The Disney Imagineering Group has just designed a new attraction, and they have asked for your expert industrial engineering opinions. This ride is a simulator where the guest is a Jedi making first contact with Asgard. If a guest is staying in a resort on the property, they get to play through an extra part of the simulator and meet Professor X. Because it is interactive, the ride time for a customer ends up being exponential with a rate μ1 = 7 per hour for regular guests, and a rate of μ2 = 4 per hour for guests who stay on property. Approximately 30% of all guests stay on property. Based on its location, only three people can wait in line to ride, and only one person can ride it at a time. The Imagineers expect that the interarrival time between any two guests to be exponential with an average of 20 minutes. Required:
a. Create a model for this system. Be sure to include how you define your state space, the list of events that can occur, the transition rate diagram, and the transition rate matrix.
b. Numerically solve for the steady state probabilities.
c. What is the expected number of guests who are in the system?
d. How long on average do guests who decide to wait spend at this attraction before leaving?
e. Disney would like to hire some actors to entertain those that are waiting in line for this attrac- tion. They estimate that it will cost approximately $75 per hour waiting in line for each guest in line on average for this entertainment. What is the expected cost per hour in the long-run?