Is there any literature for queuing analysis (waiting time, capacity etc.) of a queue with service time that depends on the position of the customer in the queue?
I have encountered a problem where a bit at position j of the queue has a service time related to $\Gamma(j,\lambda)$ and despite it being a simple model there seems to be no easy method like Pollaczek–Khinchine formula for such a regime.
I really have no clue how to analyze this system and any help would be appreciated.
