Reinforcement at detailed battle

[jugasa77]

Hello, I am playing CoGEE v1.0.0.
When playing a battle only one unit came as reinforcement although there are more units forced away from battles.
Why don't came more units as reinforcement?
How does reinforcement works?

[jugasa77]

As in Quick Combat, reinforcements may be called into battle, but may
also arrive due to battle limits. One or two units will arrive together at the
same random place in the movement sequence, at the edge of the map.
The remainder will arrive in a similar manner, at a somewhat random
rate, until all have arrived or the battle ends. The number of turns before
reinforcements arrive is shown at the top of the screen.

CoGEE manual, page 136.

When do reinforcement arrives?
Do it depends of iniatiative of the unit?