Contents

• Essentials of Probability
  • Probability on a Sample Space
    • Basic Operations on Events
    • Probability on Events
    • Other Properties
  • Conditional Probability
  • Bayes Formula
  • Independence
  • Random Variables
    • Random Variable as a Measurement
    • Probability Mass Function for a Random Variable
    • Cumulative Distribution Function
      • PMF and CDF for the 3 Coin Toss Example
    • Expectation of a Random Variable
  • Important Random Variables
    • Bernoulli Random Variable
    • Binomial Random Variable
    • Geometric Random Variable
    • Poisson Random Variable
  • Continuous-valued Random Variables
    • Properties of Continuous Random Variables
    • Expectation of a Continuous Random Variable
    • Important Continuous Random Variable: Exponential
    • Memoryless Property of the Exponential
• Inside an IMP
  • Queueing in the Network Layer at an IMP
  • Basic Single Queue Model
    • Applications of Queueing Analysis Outside of Networking
  • The Poisson Arrival Model
    • Properties of a Poisson Process
    • Interarrival Times of a Poisson Process
  • The M/M/1 Queue
    • Aside: Queueing Notation
    • Aside: The D/D/1 Queue
  • State Analysis of an M/M/1 Queue
    • Balance Equations
    • Solving the Balance Equations
  • The Finite Buffer Case: M/M/1/N
    • Blocking Probability and the Right Size Buffer
    • Throughput in the Finite Buffer Case
      • Alternate way to compute throughput of M/M/1/N: Look at the output side
      • Aside: Derivation of = Using Throughput
    • Approximation of a Finite Buffer System by the Infinite Buffer Model
  • How Long is That Line?
  • Little's Formula and Queueing Delay
    • Applying Little's Formula to an M/M/1 Queue
  • Applying the M/M/1 Results to a Single Network Link
  • Other Queueing Models
• Network Analysis
  • Queueing Networks
    • Closed Queueing Network Example
  • Nodes in a Packet Switched Network (PSN)
  • Queueing Network Model of Nodes in a PSN
  • Queueing Network Analysis of a PSN
• About this document ...