Splitting techniques for interval parameters and their application to performance models

During early phases of design and implementation, not all the parameter values of a performance model are usually known exactly. In related research contributions, intervals have been proposed as a means to capture parameter uncertainties. Existing model solution algorithms can be adapted to interval parameters by replacing conventional arithmetic by interval arithmetic. However, the so-called dependency problem may cause extremely wide intervals for the computed performance measures. Interval splitting has been proposed as a technique to overcome this problem. In this work, we give an overview of existing splitting algorithms and propose the use of a selective splitting method that significantly reduces the computational complexity of interval evaluations. Moreover, the exploitation of partial monotonicity properties to further decrease the computational complexity is discussed. The proposed methods are illustrated along the lines of two examples: a small performance model of the multiple access with collision avoidance by invitation (MACA-BI) protocol for ad hoc wireless mobile networks and a more complex model of an Enterprise JavaBeans (EJB) server implementation.