Operations Research and Optimization

  1. Stochastic Processes and Queuing Theory
    1. Introduction to Stochastic Processes
      1. Random Processes
        1. Stochastic Process Definition
          1. Sample Paths
            1. State Space
              1. Parameter Space
              2. Classification of Processes
                1. Discrete-Time Processes
                  1. Continuous-Time Processes
                    1. Discrete-State Processes
                      1. Continuous-State Processes
                    2. Markov Chains
                      1. Discrete-Time Markov Chains
                        1. Markov Property
                          1. Transition Probabilities
                            1. Transition Matrix
                              1. Chapman-Kolmogorov Equations
                              2. Classification of States
                                1. Accessible States
                                  1. Communicating States
                                    1. Irreducible Chains
                                      1. Periodic States
                                        1. Transient States
                                          1. Recurrent States
                                          2. Steady-State Analysis
                                            1. Limiting Probabilities
                                              1. Stationary Distribution
                                                1. Balance Equations
                                                  1. Ergodic Chains
                                                  2. Absorbing Markov Chains
                                                    1. Absorbing States
                                                      1. Transient Analysis
                                                        1. Absorption Probabilities
                                                          1. Expected Absorption Times
                                                          2. Continuous-Time Markov Chains
                                                            1. Poisson Process
                                                              1. Birth-Death Processes
                                                                1. Transition Rate Matrix
                                                                  1. Kolmogorov Equations
                                                                2. Queuing Theory Fundamentals
                                                                  1. Queuing System Components
                                                                    1. Arrival Process
                                                                      1. Service Mechanism
                                                                        1. Queue Discipline
                                                                          1. System Capacity
                                                                            1. Customer Population
                                                                            2. Arrival Processes
                                                                              1. Poisson Arrivals
                                                                                1. Interarrival Time Distributions
                                                                                  1. Batch Arrivals
                                                                                    1. Time-Dependent Arrivals
                                                                                    2. Service Mechanisms
                                                                                      1. Service Time Distributions
                                                                                        1. Single Server Systems
                                                                                          1. Multiple Server Systems
                                                                                            1. Service Disciplines
                                                                                            2. Kendall's Notation
                                                                                              1. Arrival Distribution
                                                                                                1. Service Distribution
                                                                                                  1. Number of Servers
                                                                                                    1. System Capacity
                                                                                                      1. Population Size
                                                                                                        1. Service Discipline
                                                                                                      2. Performance Measures
                                                                                                        1. System State Probabilities
                                                                                                          1. Steady-State Probabilities
                                                                                                            1. Transient Probabilities
                                                                                                            2. Queue Length Measures
                                                                                                              1. Expected Number in System
                                                                                                                1. Expected Number in Queue
                                                                                                                  1. Queue Length Distribution
                                                                                                                  2. Waiting Time Measures
                                                                                                                    1. Expected Waiting Time in Queue
                                                                                                                      1. Expected Time in System
                                                                                                                        1. Waiting Time Distributions
                                                                                                                        2. Utilization Measures
                                                                                                                          1. Server Utilization
                                                                                                                            1. System Utilization
                                                                                                                              1. Traffic Intensity
                                                                                                                            2. Common Queuing Models
                                                                                                                              1. M/M/1 Queue
                                                                                                                                1. Model Assumptions
                                                                                                                                  1. Steady-State Analysis
                                                                                                                                    1. Performance Measures
                                                                                                                                      1. Economic Analysis
                                                                                                                                      2. M/M/s Queue
                                                                                                                                        1. Multiple Server Analysis
                                                                                                                                          1. Erlang-C Formula
                                                                                                                                            1. Performance Calculations
                                                                                                                                            2. M/M/1/K Queue
                                                                                                                                              1. Finite Capacity Systems
                                                                                                                                                1. Blocking Probability
                                                                                                                                                  1. Effective Arrival Rate
                                                                                                                                                  2. M/M/s/K Queue
                                                                                                                                                    1. Multiple Servers with Capacity
                                                                                                                                                      1. Performance Analysis
                                                                                                                                                      2. M/G/1 Queue
                                                                                                                                                        1. General Service Times
                                                                                                                                                          1. Pollaczek-Khintchine Formula
                                                                                                                                                            1. Residual Service Time
                                                                                                                                                            2. G/G/1 Queue
                                                                                                                                                              1. General Arrival and Service
                                                                                                                                                                1. Approximation Methods
                                                                                                                                                                  1. Bounds and Estimates
                                                                                                                                                                2. Queuing Networks
                                                                                                                                                                  1. Open Queuing Networks
                                                                                                                                                                    1. Jackson Networks
                                                                                                                                                                      1. Product-Form Solutions
                                                                                                                                                                        1. Traffic Equations
                                                                                                                                                                        2. Closed Queuing Networks
                                                                                                                                                                          1. Fixed Population
                                                                                                                                                                            1. Mean Value Analysis
                                                                                                                                                                              1. Convolution Algorithm

                                                                                                                                                                          Previous

                                                                                                                                                                          7. Dynamic Programming

                                                                                                                                                                          Go to top

                                                                                                                                                                          Next

                                                                                                                                                                          9. Simulation Modeling