This book presents Poisson Counter-Driven Stochastic Differential Equations (PCSDEs) and their applications in computer systems. PCSDEs provide a mathematical framework for analyzing systems that combine continuous evolution with discrete events - a characteristic feature of many modern computer systems from network protocols to cloud computing platforms.  The first comprehensive treatment of PCSDEs in computer systems, this book bridges the gap between theoretical foundations and practical engineering applications. Through careful development of mathematical tools and concrete case studies, the author demonstrates how rigorous analysis can lead to improved system design in networking, cloud computing, IoT devices, and content delivery networks.

Vishal Misra, Ph.D., is RKS Family Professor of Computer Science in the Department of Computer Science and Electrical Engineering at Columbia University and the Vice Dean for Computing and AI in the School of Engineering. An ACM and IEEE Fellow, his research emphasis is on mathematical modeling of systems, bridging the gap between practice and analysis. His pioneering work on applying PCSDEs to network congestion control led to practical improvements in internet infrastructure, including contributions to TCP/AQM systems that have been standardized in DOCSIS 3.1.  As a graduate student, he co-founded CricInfo, which was acquired by ESPN in 2007. In 2021, he developed one of the world's first commercial applications built on top of GPT-3 for ESPNCricinfo, and has been subsequently modeling the behavior of LLMs. His work spans theoretical foundations of stochastic systems and their practical applications in modern computing systems, consistently demonstrating his ability to connect rigorous mathematical analysis with real-world impact.