Consider a single serve queue with exponential service time with parameter µ and Poisson arrivals…

Consider a single serve queue with exponential service time with parameter µ and Poisson arrivals with rate λ. New customers are sensitive to the length of the queue in the sense that a newly arriving customer that finds i other customers in the system will join the queue with probability pi = (i + 1)−1, whereas with probability 1 − pi it departs and does not return. Find the stationary probability distribution of this QS.