Question 3

The Learn-a-Lot educational theme park is about to open the great ghoul horror castle tour ride. The plan is for this new ride to re-energise this education focussed attraction. The ride runs on a conveyer belt system (moving seats akin to a monorail) using the latest curvilinear drag-free enhanced people movement technology. The ride has a ghost theme that attempts to incorporate a little history of castles and local customs prevailing in medieval Europe.

With much funds invested, Learn-a-Lots management wish to ensure positive customer (school groups) perceptions about this new ride. Although queuing for the ride is not desired, it can be seen as positive because this waiting time builds suspense among the children enhanced by viewing earlier participants faces (some stark, some excited, some pale, but all full of emotional expression) as they leave the ride via the exit door. Based on previous experience with school groups, management do not wish them to wait more than eight minutes before starting the ride.

Learn-a-Lots management have asked you to provide information about expected waiting times for the first month. They have provided you with assumptions based on the best available data forecasts.

1. Pre-arranged school groups (20 persons or less) may enter the ride at any time. Groups are served (starting the ride) following ticketed entry through a turnstile at a single operator booth. Once served, groups are taken to the start area, debriefed on safety, and loaded on a railed carriage. The service time is complete when all group participants have left the ride through the exit door.
2. The ride takes five minutes.
3. Groups arrive at a rate of nine per hour following a Poisson distribution.

Tasks: (Total 100 marks)

1. Calculate the mean numbers and mean times of groups in the system and in the queue. (20 marks)
2. Calculate the probability of a group proceeding straight to the ride without first queuing and the probability that a group will have to wait in a queue upon arrival to the ride. (10 marks)
3. The line space provided for queues is 10 metres per group. Management wish to ensure an adequate line-up space for 70% of the times that a new group arrives. How long should the line

space be to achieve this outcome? (20 marks)

4. Write a 200 word (maximum) summary layperson description of the system characteristics including any assumptions made. This will be used to inform Learn-a-Lots management.

(20 marks)

5. Make and justify recommendations for changes (if required) to improve the service system

including any assumptions required. (30 marks)