I have an M/M/1 queueing system in which customers arrives at rate $\lambda$ and are served at rate $\mu$, but, upon entry, each customer can be randomly dropped with probability $1-p$ or enter the queue with probability $p$, indipendently from queue state or any other system variable.
How can I find the probability that, in a time interval of length $T$, no packets are being dropped?