1. (2 points) Read Chapter #29.8 (Continuous-time Markov Chain) of the attached, and write a one-page summary report. The summary report should be prepared on a word processor. Be concise in your writing and consult technical writing references as needed. The body of the summary report has to include the sections outlined as follows: (a) Summary of the Chapters’ main points and (b) Your opinion of the Chapter including the most important information you learned.
2. (Hillier & Lieberman’s OR textbook Problem #29.8-1 (10th edition) or #16.8-2 (9th edition) Reconsider the example presented at the end of Sec. 29.8 (please find the attached). Suppose now that a third machine, identical to the first two, has been added to the shop. The one maintenance person still must maintain all the machines. (a) Develop the rate diagram for this Markov chain (1 point). (b) Construct the steady-state equations and solve these equations for the steady-state probabilities (1 point).
3. (Modification of Hillier & Lieberman’s OR textbook Problem #16.8-3 (9th edition) or #29.8-2 (10th edition)) The state of a particular continuous time Markov chain is defined as the number of jobs currently at a certain work center, where a maximum of four jobs are allowed. Jobs arrive individually. Whenever fewer than four jobs are present, the time until the next arrival has an exponential distribution with a mean of ½ day. Jobs are processed at the work center one at a time and then leave immediately. Processing times have an exponential distribution with a mean of ¼ day. (a) Construct the rate diagram for this Markov chain (1 point). (b) Determine the steady-state probabilities (1 point).