I am working on two queues in tandem; the first queue is M/G/1 with hyper-exponential service times and the second queue has exponential service times. I want to know if the second queue can be modeled as an M/M/1 queue, or equivalently, the departure process of the first queue has Poisson distribution.
I have run simulations for two tandem queues and noticed that the simulation results for total delay match the sum of the analytical values for delays in M/G/1 and M/M/1 queues. I want to know if there is a good reference to show that the departure process of M/G/1 queue with hyper-exponential service times has Poisson distribution.