PSEUDO INVERSE FUNCTIONS OF SERVICE CURVES FOR DEADLINE CALCULATIONS

This paper proposes the concept of pseudo inverse functions (PIFs) of service curves (SCs) to facilitate the deadline calculation in service curve based earliest deadline first policy (SCED). Owing to the possible non-invertible characteristic of SCs, a procedure is developed to make SCs invertible and then to get their PIFs. First, a curve instead of a function is utilized to get an inverse curve. Then, the inverse curve is mapped into a PIF. The PIF of SC is named delay curve (DC). This PIF is much like a transform, for example, Laplace Transform. The calculation is then easier by using the inverse counterpart than the original function. Actually, the DC is a new performance curve, which may extend to the other types of performance curves with usefulness for performance evaluation. Within SCED, it can be found the DC is the key factor for deadline calculation. Our proposed concept of PIF provides a way to derive the DC and the DC makes deadline calculation straightforward. In this paper, the practical procedure of PIF is developed in order to realize the calculation of DC and also theoretically verify the correctness of PIF.