Part 5: Markov Chains and Poisson Processes

Chapter 18: Continuous-Time Markov Chains and Birth-Death Processes

Intermediate~240 min

Learning Objectives

  • Derive the Poisson process from its defining properties and prove key consequences
  • Model compound and non-homogeneous Poisson processes for wireless traffic
  • Write the generator matrix of a CTMC and solve the Kolmogorov equations
  • Analyze birth-death processes and the M/M/1 queue: stationary distribution, mean delay
  • Apply Erlang-B and Erlang-C formulas to dimension channels and buffers

Sections

Prerequisites & Notation
nextSpecial
The Poisson Process
Compound and Non-Homogeneous Poisson Processes
Continuous-Time Markov Chains
Birth-Death Processes and the M/M/1M/M/1 Queue
M/M/cM/M/c, M/M/1/KM/M/1/K, and Erlang Models
Chapter Summary
Special
Exercises
References & Further Reading
Special

Prerequisites

Discrete-time Markov chains (FSP Ch. 17)Exponential distribution and memoryless property (FSP Ch. 6)Matrix exponential and eigenvalue decompositionConditional probability and total probability (FSP Ch. 2)

💬 Discussion

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