Solution
= Solution
The nonzero off-diagonal rates are
$$
(c,r,b)\to(c+1,r,b):\lambda,
\quad(c,r,b)\to(c-1,r+1,b):\mu c,
$$
$$
(c,r,b)\to(c,r-1,b+1):\mu r,
\quad(c,r,b)\to(c,r,b-1):\mu b,
$$
with a transition involving a negative coordinate omitted. These represent arrival, the two metamorphoses, and death. The diagonal generator entry is consequently \b[$-(\lambda+\mu(c+r+b))$], so the holding rate is $\lambda+\mu n$.