Say there are two queues (1 and 2) in series.
The latency will be $t_1 + t_2$ without overlapping of their service times ($t_1$ and $t_2$ respectively).
If there is a overlapping, the latency will be $t_1 + t_2 - T_o$ where $T_o$ is the overlapped time. (Specifically $T_o = \min(t_1,t_2)$ in my case)
To my best understanding, queueing model is not suitable for modeling the overlapped service times. However, there would be some works for extension cause this overlapping is very common behavior, I believe.
How can I model overlapping service times in queueing model?