Igor,
Yes the map is always unbalanced for someone (Yellow or White). What's the problem with that? It's 100% impossible to balance it evenly for both players as I have shown. This is well known in all turn based games (Risk, Axis and Allies, Chess etc) that involve moving men.
Also as I explained having all production come at the end of all players turns leads to the problem that Yellow gets an advantage because he doesn't have to defend his cities because he gets instant production.
My solution was that players should bid for turn order so that it's not random and so that moving first has a cost in the amount of gold you bid. Also I pointed out that map makers should put more space between cities so that newly produced armies can't immediately attack and must spent a turn moving which allows the other player time to equalize his production. Go back to the W----N-----------N----Y example again with both sides starting with 2 armies but the space between the 2 N cities requiring more than 1 turn of movement. On turn 1 White captures his neutral and starts production in both cities. Yellow captures his neutral and starts production in both cities. On turn 2 White has 4 armies to Yellows 2 but he can't reach any Yellow cities so must spend a turn between the neutral cities. On Yellows turn he reaches 4 armies and can defend his neutral city with 4 armies. On turn 3 White has 4 armies that can reach Yellows city with 4 armies and he also has 2 new armies but they can't reach anything. In this well designed map there is no advantage of going first because there is space between the cities.
If you want pure balance then wait for the next update and play simultaneous move games. Those are 100% equal which is why they were so popular in DLR.
KGB