Queuing Theory and Modeling

Unit I: Probability and Random Variables

• Fundamentals of Probability

  • Axioms of Probability

  • Conditional Probability

  • Baye's Theorem

• Random Variables

  • Discrete and Continuous Random Variables

  • Moments and Moment Generating Functions

• Probability Distributions

  • Binomial Distribution

  • Poisson Distribution

  • Geometric Distribution

  • Uniform Distribution

  • Exponential Distribution

  • Normal Distribution

Unit II: Two-Dimensional Random Variables

• Joint Distributions

  • Marginal and Conditional Distributions

• Covariance and Correlation

• Linear Regression

• Transformation of Random Variables

• Central Limit Theorem

  • For independent and identically distributed random variables

Unit III: Random Processes

• Classification of Random Processes

• Stationary Processes

• Markov Processes

• Poisson Processes

• Discrete Parameter Markov Chain

  • Chapman-Kolmogorov Equations

  • Limiting Distributions

Unit IV: Queueing Models

• Markovian Queues

  • Birth and Death Processes

• Queueing Models

  • Single and Multiple Server Queueing Models

  • Little's Formula

• Queues with Special Conditions

  • Queues with Finite Waiting Rooms

  • Queues with Impatient Customers: Balking and Reneging

Unit V: Advanced Queueing Models

• Finite Source Models

• M/G/1 Queue

  • Pollaczek-Khinchin Formula

• Special Cases

  • M/D/1 and M/EK/1 Queues

• Series Queues

• Open Jackson Networks