Queueing Theory Explained

Queues are everywhere, shaping how people, tasks, and resources interact in modern systems. From call centers to cloud computing, understanding and managing waiting lines is essential for building efficient and scalable operations. This book is a comprehensive guide to queueing theory, designed for both students and professionals who want to master the mathematics and applications of this powerful framework. With a balance of mathematical rigor and applied examples, this book equips readers to design systems that are efficient, scalable, and effective across diverse industries.

Inside, you will learn:

• Core Models: M/M/1, M/G/1, and M/M/c systems with detailed derivations and performance metrics such as Little's Law and the Pollaczek-Khinchine formula.

• Networks of Queues: Open and closed systems, Jackson networks, and Mean Value Analysis.

• Advanced Topics: Markov chains, phase-type distributions, bulk arrivals, and retrial queues.

• Scheduling Disciplines: Priority, shortest job first, and fair queuing with their impact on system performance.

• Simulation Techniques: Practical approaches for analyzing systems that defy closed-form solutions.

• Real-World Applications: Case studies in computer systems, cloud computing, data centers, telecommunications, CPU scheduling, and call center staffing.

• Future Directions: AI-driven optimization, cost-benefit analysis, and the potential role of quantum computing.