1. Assuming a Poisson arrival distribution and an exponential service time distribution, apply queueing models to the case situation and evaluate the results. Is this a single-server model or a multiple-server model?

Bourbon County Court "Why dont they buy another copying machine for this office? I waste a lot of valuable time fooling with this machine when I could be preparing my legal cases," noted Mr. H.C. Morris, as he waited in line. The self-service copying machine was located in a small room immediately outside the entrance of the courtroom. Mr. Morris was the county attorney. He often copied his own papers, as did other lawyers, to keep his legal cases and work confidential. This protected the privacy of his clients as well as his professional and personal ideas about the cases. He also felt awkward at times standing in line with secretaries, clerks of the court, other attorneys, police officers and sheriffs, building permit inspectors, and the dog wardenall trying, he thought, to see what he was copying. The line for the copying machine often extended out into the hallways of the courthouse. Mr. Morris mentioned his frustration with the copying machine problem to Judge Hamlet and his summer intern, Dot Gifford. Ms. Gifford was home for the summer and working toward a joint MBA/JD degree from a leading university. "Mr. Morris, there are ways to find out if that one copying machine is adequate to handle the demand. If you can get the Judge to let me analyze the situation, I think I can help out. We had a similar problem at the law school with word processors and at the business school with student lab microcomputers." The next week Judge Hamlet gave Dot the go-ahead to work on the copying machine problem. He asked her to write a management report on the problem with recommendations so he could take it to the Bourbon County Board of Supervisors for their approval. The board faced deficit spending last fiscal year, so the tradeoffs between service and cost must be clearly presented to the board. Dot's experience with analyzing similar problems at school helped her know what type of information and data was needed. After several weeks of working on this project, she developed the information contained in Exhibits 11.36, 11.37 and 11.38. other case exhibits. Direct wages do include employee benefits but not work opportunity costs or ill-will costs, etc. Dot was not quite as confident in evaluating this situation as others because the customer mix and associated labor costs seemed more uncertain in the county courthouse. In the law school situation, only secretaries used the word processing terminals; in the business school situation, students were the ones complaining about long waiting times to get on a microcomputer terminal. Moreover, the professor guiding these two past school projects had suggested using queueing models for one project and simulation for the other project. Dot was never clear on how the method of analysis was chosen. Now, she wondered which methodology she should use for the Bourbon County Court situation