Avoid connection of points when there is empty data - gnuplot

Question

I am trying make a line chart using Gnuplot. I need to get something like the following but with an exception:
In the example above you can see a straight line which joins two separate points over empty data. It is the one that crosses the '2016-09-27 00:00:00' x tick. I would like there would be a empty space instead of that straight line. How could I achieve this?
This is the current code:
set xdata time
set terminal pngcairo enhanced font "arial,10" fontscale 1.0 size 900, 350
set output filename
set key off
set timefmt '"%Y-%m-%d %H:%M:%S"'
set format x "%Y-%m-%d %H:%M"
set xtics rotate by -80
set mxtics 10
set datafile missing "-"
set style line 1 lt 2 lc rgb 'blue' lw 1
set style line 2 lt 2 lc rgb 'green' lw 1
set style line 3 lt 2 lc rgb 'red' lw 1
plot\
fuente using 1:2 ls 1 with lines,\
fuente using 1:3 ls 2 with lines,\
fuente using 1:4 ls 3 with lines

Answer 1

Three options:
In the data file, put an empty line where the gap is. This results in exactly what you want, but would also affect the other data from that file.
Use every to only plot a portion of the data and plot it twice, once up to the gap, once from the gap. Suppose that the gap occurs between data points 42 and 43 in your case, then you could use:
plot\
fuente using 1:2 ls 1 every ::::41 with lines,\
fuente using 1:2 ls 1 every ::42 with lines,\
fuente using 1:3 ls 2 with lines,\
fuente using 1:4 ls 3 with lines
(The every statement takes up to six arguments separated by colons but you can leave them empty for default values. The fifth argument is the end point, the third is the starting point.)
If you use - for missing data in your file (as indicated by your set datafile missing "-"), you have modify your using statement for this to be effective:
plot\
fuente using 1:($2) ls 1 with lines,\
fuente using 1:3 ls 2 with lines,\
fuente using 1:4 ls 3 with lines

Answer 2

Of course, you can always change your data and e.g. insert empty lines (as #Wrzlprmft suggested) when data is missing which will interrupt your line.
With large datasets and a lot of "breaks" this would be painful if you have to do it manually.
I would say that there is a solution without changing your data.
Let me ask: "What do you consider as missing data?"
My assumption would be: you have e.g. a data logger which takes values every 10 minutes.
If for some reason the logger did not take some data there will be a "gap" of missing data.
Now, you can define what you consider as a gap, e.g. >1 hour of no data would be a gap.
Hence, you simply compare two consecutive values t0 and t1 and if the difference is larger then your gap you change the line color from whatever color to transparent (according to the scheme 0xaarrggbb). Check help linecolor variable and help colorspec.
Script:
### don't show line in missing data gaps
reset session
myFmt = "%Y-%m-%d %H:%M"
# create some random test data
set print $Data
tStart = "2016-09-27"
tEnd = "2016-10-10"
t0 = strptime(myFmt,tStart)
t1 = strptime(myFmt,tEnd)
y0 = 100
do for [t=t0:t0+(t1-t0)*0.2:600] { print sprintf("%s %g",strftime(myFmt,t),y0=y0+(rand(0)-0.5)) }
do for [t=t0+(t1-t0)*0.3:t0+(t1-t0)*0.5:600] { print sprintf("%s %g",strftime(myFmt,t),y0=y0+(rand(0)-0.5)) }
do for [t=t0+(t1-t0)*0.8:t0+(t1-t0):600] { print sprintf("%s %g",strftime(myFmt,t),y0=y0+(rand(0)-0.5)) }
set print
set format x "%d.%m." timedate
gap = 3600 # 1 hour
myColor(tCol,color) = (t0=t1, t1=timecolumn(tCol,myFmt), t1-t0>gap ? 0xff123456 : color)
set multiplot layout 2,1
plot $Data u (timecolumn(1,myFmt)):3 w l lc rgb 0xff0000 ti "data as is"
plot t1=NaN $Data u (timecolumn(1,myFmt)):3:(myColor(1,0x0000ff)) w l lc rgb var ti "with removed gaps"
unset multiplot
### end of script
Result: