customer service problem

#1
N customers circulate in a closed system with two servers. In Server 1 and Server 2, service times are exponential with parameters µ1 and µ2, respectively. Let state K denotes that there are k customers in Stage 1(thus N-k customers in stage 2). I'd like to determine P(K), which is the probability of K happening. My clue is to model it using death-birth process, but I can't figure out what’s the birth rate and death rate. I'd appreciate any help.