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spikkelvissie

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I am look for a mathematical queuing model that can help with/solve the following scenario. I believe this scenario can me modeled in a dynamic simulation, but I am in need of a solution for a static model.

Scenario:

You are at a port. There is a steady, equally distributed arrival rate of incoming boats. A single queue of boats form in front of a channel. The channel is narrow and therefore the boats cannot pass each other in the channel. Inside the port are 2 berth with a constant service rate. The boats in the queue can only proceed to a berth if the channel is open and a berth is available. The boats that have been serviced at the berth has to return back through that same channel. If an incoming boat and outgoing boat wants to use the channel at the same time, the outgoing boat gets priority. There are no queues inside the port at the berths or at the channel going outward.

In summary: There is only 1 queue, outside the port at the channel, the queue time depends on the availability of the channel, the availability of the berth, the service time at the berth, etc.

Is there a queuing model that describes this scenario?

All of the network models I have looked at assumes the outflow uses a different channel than the inflow and that there are queues inside the port as well.

Please advise. Thank you.