Here is a list of 100 chapter titles for a book or course on Queueing Theory, progressing from beginner to advanced topics in mathematics:
- Introduction to Queueing Theory: Basic Concepts
- What is a Queue? Basic Terminology and Definitions
- Applications of Queueing Theory in Real Life
- The Structure of Queueing Systems: Components and Classifications
- Types of Queues: FIFO, LIFO, Priority, and Others
- The Birth-Death Process in Queueing Theory
- Arrival Processes: Poisson and Non-Poisson Arrivals
- Service Processes: Exponential and Deterministic Service Times
- Understanding the Concept of Queue Length
- Single-Server Queues: Basic Analysis
- The M/M/1 Queue: Basic Queueing Model
- The M/M/c Queue: Multiple Servers, Single Queue
- Little's Law: Relationship Between Average Queue Length and Waiting Time
- The Steady-State Distribution for M/M/1 Queue
- Key Performance Metrics: Utilization, Throughput, and Waiting Time
- The M/M/1 Queue with Finite Capacity
- The M/M/1 Queue with an Infinite Server
- The Erlang B and Erlang C Formulas
- Waiting Time Distribution in M/M/1 Queues
- Probability Distribution of the Number of Customers in M/M/1 Queues
- The Concept of Queueing Network
- The M/G/1 Queue: General Service Time Distribution
- The Pollaczek-Khinchin Formula
- The M/M/1 Queue in the Context of Computer Networks
- Queues in Telecommunications and Networking
- Understanding Blocking and Loss in Queueing Systems
- Queueing with Multiple Classes of Customers
- Service Time Variability: Impact on Queueing Performance
- Little’s Law in Multi-Class Queues
- Queueing Systems in Manufacturing and Production Lines
- Basic Markov Chains in Queueing Theory
- Transient and Steady-State Behavior of Queueing Systems
- Capacity Planning and Queueing Analysis in Service Industries
- The M/M/1 Queue with Balking
- The Concept of Server Idle Time and Queueing Efficiency
- The M/M/c Queue: Key Performance Measures
- Performance Evaluation of Queueing Systems in Cloud Computing
- Simulation of Simple Queueing Systems
- Service Discipline: FIFO vs Non-FIFO Queues
- Multi-Server Queueing Systems: Comparison and Analysis
- Understanding Queueing Delays: Statistical Modeling
- Connection between Queueing Theory and Optimization
- Probability of Delay in Single and Multi-Server Queues
- The M/G/1 Queue with Vacation Times
- Approximations for Queues with Large Numbers of Servers
- The M/M/1 Queue with Multiple Arrival Streams
- The Role of Randomness in Queueing Systems
- The M/G/1 Queue: Mean Waiting Time Analysis
- The G/G/1 Queue: General Arrival and Service Processes
- Priority Queueing Systems and Their Analysis
- Multiclass Queueing Models
- The M/M/c Queue with a Finite Buffer
- The Birth-Death Process in Queueing Systems
- Queueing Networks: Product Form Solutions
- Customer Behavior: Balking, Reneging, and Jockeying
- Analyzing the M/G/1 Queue using the Pollaczek-Khinchin Formula
- Stochastic Processes in Queueing Theory
- Queueing Theory in Telecommunications and Call Centers
- The Impact of Service Time Variability on Performance
- Optimization of Queueing Systems: Techniques and Strategies
- Applications of Queueing Theory in Traffic Flow
- Queueing in Manufacturing and Inventory Systems
- Queueing Analysis in Computer Systems and Web Servers
- Network of Queues: Theory and Algorithms
- The G/G/1 Queue with Phase-Type Distributions
- Customer Arrival Time Analysis and its Impact on Queue Performance
- Understanding Retrial Queues: Definition and Applications
- The M/M/1/K Queue and Its Application to Blocking Systems
- Multi-Server Queueing Models with Finite and Infinite Buffers
- Heavy-Traffic Approximations in Queueing Theory
- Markov Chains in Queueing Network Analysis
- Performance Metrics for Multi-Class Queueing Systems
- Queueing Models with Server Failures and Repairs
- Queuing Theory for Computer Networks: Latency and Throughput
- Real-Time Processing and Queueing in Distributed Systems
- Service Time Distributions and their Effect on Performance
- Understanding Queues in the Internet of Things (IoT)
- The Use of Simulation in Queueing System Analysis
- Applying Queueing Theory to Resource Allocation Problems
- Approximation Methods in Queueing Analysis
- Queueing Theory in Financial Systems and Risk Management
- The G/G/c Queue and its Complexities
- Performance of Queueing Systems with Preemptive Priority
- The Impact of Correlated Arrivals on Queue Performance
- Matrix-Analytic Methods in Queueing Theory
- An Introduction to Stochastic Network Models
- Modeling and Analysis of Parallel Queueing Systems
- Handling Non-Markovian Arrivals and Services
- Modeling of Queues with Multiple Feedback Systems
- Server Scheduling and Load Balancing in Queueing Theory
- Understanding Networks of Queues: Jackson’s Theorem
- Congestion Models in Multi-Class Queueing Systems
- The Role of Queueing Theory in Real-Time Systems
- Connection between Queueing Theory and Game Theory
- Solving Large-Scale Queueing Systems: Techniques and Approximations
- Queueing Theory in Supply Chain Management
- Multi-Server Queues in Cloud Computing
- Queueing Models for MIMO Systems
- Analysis of Queueing Systems with Non-Exponential Service Times
- Advanced Topics in Queueing Theory: Stochastic Networks and Infinite Servers
This list covers a wide range of Queueing Theory topics, from foundational concepts like basic queue models and performance measures, to more complex topics like multiclass systems, heavy-traffic approximations, and applications in fields such as telecommunications, cloud computing, and supply chain management.