I may have found a solution to my own question, but I am not sure:
v.kernel -v input=MY_LOCATIONS net=MY_NETWORK output=MY_OUTPUT stddeviation=57.735 distmax=1 mult=200 kernel=uniform
The parameters and values in bold are important. Where do they come from? The kernel surrounding each dot has the uniform distribution with a range of 100 m at both sides of the dot location. Hence, the 'range' (b - a) of the uniform distribution is 200 m. The standard deviation of a uniform distribution 1 / (b - a) is (b - a) / sqrt(12), hence the standard deviation parameter is 200 / sqrt(12) = 57.735 (reference)
Because the height of the uniform distribution is 1/200, I multiply the result with 200 (hence parameter mult=200).
Eventually, I get line segments having values indicating the number of dots over a length of 100 m.
The result seems to be correct, but I am not sure.
Well, I'm not so sure that my use of the module is correct after all. Overall, the kernel density estimate increases on segments where more dots occurs, as it should be. But there are some contradictory results that I cannot explain. Below is a screenshot, showing the network (thin dashed line), the locations on the network (red dots) and the kernel density estimate result having a value of 5 or more (thick purple lines). I don't understand the result for the two regions indicated in orange. Less than 3 dots over a span of 100 m should never have a kernel of more than 3 (yet, it is 5 in my result). Also, a segment with about 8 dots over just over 100 m should have a kernel density estimate of at least 5, but it is less in my output (hence, no thick purple line). Can anybody explain this? Am I using the GRASS module correctly?
The module v.kernel has changed in GRASS 7.2.2. Here is an update of how I would use the module now:
g.region res=1 n=%YMAX% s=%YMIN% e=%XMAX% w=%XMIN%
v.in.ogr dsn=./network.shp output=V_NETWORK --overwrite --quiet
v.in.ogr dsn=./events.shp output=V_EVENTS --overwrite --quiet
v.kernel --overwrite --verbose input=%input% net=%net% net_output=%net_output% radius=%radius% dsize=%dsize% segmax=%segmax% distmax=%distmax% multiplier=%multiplier% node=%node% kernel=%kernel%
v.out.ogr -sce input=V_KERNEL_OUTPUT dsn=. olayer=v_kernel format=ESRI_Shapefile type=line --overwrite --quiet
g.remove -f type=vector name=V_KERNEL_OUTPUT --quiet