I have a markov chain from https://ieeexplore.ieee.org/document/9766097 as follows
The state transition matrix is as below
The analysis pertains to packet drop rate for ONE device with certain arrival($\lambda$) and transmission success probability($\mu_1$) where $\bar\lambda$ stands for no arrivals ($1-\lambda$) and $\bar\mu_1$ pertains to transmission failure probability ($1-\mu_1$).
The drop rate for ONE device is given by $\pi_d\bar\mu_1$ where $\pi_d$ is the steady state probability for the markov chain with delay bound $d$ (after which a packet will be dropped) in state $d$
I need to calculate the combined drop rate for N devices which are identical and symmetrical (i.e. have the same probability for successful transmission). What is the correct approach to extend this analysis for N devices? May be it is trivial, but I am missing the point.
I think you mean expected drop rate (since actual drop rate is stochastic).
Let $D_i$ be the drop rate of device $i$. You are asking about the following quantity:
$$E\left[ \sum_{i=1}^N D_i \right]$$
Where we are assuming the $D_i$ are iid.
You pointed out that $E[D_i] = \pi_d\bar \mu_1$ therefore, by linearity of expectation, we should expect $N\pi_d\bar \mu_1$ combined drop rate.
The steady state distribution of combined drop rate would be the discrete convolution of $N$ copies of $\pi_d$