Stochastic Network Calculus

Network calculus is a theory dealing with queuing systems found in computer networks. Its focus is on performance guarantees. Central to the theory is the use of alternate algebras such as the min-plus algebra to transform complex network systems into analytically tractable systems. To simplify the ana- sis, another idea is to characterize tra?c and service processes using various bounds. Since its introduction in the early 1990s, network calculus has dev- oped along two tracks―deterministic and stochastic. This book is devoted to summarizing results for stochastic network calculus that can be employed in the design of computer networks to provide stochastic service guarantees. Overview and Goal Like conventional queuing theory, stochastic network calculus is based on properly de?ned tra?c models and service models. However, while in c- ventional queuing theory an arrival process is typically characterized by the inter-arrival times of customers and a service process by the service times of customers, the arrival process and the service process are modeled in n- work calculus respectively by some arrival curve that (maybe probabilis- cally) upper-bounds the cumulative arrival and by some service curve that (maybe probabilistically) lower-bounds the cumulative service. The idea of usingboundstocharacterizetra?candservicewasinitiallyintroducedfor- terministic network calculus. It has also been extended to stochastic network calculus by exploiting the stochastic nature of arrival and service processes.

Network calculus, a theory dealing with queuing systems found in computer networks, focuses on performance guarantees. The development of an information theory for stochastic service-guarantee analysis has been identified as a grand challenge for future networking research. Towards that end, stochastic network calculus, the probabilistic version or generalization of the (deterministic) Network Calculus, has been recognized by researchers as a crucial step.

Stochastic Network Calculus presents a comprehensive treatment for the state-of-the-art in stochastic service-guarantee analysis research and provides basic introductory material on the subject, as well as discusses the most recent research in the area. This helpful volume summarizes results for stochastic network calculus, which can be employed when designing computer networks to provide stochastic service guarantees.

Features and Topics:

• Provides a solid introductory chapter, providing useful background knowledge

• Reviews fundamental concepts and results of deterministic network calculus

• Includes end-of-chapter problems, as well as summaries and bibliographic comments

• Defines traffic models and server models for stochastic network calculus

• Summarizes the basic properties of stochastic network calculus under different combinations of traffic and server models

• Highlights independent case analysis

• Discusses stochastic service guarantees under different scheduling disciplines

• Presents applications to admission control and traffic conformance study using the analysis results

• Offers an overall summary and some open research challenges for further study of the topic

Researchers and graduates in the area of performance evaluation of computer communication networks will benefit substantially from this comprehensive and easy-to-follow volume. Professionalswill also find it a worthwhile reference text.

Professor Yuming Jiang at the Norwegian University of Science and Technology (NTNU) has lectured using the material presented in this text since 2006.

Dr Yong Liu works at the Optical Network Laboratory, National University of Singapore, where he researches QoS for optical communication networks and Metro Ethernet networks.

Key Topics:

• Queuing systems

• Performance analysis and guarantees

• Independent case analysis

• Traffic and server models 

• Analysis of scheduling disciplines 

• Generalized processor sharing 

• Open research challenges