A fourth-order algorithm with automatic stepsize control for the transient analysis of DSPNs

This paper presents on efficient and numerically reliable method for the transient analysis of DSPNs. An analysis algorithm based on the method of supplementary variables is redesigned in order to improve its efficiency (with respect to both CPU-time and memory space) and its numerical quality (control of numerical errors) and to remove earlier restrictions (concerning the initial enabling of deterministic transitions). Significant features of the redesigned algorithm of fourth order (with respect to the step size) are an automatic stepsize control and a two-stage relative error control. Furthermore a formal way of dealing with discontinuities in the transient state equations is developed. This allows to cope with initially enabled deterministic transitions and also improves the numerical quality of the algorithm. Numerical experiments with a queueing system with failure and repair illustrate the advantages of the new algorithm.