Question

*PLEASE ANSWER LETTERS A-F THOROUGHLY*

The Twelve-stars Amusement Park

The Twelve-stars traveling amusement park has recently set up operation in the East Bay. The arrival rate of patrons at the park is estimated as 35 per hour. There is one admissions gate, staffed by a single worker. Admissions can be conducted at an estimated rate of 40 per hour. 40% of patrons go directly to the Ferris wheel, while 30% go to the rollercoaster. The remaining 30% go to the zombie house. The service rate of the Ferris wheel is 18 patrons per hour, while the service rate of the roller coaster is 15 patrons per hour. The service rate of the zombie house is 16 patrons per hour. All of the patrons leaving the Ferris wheel go to the house of mirrors. In addition, 40% of patrons leaving the roller coaster go to the house of mirrors. The house of mirrors serves patrons one at a time at a rate of 25 per hour. All patrons leaving the house of mirrors as well as remaining patrons leaving the rollercoaster all go to the exit gate. In addition, all patrons leaving the zombie house go directly to the exit gate. There is one worker at the exit gate, who can process exiting patrons at a rate of 38 per hour. It is desired to determine for this amusement park, the expected number of patrons waiting at the admission gate, exit gate, and at each ride. It is also desired to determine the expected time patrons spend waiting at each of these locations. If an additional worker was available, at which "station" (i.e., entry gate, exit gate, or ride) should this worker be placed?

The dept. of public safety for Alameda County would like to know what the average number of patrons is expected to be in the park over the course of a day in order to determine whether this meets with safety code and fire Marshall regulations. Current regulations do not allow for more than 40 patrons in the park at any one time. What would you report for this? (i.e., is the requirement met?) (Note that you can treat each station as a single server system!!!!!) Make sure to show your calculations and report your results regarding park operations.

A) Write a short summary of the case, including the purpose of your analysis. B) Show and explain the model you used to evaluate the amusement park system.

C) Show any calculations you used to obtain your results. (Hint: for each gate and ride you will need l, lq, and wq.)

D) Display a summary of results.

E) Answer any questions posed with the case in addition to the summary of results. (i.e., at what ride would you place an additional worker, and are park limitations on patrons being met?)

F) Write a brief conclusion and recommendations. A few sentences will suffice.

Answer 1

Solve this problem by applying the singel server model. In single server model the applicable formulas are as follows:

Using these find the l, lq, and wq

We can see the required values and formulas. We can also see that the total customers in the park is less than 40. This means that there is no need of adding a server.