that tool draws lines to the edges of the nearest features. I specifically need the lines to coincide with a vertex of the near feature so that I can use them to build a network dataset in Network Analyst. Thanks networkanalyst near# generate near #verticies

[AlfonsoYañez_Morillo]

Why don't you use the same approach but instead of using the polyline layer directly you use a point layer that have been previously obtained from the vertices (Feature Vertices to Points). Then you are forcing to identify the the closest vertex, obtain pair of points and create the lines.