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I have a model where three conveyors merge from individual sources. All three sources release entities at an inter-arrival rate of 4.5 s. At the merge there is a server which has a processing time of 1 s and a 0 buffer capacity. In the image below I have two models with the exact same properties, the only difference is the conveyor speed. The top model has a conveyor speed of 0.5 m/s and a queue forms reaching a length of infinity as time passes. The bottom model has a conveyor speed of 2 m/s and a queue never forms. Why is it that a queue forms in the top model? Can someone please explain? It does not make sense to me why such a long queue forms. Please explain using queuing theory or mathematics, or Simio logic if necessary.

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