I have a multiserver queuing model set up in Excel to simulate a restaurant, but I am not sure if a M/M/k model is correct. The restaurant I am trying to model is a brewbup where, once served, individuals spend time in the system and may even come back to the server for another beverage. I am unsure how to model their time in the system with this consideration. I tired increasing the service time to reflect the purchase and extra time an individual stays in the system, but with service time so much longer than arrival rate I get extremely long. Obviously I can increase the number of serves and I start getting results more consistent with what I would expect, but I am not sure how to interpret this. Do the extra servers represent the extra trips an individual makes back to the bar for another drink?
If there isn't an explanation for the extra server approach, are there good probability models for the situation I described above? Thats is, is there a way to model the extra time after the first service an individual stays in the system without causing huge large wait times?