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A student works evenings in the WU library to assist patrons with the eight scan

ID: 328466 • Letter: A

Question

A student works evenings in the WU library to assist patrons with the eight scanners on the main floor after the full-time staff has left. Most of the job is to answer questions and help new scanner users get started and understand how the scans will be saved. On average, the student gets four requests per hour according to a Poisson distribution. Most of the issues are simple, but the student will stay with the patron while they scan a few pages and feel comfortable with the equipment and process. On average, the student will spend six minutes on each patron request (exponential distribution), but an older faculty member may take a lot more time. The job does not pay well, but the student understands that the trade-off is that they have some idle time to study. The administration is concerned that there is too much idle time and wants to re-evaluate this process. How would you analyze this system?

In OM Explorer, which waiting line model would we select to solve this problem?

Note: Please note the time unit you are using. You must use the same time unit for each question.

What would you enter for the arrival rate (as used in the mathematical models or the templates we used in class)?

  

What would you enter for the service rate (as used in the mathematical models or the templates we used in class)?

  

Explanation / Answer

Since there is one server, the model is M/M/1. But note that the system capacity is restricted to 8 (number of scanners). So, the appropriate model will be the M/M/1 with Finite System Size.

Arrival Rate = lambda = 4 per hour

Service rate = mu = 1 person in 6 minutes = 10 per hour