New models usually take 2 years to make it from sign off to production.
During nearly all of that time the previous model stays in production (in fact the last facelift is normally two years from end of production.
For the first 12-15 months the new models are developed in off-line pilot areas. Some of the cars you see in the "prototype photos" will be these cars. Often they have soft tooled parts and may even have temporary parts used from older cars. As this time line progress the need to not only develop the car, but start working out how to make it begins. Test production runs of the cars may start as early as 9 months out, but will only be a handful of cars that later will be used for testing and eventually destroyed. At around 3-4 months out, final production test may take place of up to 50 cars (built in series with current production if it is possible). This allows refinement of the processes and of course training of the operators. Finally, end of production takes place of the current model takes place and the model begins. Depending on the extent of the change, this defines the "gap" between the two.
Working in manufacturing for nearly 20 years, I have seen gaps as big as 9 months (Ford Escort to Jaguar X-Type at Halewood) where the whole factory was refitted, and gaps as small as 10 cars (minor facelift on the Carina E in the UK). I have yet to see series production of old and new models together (I honestly think the logistics around parts makes this near impossible), but i know some specialist assemblers like Valmet may do this. I have seen 7 different models on the same line though.
For a model launch the distributors in Europe normally like about 10,000 cars available for high volume models, which as the volume production does need some ramp up, might take 3-4 months. Allowing for 0-1 month change over, old models normally stop 4 months before the market release of new models (helps clear old stock and creates demand). When I worked for Mercedes on W204, Bremen and Sindelfingen were still knocking W203 flat way after W204 was announced and shown.
There is no way the factory can be idled for long (0-1month) and the market can't stand the loss of sales due to no production for long either. What you might find is that new orders are stopped (maybe 2 months before E.O.P) to allow stable parts ordering and a clean "build out". This is often the time you see the Special Models. NOT to use up old parts (as my dad told me) as most parts are made to order only days before the car is assembled, but to allow the manufacturer to control the specs. You can't order exact;y what you wanted but you can have "free options" instead. The W203 Sport Edition specification was a good example.
Hope this helps.
As I said 20 years in cars inducing Mercedes - if any wants to light my blue touch paper.