Mathematical Modeling and Analysis

The mathematical modeling and analysis continues to play an important role for computer systems, applications and services.  We seeks to explore and solve fundamental, theoretical problems in areas including mathematical analysis of system/application data; formulating and solving mathematical models of system/application workloads, performance, capacity planning (short-term and long-term), service-level agreements, etc; short-term and long-term, forecasting of system/application workloads, performance and capacity planning; and methods for system/application traffic generation and benchmarking.  In each case, our modeling and analysis focuses on multiple time scales, at both micro and macro levels.   

The focus of our research in this project is on stochastic models and queueing theory.  Our analysis of data from a wide range of systems demonstrates complex arrival and service patterns that include short-range dependencies, long-range dependencies, heavy-tail distributions and non-stationary effects.  While such behaviors often cannot be addressed with traditional methods, we demonstrate that these complexities can have a significant impact on performance (several orders of magnitude).  Our research has further established fundamental results for the mathematical analysis of stochastic models and queueing networks with these complex characteristics, which include approximate methods and asymptotic results.

These mathematical studies, motivated by new fundamental problems of practical importance, also provide solutions to theoretical issues related to areas such as quality of service, scalability, pricing models, statistical inference of system characteristics, trading mechanisms, predictive models, dynamic scheduling algorithms, load balancing, admission control, buffer management, inventory management, profit and risk management, and service-level-agreements based on response-time distributions.  In turn, these theoretical results have been further exploited to develop practical solutions for performance problems in many different areas of research, including traffic generation and benchmarking, model validation, capacity planning, workload and performance forecasting, power-consumption models, generating and serving dynamic content, resource control and management, cooperative caching, dynamic offload, and network and server design.