A Harmonical Model for Approximating the Identity in Min-Plus Convolution

Min-plus convolution is an algebra system that has applications to computer networks. Mathematically, the identity of min-plus convolution plays a key role in theory. On the other hand, the mathematical representation of the identity, which is computable with digital computers, is essential for further developing min-plus convolution (e.g., de-convolution) in practice. However, the identical element in min-plus convolution is defined as infinity over infinite interval, making digital computation of the identity difficult because digital computers only provide finite range of numbers for numerical computations. Consequently, the issue of numerical approximation of the identical element is worth discussing. This paper proposes a harmonic model for finite approximation of the identical element in the min-plus convolution. Key-Words: Min-plus convolution, Fourier analysis, approximation, generalized functions.