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Queuing Theory

The price of tickets varies depending on the seat location in the Stadium. These seats are color-coded on a diagram so that the single cashier can show purchasers the diagram, have them decide on their seat, and pay for their ticket. The cashier can complete a transaction (selling a ticket) in 2 minutes. 4 Ticket purchasers arrive at the single cashier booth every 10 minutes. Arrivals follow a Poisson distribution while service time follows an exponential distribution.


  1. What is the Utilization rate of the ticket sale process? (3 marks)

         

  1. Determine the average number of persons in the line. (3 marks)

  2. How long does it take from the time a person joins the line to when they get their ticket? (3 marks)


  1. What is the average time a person spends in the line? (3 marks)


  1. What is the probability that there is no line? (3 marks)

  2. What is the probability that there is 1 person at the cashier and 2 persons waiting in line? (4 marks)


  1. If the color-coded diagram is placed on the walls leading up to the cashier, persons can decide their seating preference before they get to the cashier and the transaction time is cut in half. How many minutes would be saved for persons in the line?  (6 marks)

Decision-Science   Queuing-Theory   
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