Analysis of a MAP/M/1/N Queue with Periodic and Non-Periodic Piecewise Constant Input Rate

This paper considers a queuing system with finite buffer, constant main MAP flow, and an additional periodic (non-periodic) Poisson piecewise-constant flow of customers. The eigenvalues the probability translation matrix Kolmogorov input intensities is analyzed. definition transition mode time based on analysis determinant introduced for first time. An analytical solution to equation piecewise arrival service found, solutions are analyzed, numerical calculations illustrating this approach presented.