As stated in Lamport's papers for the bakery algorithm he states that the ticket numbers are unbounded specifically
The range of values of number is unbounded.
and
Fortunately, practical considerations will place an upper bound on the value of number[i] in any real application. For example, if processors enter the doorway at the rate of at most one per msec, then after a year of operation we will have number[i] < $2^{35}$—assuming that a read of number[i] can never obtain a value larger than one which has been written there.
What I don't understand is, why does Taubenfeld's Black-White Bakery Algorithm solves this problem and thus considered bounded.
I see no reason why the usage of the extra color register would solve such a problem?
Thanks
