A real life system that faces and solves the dining philosophers problem
The dining philosopher's problem is a worst case scenario used to illustrate issues in algorithms. It's a test case. You probably won't find a static one-to-one mapping between it and a real world case.

However, similar situations can occur dynamically. If at any point the graph of actors waiting for resources forms a cycle, you are stuck in a deadlock. Most of the time this happens with n = 2 actors, but sometimes you can get more complicated deadlocks.