Queueing Theory and Scheduling

  1. Basic Markovian Queueing Models
    1. Overview of Markovian Models
      1. Assumptions and Limitations
        1. Solution Methodology
        2. The M/M/1 Queue
          1. Model Assumptions
            1. State-Space Description
              1. Transition Rate Diagram
                1. Balance Equations
                  1. Steady-State Probabilities
                    1. Derivation
                      1. Geometric Distribution
                        1. Stability Condition
                        2. Performance Measures
                          1. Average Number in System (L)
                            1. Average Number in Queue (Lq)
                              1. Average Time in System (W)
                                1. Average Time in Queue (Wq)
                                  1. Server Utilization (ρ)
                                    1. Probability Distribution
                                    2. Transient Analysis
                                      1. Busy Period Analysis
                                      2. The M/M/c Queue
                                        1. Model Assumptions
                                          1. State-Space and Transition Diagram
                                            1. Steady-State Probabilities
                                              1. Erlang C Formula
                                                1. Performance Measures
                                                  1. Probability of Waiting
                                                    1. Average Waiting Time
                                                      1. Average Number in System
                                                        1. Average Number in Queue
                                                          1. Individual Server Utilization
                                                          2. Optimal Number of Servers
                                                          3. The M/M/1/K Queue
                                                            1. Model Assumptions
                                                              1. State-Space and Transition Diagram
                                                                1. Steady-State Probabilities
                                                                  1. Blocking Probability
                                                                    1. Effective Arrival Rate
                                                                      1. Performance Measures
                                                                        1. Average Number in System
                                                                          1. Average Waiting Time
                                                                            1. Throughput Analysis
                                                                            2. Comparison with M/M/1
                                                                            3. The M/M/c/K Queue
                                                                              1. Model Assumptions
                                                                                1. State-Space and Transition Diagram
                                                                                  1. Steady-State Probabilities
                                                                                    1. Blocking Probability
                                                                                      1. Performance Measures
                                                                                        1. Design Considerations
                                                                                        2. The M/M/c/c Queue (Erlang B)
                                                                                          1. Loss Systems
                                                                                            1. Model Assumptions
                                                                                              1. Erlang B Formula
                                                                                                1. Blocking Probability
                                                                                                  1. Performance Measures
                                                                                                    1. Applications in Telephony
                                                                                                    2. The M/M/∞ Queue
                                                                                                      1. Model Assumptions
                                                                                                        1. State-Space Description
                                                                                                          1. Poisson Distribution of System Size
                                                                                                            1. Performance Measures
                                                                                                            2. Finite Population Models
                                                                                                              1. M/M/1/N/N Queue
                                                                                                                1. M/M/c/K/N Queue
                                                                                                                  1. Machine Repair Models
                                                                                                                    1. Performance Analysis

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                                                                                                                  2. Mathematical Foundations

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                                                                                                                  4. Advanced Queueing Models