- instructions contains step by step directions for getting started with Matlab.
- Download this zip file of all programs mentioned on this page
- showmatrix.m displays a matrix, no matter how wide it is. It can be edited to change the number of decimal places shown.
- graph_matrix.m produces a graphical display of a transition matrix. Output
- invariant.m finds an invariant distribution corresponding to a transition matrix.
- transientvisits.m computes the
expected number of visits to transient states.

- gambler.m sets up and displays the transition matrix for Gambler's wealth. Output
- gambler_dist.m computes the distribution of Gambler's wealth after n hands. Output
- gambler_length.m computes the distribution of the length of the game. Output
- gambler_visits.m displays the expected number of visits to transient states matrix W, the expected length of the game, and the probability of hitting matrix U. Output
- gambling.m generates one outcome of Gambler's wealth, with an algorithm specifically designed for this problem.
- gambling_outcomes.m generates
several outcomes of Gambler's wealth.

- rando.m generates a random variable in {1, 2, ..., n} given a distribution vector.
- chain.m simulates a Markov chain on {1, 2, ..., n} given an initial distribution and a transition matrix. It uses rando.m. It is a good idea to use a different .m file to set up mu and P, then run chain.m or manychains.m
- manychains.m generates multiple simulations using chain.m. Output
- generalchain.m simulates a Markov chain with a general state space given an initial distribution and a transition matrix. Output
- manygeneralchains.m generates
multiple simulations using generalchain.m.

- queue.m sets up matrices for a simple discrete
queueing model.
It uses graph_matrix.m, found above.
Output

- component.m sets up matrices to model the age of a component with possible replacement
- replacement_policies.m uses component.m to compare possible replacement policies
- component_examples.m sets up three examples of life length distributions and computes the optimal scheduled replacement times.
Output

- poisson.m simulates a Poisson process.
- manypoisson.m generates many outcomes of the Poisson process using poisson.m. Output
- poisson_probs.m displays the probability distribution of the Poisson process as a function of time. Output
- poisson_arrivals.m simulates the arrival times of a homogeneous Poisson process.
- manypoisson.m generates many outcomes of the Poisson process using poisson_arrivals.m.
- bid.m simulates Poisson arrivals of iid bids for an item.
- bid_display.m displays the arrivals and values of bids.
- bid_return.m calculates the expected return on a bidding strategy.

- process.m simulates a general Markov process on {1, 2, ... n} given an initial distribution, sojourn parameters, and a transition matrix.
- manyprocesses.m generates multiple simulations using process.m. Output for process_ex_1.m
- distribution.m computes and graphs the distribution of a Markov process over time Output for process_ex_1.m
- process_ex_1.m sets up parameters for a three-state Markov process.
- process_ex_2.m determines the parameters lambda and Q for a Markov chain, which can then be used to determine a Markov process.
- process_ex_bd.m sets up parameters for a simple birth/death process.
- repair.m sets up matrices for a model of
the number of machines working and the number in repair.
Output

- yule.m simulates the Yule process (a pure birth process)
- manyyule.m generates many outcomes of the Yule process using yule.m. Output
- process_ex_yule.m sets up parameters for a Yule process