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Part I. Introduction to Queueing: 1. Motivating examples; 2. Queueing theory terminology; Part II. Necessary Probability Background: 3. Probability review; 4. Generating random variables; 5. Sample paths, convergence, and averages; Part III. The Predictive Power of Simple Operational Laws: ’What If’ Questions and Answers: 6. Operational laws; 7. Modification analysis; Part IV. From Markov Chains to Simple Queues: 8. Discrete-time Markov Chains; 9. Ergodicity theory; 10. Real-world examples: Google, Aloha; 11. Generating functions for Markov Chains; 12. Exponential distributions and Poisson Process; 13. Transition to continuous-time Markov Chains; 14. M/M/1 and PASTA; Part V. Server Farms and Networks: Multi-server, Multi-queue Systems: 15. Server farms: M/M/k and M/M/k/k; 16. Capacity provisioning for server farms; 17. Time-reversibility and Burke’s Theorem; 18. Jackson network of queues; 19. Classed network of queues; 20. Closed networks of queues; Part VI. Real-World Workloads: High-Variability and Heavy Tails: 21. Tales of tails: real-world workloads; 22. Phase-type workloads and matrix-analytic; 23. Networks of time-sharing (PS) servers; 24. M/G/I queue and inspection paradox; 25. Task assignment for server farms; 26. Transform analysis; 27. M/G/I transform analysis; 28. Power optimization application; Part VII. Smart Scheduling: 29. Performance metrics; 30. Non-preemptive, non-size-based policies; 31. Preemptive, non-size-based policies; 32. Non-preemptive, size-based policies; 33. Preemptive, size-based policies; 34. Scheduling: SRPT and fairness.

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