An introduction to the mathematics of end-to-end quality of service in complex distributed information systems (DIS)

End-to-end quality of service (QoS_ete) in large scale distributed information systems is the basis for intelligent system acquisition and design. Without the engineering capability to design systems that efficiently match resources to pre-defined user requirements, users either receive unacceptably low levels of service or expend unnecessary capital. The current barriers to achieving QoS_ete include a lack of understanding of user requirements, the lack of a practical interface between the users and system designers, the lack of a common framework for integration of concepts between the various areas of expertise within the system, and the lack of a mature composability theory that allows such systems to be designed in a modular sense. This paper assumes solutions to the first of these two barriers, adopts as its common framework for integration the Lawrence QoS model, and presents an introduction to the formalization of the mathematical foundation required to address the final barrier. After identifying the necessary mappings between the QoS model and both the user and the system, a rudimentary composability theory is presented for special cases within the model