Spectral performance evaluation of parallel processing systems

The aim of this paper is that spectral determinants are objects that can be effectively used as a performance prediction tool for the modern parallel processing systems. In the aim to confirm this we give the matrix representation of the linear evolution operator of the certain class of parallel processing systems. An explicit polynomial expression of the corresponding spectral determinant has been established and eigenvalues were computed. Derived eigenvalues were validated against the results of the simulation. The strong agreement between computed results and those obtained through the simulation has been found.