MS&E 121 |
Introduction to Stochastic Modeling |
| General Info | Contact Info|
Announcements | CourseOutline
| Course Materials | Handouts
| Assignments| Links |
1. Introduction and Review Discussion of stochastic modeling Review of basic probability, with applications 2. Computer Experimentation The role of computer experimentation Random number generation The law of large numbers The central limit theorem Applications to computer simulation Confidence intervals 3. Forecasting and Regression Models Basic forecasting ideas Prediction in the presence of historical data (applications to economics and finance) Linear regression Regression in the presence of nonlinear trends Autoregressive time series models 4. Discrete-time Markov Chains Categorical time series The Markov property Transition matrix and transition graph Computing the n-step Transition Probabilities Simulation of Markov chains Applications to bond ratings, card shuffling, molecular dynamics, queueing, inventory, etc First-step analysis and the gambler's ruin problem Steady-state analysis Steady-state simulation Estimating transition probabilities from historical data Pricing American options 5. Continuous-time Markov chains Modeling reliability via the failure-rate function The memorylessness property of the exponential distribution Other essential properties of the exponential distribution Simulation of models specified by exponential distributions Examples drawn from call centers, telephone networks, service engineering, etc Markov property in continuous time The embedded discrete-time Markov chain The rate matrix and the transition rate diagram Computing the transient probabilities Steady-state analysis Birth-death processes 6. Modeling Systems with Congestion Effects M/M/1 queue Loss models Many-server systems Little's Law Understanding the effect of non-exponential service times (Method of stages; M/G/1 queue) Open and closed network models Discrete-event simulation 7. Inventory Management and the Principle of Dynamic Programming Systems with no inventory carry-over (the newsvendor problem) Systems with inventory carry-over ((s,S) inventory policies) Principle of dynamic programming
| Management Science &
Engineering Dept | Stanford University
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