If you have ArcGIS 10.2, you can try the new Optimized Hot Spot Analysis tool. To constrain your analysis to the road network you can:
1) Create a buffer around the road network and use this as your Bounding Polygon when you run Optimized Hot Spot Analysis (you might have to experiment a bit with different buffer widths).
2) Run Optimized Hot Spot Analysis on your accident point data and use the buffer polygon for the parameter called: Bounding Polygons Where the Incidents Are Possible. This will aggregate the events into fishnet polygons along the road network. It will automatically identify an appropriate scale of analysis and will apply an FDR correct to results.
Keep in mind that this answers the question: where are there lots of accidents. It does not take into account differences in the density of the road network or traffic volumes.
There are no doubt many ways to analyze your data; I hope this suggestion is helpful.
Best wishes!
Lauren
Lauren M. Scott, PhD
Esri
Geoprocessing, Spatial Statistics