MS&E 121

Introduction to Stochastic Modeling

| General Info | Contact Info | Announcements | Course Outline | Course Materials | Handouts | Assignments | Links |

---

Links

Operations Research Related Links

• The Institute for Operations Research and Management Science
• Chain Reaction, an article about Professor Hau Lee's work in supply chain management in The Economist.

General Interest Links

• A biography of Markov himself.
• Euro coin accused of unfair flipping!
• A review of the book "Lies, Damned Lies, and Statistics: Untangling Numbers from the Media, Politicains, and Activists", by Lynn Arthur Steen. Notices of the American Mathematical Society, February 2003.
• Buffon's Needle Example: This model is one of the earliest examples of probability modeling, and was studied in the 1700's.

Probability and Stochastic Processes Links

• Rice University Virtual Statistics Lab has applets that demonstrate many statistical concepts.
• Virtual Laboratories in Probability and Statistics contains interactive resources such as applets, data sets, graphics, biographies, etc.
• Central Limit Theorem: The CLT is probably the most fundamental result in probability and statistics (hence, the designation "central limit theorem"!)

1. See http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html for an illustration of the CLT via Galton's machine.

2. Play with the parameters underlying the CLT at http://www.stat.sc.edu/~west/applets/binomialdemo2.html

• Confidence Intervals: The notion of a confidence interval is a key idea in frequentist statistics. Please visit http://www.ruf.rice.edu/~lane/stat_sim/conf_interval/index.html and http://www.ruf.rice.edu/~lane/stat_sim/normal_approx_conf/index.html for a refresher on the statistical interpretation of a confidence interval, and various caveats associated with their use.
• Brownian Motion: Brownian Motion is one of the most important and widely used stochastic processes. Please visit http://www.ms.uky.edu/~mai/java/stat/brmo.html for a simulation of 2 and 1 dimensional Brownian Motion. Brownian Motion has sample paths that are self-similar. Please visit http://www.stat.umn.edu/~charlie/Stoch/brown.html to see an illustration of this by zooming into a brownian sample path.
• Convergence of Empirical Distribution: Please visit http://www.ms.uky.edu/~mai/java/stat/EmpDis.html for a graphical simulation illustrating how the empirical distribution converges to the actual distribution from which the observations are sampled.

Applications of Markov Processes, Queueing Theory and Simulation

• Queueing models: Please visit

1. http://keskus.hut.fi/~esa/java/queue/I/ for a simulation of a single server queue.

2. http://keskus.hut.fi/~esa/java/queue/II/ for a toy program that lets you build a queueing network and simulate its behavior.

• Epidemic Dynamics: A simulation of how an epidemic spreads across a population is available at http://www.stat.sc.edu/~west/javahtml/epid.html. The underlying model is (apparently) a "box model": an interacting particle system in which the population is divided in groups, and the likelihood of contact between any two individuals depends on whether they belong to the same group or not. In this particular example infected individuals are never removed from the population. For a survey on the modeling of epidemics see for example http://www.ma.hw.ac.uk/epi/skye97/heterog.ps.
• Modeling Customer Relationships as Markov Chains by Phillip E. Pfeifer and Robert L. Carraway
• Student flow in a university department: results of a Markov analysis
• A Markovian Model for the Valuation of Human Assets Acquired by an Organizational Purchase
• Queueing theory applied to data processing networks
• Staffing a centralized appointment scheduling department in Lourdes Hospital
• Allocating telecommunications resources at L. L. Bean, Inc.
• Improving the New York City arrest-to-arraignment system
• Reducing waiting time at security checkpoints

---

| Management Science & Engineering Dept | Stanford University |