I am trying to model the crowding behavior of solid objects trying passing through a small opening (like a door) using Queuing theory. I can assume that the objects are arriving at the door according to a Poisson process with arrival rate $\lambda$, and the objects are "processed" at the door at a deterministic rate $\mu$ making this a simple $M/D/1$ queuing model. However, in this current model, no matter how crowded the entrance of the door is, the service rate remains constant. Unfortunately, this does not model the inability of the objects to inter-penetrate (if too many people try to get through a door, no-one gets through).
Is there a model in queuing theory, where the service rate is affected by how long the queue is? Any references, or leads will be deeply appreciated.