# Markov Process:Poisson Queue with exponential services

A single-server queue has Poisson arrivals at finite rate $\lambda > 0$ and exponential services at finite rate $\mu > 0$. When there are $n$ customers in the system an arrival joins the queue with probability $\frac{1}{(n+1)}$ and decides not to join with probability $\frac{n}{(n+1)}$. Let $X_t$ be the number of customers in the system at time $t$.
What are the transition rates for the Markov process $(X_t)$.