Consider an $M/M/c$ loss system (called station 1) with arrival rate $\lambda$, where customers who find all channels busy (and are lost) are served at a secondary infinite channel facility (called station 2). Customers who are served at station $1$ leave the system and do not go to station 2. Service times at both stations follow some arbitrary distribution with service rate $\mu$.
Let $N_i$ be the number of customers at station $i$ in steady state $i = 1, 2$. Compute $E(N_{2})$
I need help with this queue theory problem. I tried many things like finding first the joint distribution $P(N_1 = m, N_2 = n) = p_{mn}$ where $m = 0, 1, \ldots, c$ and n = 0, 1, ... with not much luck.
I also tried to do this and find balance equations for $p_{mn}$ but again could not find much luck.
Maybe someone can please assist me. My book does not have many examples and I want to understand this problem. Thanks