The university library has to decide on the most optimal configuration for the student copy machines. Student demand for making copies peak during the evening 6pm-12 midnight hours and the library wants to minimize the wait times for the students while not investing more than necessary in the copy machines. The options for the service configurations are as follows:
1) Use a single copy machine that can make a maximum of 300 copies per hour. Due to the variability in the size and nature of the jobs, an average job is completed anywhere between 1 minute to 10 minutes (assume a uniform distribution).
2) Use two copy machines each of which can make a maximum of 100 copies per hour. Since these are slower machines compared to that in #1, the service times follow a uniform distribution between 3 minutes and 20 minutes. The options for the queue configurations are either to have a single queue (for either of the above two options) or have two dedicated queues (for option #2). The time between arrivals of students to the copy machine system is approximately one student every 4 minutes. Assume this inter-arrival time follows an exponential distribution.
Looking at the options, make the following decisions:
1) Can either configuration sustain the arrival rates of the students? Give reasons.
2) Which configuration seems to be the better option to adopt? Why?
3) Would your decision on the above change and how if the following happens:
- The inter-arrival time changes to a triangular distribution between 1 minute and 6 minutes with the most likely time being 2 minutes?
- The service times change to exponential distributions (mean time of 5 minutes with the single machine option #1 and 10 minutes with the two-machine option #2)
4) For all analysis, use appropriate models and solution approached to determine your answers.
Write a short executive report on the above decisions and findings, and provide all the calculations, models and analysis in the appendices. Submit any supplemental files that you may have used for answering the question.