There has been a persistent pursuit during the past decade for generalizing network calculus - a theory of deterministic queuing systems to its stochastic counterpart. This research is to offer an answer for this pursuit and to establish a possibility-based network calculus theory that further extends the scope of this research line. The key methodology behind such a development is to apply Legendre transform at the sample-path level. Pilot research has shown some distinguished features that include: i) symmetric and decomposed characterization for traffic and service; ii) removal of highly nonlinear (min,+) convolution and de-convolution operators; iii) representation of single-node and tandem system performance bounds by summation of random variables; iv) recapture of effective bandwidth (capacity) and large deviations properties defined through the momentum generating functions; and v) tight bounds and improved scaling factor in the large deviations regime. It is expected that this research will open a new frontier in queuing theory and practice.
The proposed research will lead to a new theory for performance guarantees in queuing and other service systems that is expected to provide more accurate assessment of system performance and better management of system resources. Such a new theory will justify the vision of offering performance guarantees in diverse engineering and social systems such as communications networks (wireless, sensor networks and the high-speed Internet), supply chain and logistic systems, transportation and healthcare delivery systems; empowers the private sector to generate more value-adding business models (e.g. premium vs. ?best effort? service grades); and influences the public sector to construct robust infrastructures and to effectively assume its critical social responsibilities.
