ECS 256 Term Project

• Due Sunday, Dec. 4, 11:59 pm.
• Submit to my handin site on CSIF (NOT the TAs' sites), username matloff, directory 256project.
• In order to be sure to at least get some work submitted before the deadline, it's best that you submit multiple times, as your report becomes more complete. Each submission will overwrite the last.
• A written report, in LaTeX, is required, along with all R code, graphics files (must be generated by R) and so on. You must include both the LaTeX and graphics files that produced your report AND the PDF output file.
• Your LaTeX file must be named ProjectReport.tex, and the corresponding PDF ProjectReport.pdf. The grading script will look for these; don't disappoint the grading script!
• The name of your submitted file must be of the form email1.email2....tar , where each emaili is the UCD e-mail address of group member i, e.g. bclinton.gwbush.bobama.dtrump.tar. Note the periods separating fields. Don't get the address wrong! Otherwise the grading script may not give someone credit.
• Your .tar file must contain only regular files, NO SUBDIRECTORIES!!!!
• And .tar does NOT mean .tar.gz or .tar.bz2 (or for that matter .rar, which one student used once). The grading script will execute

  tar xf youraddresses.tar  # unpack
  ls ProjectReport.tex ProjectReport.pdf  # check for proper files
  xpdf ProjectReport.pdf  # view PDF
  

  Note that the script will NOT do cd.

• Place all your code in a file TermProject.R, as well as in an Appendix to your report (LaTeX \appendix \section{}). I may execute your code, so make sure it is runnable.
• HUGELY IMPORTANT--DON'T FORGET THIS! Include a section in your report with one subsection for each team member. The subsection title should indicate the member's name, e.g. "Participation by Mary Smith," and should be fairly detailed as to what Mary's contribution to the project effort entailed. Don't forget this section!
• Writing must be clear, and up to the standards of the profession: Clear, engaging writing, using correct grammar. Writing need not (and should not) be pretentious, but avoid being too colloquial ("the mean was kinda low"). Presentation need not be fancy, but graphs and tables should be used to illustrate all numerical results. If your team discussed multiple approaches, briefly describe the alternate plans that you chose not to pursue.
• Groups that put in a reasonable amount of time--and thought!-- almost always receive an A or A+ grade on the project. (Individual grades may possibly be affected by the amount each team member contributed, but it is extremely rare for different members of a team to get different Project grades, unlike the Homework situation.) As explained earlier, your Project grade may have a major impact on your course grade, e.g. a B grade becoming A-.

Here we will model a health maintenance organization (HMO) advice system. Nurses field calls from patients, who describe their symptoms. Advice might be to, say monitor the situation for another day, make an appointment with a physician or whatever. Here are the variables (note: probability convention is capital letters for random variables) and parameters (lower-case).

• There is a virtual waiting room, i.e. the queue, accommodating a maximum of m patients. The number currently waiting is K.
• The number of nurses N will vary in time from 0 to n, as follows:

  If upon completion of a phone call, there are 0 patients waiting in the queue, the number of nurses will be reduced by 1 (with a minimum of 0). If a patient arrival occurs at the time the queue is full, either 1 new nurse will be added (with a maximum of n), with probability p, or the call will be terminated, with an apology to the patient.

• Call duration is exponentially distributed with mean μ.
• Intercall arrival time is exponentially distributed with mean ν.

Using parameter values, and especially success criteria, of your choice, investigate the effects of varying the parameters.

Here you will explore the value of using the Method of Stages (MoS) to circumvent the restriction that event times in continuous-time Markov chains must have exponential distributions. The method itself is described in the blog post of Oct. 28, 1625.

The question you will address is simple:

Is the MoS an accurate and feasible approach to the problem of nonexponential distributions in Markov chains?

This problem is highly open-ended. Make sure to stick to this central issue, though: How well does the MoS work for Markov chains? Do not simply investigate the question of whether the MoS is a good approximation to a nonexponential distribution in its own right.