• Homework 1 -- Probability Review -- Due Sept 8
  • For problem 2.2: you should think of T as the response time for an arbitrary job; S as the size of that job; and Slow as the slowdown of that job. You are looking for E[Slow] = E[T/S] for this arbitrary job. Clearly the job's response time and its size are *not* independent. However there are other quantities that *are* independent for the job.
  • For problem 3.67 : First make sure that you've read the undergraduate probability text and understand how to solve P{Both boys | At least one boy}. That's the approach you should be thinking about, but now with more categories.
• Homework 2 -- Convergence, z-transforms, Operational Laws -- Due Sept 15
  • You are free to skip writing up ONE problem of your choosing. You *MUST* indicate clearly on your homework WHICH problem you are choosing to skip and not have graded. If you do not indicate the problem, we will assume that you're skipping the last problem and will not grade that one.
• Homework 3 -- More Operational Laws -- Due Sept 22
• Homework 4 -- DTMCs -- Due Sept 29
• Homework 5 -- Ergodicity -- Due Oct 6
  • Note: There are only 7 problems here, and you get to skip one, so only 6 this time.
  • If you want more practice, you can try 9.9 and/or 25.10 in your textbook.
  • For problem 10.7 part f : You'll find that after you simplify the partial fraction decomposition, one of the terms will end up being 0. This will make your answer a lot nicer!
• Homework 6 -- Exponentials and Poisson Process -- Due WEDNESDAY Oct 11, at start of class
  • Exercise 11.11 has two added parts.
• Homework 7 -- from M/M/1 to M/M/k -- Due Oct 27, at start of class
• Homework 8 -- M/M/k, Burke, and Jackson -- Due Nov 3, at start of class
• Homework 9 -- Classed Jackson and General Distributions -- Due Nov 10, at start of class
• Homework 10 -- M/G/1 and Renewal-Reward -- Due Nov 17, at start of class
  • When doing Renewal-Reward problems, please clearly specify the relevant parameters, such as: how you're defining the renewal cycle, what is the rate at which reward is being earned, what is the total reward in each cycle, etc.
• Homework 11 -- M/G/1 and Busy Periods -- Due Wednesday Nov 29, at start of class
  • No late minutes on this homework -- solutions going out in Wednesday's class.
  • I apologize: We're not getting to Chpt 30 in time for this homework. Please move Exercise 30.5 to HW 12. You can still skip one problem of your choice on HW 11.
  • Exercise 27.1: Assume that E[S] = 1/mu, i.e. mu and E[S] are reciprocals.
  • Exercise 27.3: It helps to follow the same process that we used in class for deriving the Laplace transform of a busy period, where we first derive the Laplace transform of B(x) and then use that to derive the Laplace transform of B. This time, however, you are deriving the Laplace transform of B_{short}(x) and B_{short}, where the "short" indicates that only short jobs are allowed.
  • Exercise 26.5: Remember that you're using Distributional Little's Law as defined in class. This is the one that relates N_Q(z) to A_{T_Q}(z) to T_Q(s). See my lecture on Chpt 27!
  • Exercise 26.11 -- Go back and look at Exercise 25.7 and use that interpretation. This is only a few lines of argument (no math).
• Homework 12 -- Scheduling -- Due Wednesday Dec 6, at start of class
  • Exercise 30.3: HINT: Think about the CTMC for the M/M/1 with different scheduling policies.

Class Topics/Relevant Papers