An Overview for Markov Decision Processes in Queues and Networks <s> Objective one: Input control <s> Semi-Regenerative Decision Models Description of Basic Decision Model Rigorous Definitions and Assumptions Examples of Controlled Queues Optimization Problems Renewal Kernels of the Decision Model Special Classes of Strategies Sufficiency of Markov Strategies Dynamic Programming Discounting in Continuous Time Dynamic Programming Equation Bellman Functions Finite-Horizon Problem Infinite-Horizon Discounted-Cost Problem Random-Horizon Problem Average Cost Criterion Preliminaries: Weak Topology, Limit Passages Preliminaries: Taboo Probabilities, Limit Theorems for Markov Renewal Processes Notation, Recurrence-Communication Assumptions, Examples Existence of Optimal Policies Existence of Optimal Strategies: General Criterion Existence of Optimal Strategies: Sufficient Conditions Optimality Equation Constrained Average-Cost Problem Average-Cost Optimality as Limiting Case of Discounted-Cost Optimality Continuously Controlled Markov Jump Processes Facts About Measurability of Stochastic Processes Marked Point Processes and Random Measures The Predictable s-Algebra Dual Predictable Projections of Random Measures Definition of Controlled Markov Jump Process An M/M/1 Queue With Controllable Input and Service Rate Dynamic Programming Optimization Problems Structured Optimization Problems for Decision Processes Convex Regularization Submodular and Supermodular Functions Existence of Monotone Solutions for Optimization Problems Processes with Bounded Drift Birth and Death Processes Control of Arrivals The Model Description Finite-Horizon Discounted-Cost Problem Cost Functionals Infinite-Horizon Case with and without Discounting Optimal Dynamic Pricing Policy: Model Results Control of Service Mechanism Description of the System Static Optimization Problem Optimal Policies for the Queueing Process Service System with Two Interacting Servers Analysis of Optimality Equation Optimal Control in Models with Several Classes of Customers Description of Models and Processes Associated Controlled Processes Existence of Optimal Simple Strategies for the Systems with Alternating Priority Existence of Optimal Simple Strategy for the System with Feedback Equations for Stationary Distributions Stationary Characteristics of the Systems with Alternating Priority Stationary Characteristics of the System with Feedback Models with Alternating Priority: Linear Programming Problem Linear Programming Problem in the Model with Feedback Model with Periods of Idleness and Discounted-Cost Criterion Basic Formulas Construction of Optimal Modified Priority Discipline Bibliography Index Each chapter also includes an Introduction, and a Remarks and Exercises section <s> BIB001 </s> An Overview for Markov Decision Processes in Queues and Networks <s> Objective one: Input control <s> Optimization Criteria. Finite Horizon Optimization. Infinite Horizon Discounted Cost Optimization. An Inventory Model. Average Cost Optimization for Finite State Spaces. Average Cost Optimization Theory for Countable State Spaces. Computation of Average Cost Optimal Policies for Infinite State Spaces. Optimization Under Actions at Selected Epochs. Average Cost Optimization of Continuous Time Processes. Appendices. Bibliography. Index. <s> BIB002
The input control is to apply the MDPs to dynamically control the input process of customers in the queues and networks, including the input rate control, the interval time control, and the admission access control (e.g., probability that an arriving customer chooses entering the system or some servers). queues and networks, including the service rate control, the service time control, and the service process control. (a) The service rate control: Kitaev and Rykov BIB001 , Sennott BIB002 