M&Ms Homework Session I 2009

Prof Scott Smith's lectures on Modeling
Due Weds Sept 30th in class

  1. Write a few scintillating paragraphs on the trade-offs of precision and elegance in modeling as discussed in class.
  2. Draw a Petri Net diagram for dining philosophers with two philosophers, each picking up their two forks simultaneously when they want to eat. (Note this problem should be easy since there is a link below with the picture and simulation for four philosophers, and we already did this two philosophers diagram in class). Argue informally why this Petri net can continually do transitions, i.e. it will never deadlock.
  3. Draw a Petri net for two philosophers dining, modeling the case where each philosopher first picks up their left fork and then picks up ther right fork. Describe one state (tokens in certain places) where this Petri net is in a deadlock and the philosophers are going to starve to death. Is there any way these two philosophers eat and think for a long time but still avoid starvation? If there is, describe the Petri Net transition sequence illustrating this.

  4. a) Warm-up: write down the rules for playing the dining philosophers game as we did in class
    b) Recall we remarked that one way dining philosophers applies to computers is viewing each program (e.g. Skype / iChat) as a philosopher and each fork as a shared resource (e.g. Video camera / microphone). Point out good and bad points on using dining philosophers to model how different computer programs compete for resources, in terms of our elegance vs precision tradeoff of models.
    c) Now do the same but for the Petri net modeling of the dining philosophers game as we played it in class: what properties did the Petri net abstraction catch the essence of, and what properties did it miss?
To help you with Petri Nets, feel free to look at the following: If you have any questions email me or stop by my office in NEB 214.

Note: some of these problems may be hard. Just give them a good shot. If you spent three hours on this homework thats enough.