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Real life queue - how to model?

  1. Apr 24, 2015 #1
    People queuing to pick up photos at an event. They have a bar-coded docket. By scanning the docket, printing is initiated on one of eight printers. Each printer takes 40 seconds to print a photo - the software chooses the least heavily loaded print queue - or uses a round-robin approach if print jobs are zero. Working together the printers can produced a print, on average, every 5 seconds.

    Scenario A
    Each printer has a bar-code reader. Person walks up to one of eight "print stations" and scans their docket. 40 seconds later they have their print. So this is not spreading the load via software, this is much like a shop queue with people going to the next available print station.

    Scenario B
    People enter a "walking maze" - a zigzag line estimated to take 40 seconds to walk through. The dockets are scanned at the entry to the maze. At least initially, when the person arrives at the printer line, their print will be ready for them. This gives the illusion of no wait time - they just happen to be walking while waiting.

    Criteria: A constantly moving line is "better" than a line which requires people to stop and wait. This is more a people perception thing.

    What models can I use to compare these scenarios? The number of printers can vary - so I can use this to increase the flow rate. I'd like to be able to see under what conditions scenario B would result in a stopped line of people. If someone can point me to the sources of information I need, that would be greatly appreciated.

    I'm a queuing theory newbie but I learn fast...
  2. jcsd
  3. Apr 24, 2015 #2
    I'm, not sure what the question is.
    Some things just happen if the circumstances make it likely.
    I don't know of a theory which requires things to stand in a line on order for the truth to be known.
    I'm quite left leaning but not that bad,
  4. Apr 27, 2015 #3

    Stephen Tashi

    User Avatar
    Science Advisor

    If you want a theoretical approach, you can begin by picking the appropriate Kendall notations for you scenarios:

    If you can write computer programs, I'd suggest using computer simulations to analyze the problem.
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