1916 military Lugers

[berkmberk1]

By 1916, mid-way thru the war, DWM was cranking out pistols by the thousands. Were they still selling any on contract or commercially? Along with that question, I ask - If many or most (or all) production was going to the military, why are only some of the pistols unit marked. I was wondering as my 1916 DWM army model is sans any markings outside of the SN. Were some side arms assigned/permanently issued to individual officers (i.e field grade who always get the perks) and therefore not stamped with a unit marking? Perhaps a pistol like this never actually made it OUT of the supply chain........???