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Math Help - Queuing Model

  1. #1
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    Queuing Model

    Hi all,

    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?

    Thanks
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  2. #2
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    Re: Queuing Model

    Hey Tabby.

    Have you tried using two input queues: one for the initial visit and one for a repeat?

    This way you look at the sum of both queues and you can work on a feedback model that is restricted to one of the two queues while leaving the input one as is.
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  3. #3
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    Re: Queuing Model

    I have not tried using two input queues. Would I need a queue for every repeat purchase? Right now I have it so that one column has the interarrival times, the next has the service time and then I have a column that looks up the service time in a probability table that draws a random number of beverages and food items conditioned on the service time (excluding the wait time). So, if I add another queue wouldn't that only capture the situation where a customer gets one more beverage and then leaves? I would l need to make the number of queues a rand variable...no?

    I might be completely misinterpreting what you are saying. I am new to this type modeling. If I am off base, do you know of any literature or the exact term I should google? I am seeing mixed results for multiple queues and some of the white papers seem like a little much for what I am trying to accomplish.

    Like I said in my original post, the results I am getting actually seem pretty good, but I still think model is incorrect. The results using the "infinite" server model are consistent with my naive approach, which was a deterministic non-homogeneous poisson processes with rate parameter varying by time of day and season. I don't have the right data for a standard regression or poisson regression for that matter, so I am still set on trying to model probabilistic properties of the system rather aggregate system output...if that makes sense.

    Thanks again for the help.
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  4. #4
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    Re: Queuing Model

    Try searching for Feedback Queueing Models in google, the literature, and on textbook stores or libraries.
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