Matrix-analytic solution of system of integral equations in three tandem servers

Abstract

A matrix-analytic method is proposed for solving a system of linear integral equations arises in three tandem servers. The approach is by modelling the cumulative distribution function (cdf) of the service time as a matrix exponential function. The method transforms the system of linear integral equations into a system of linear algebraic equations, hence can produce closed-form solutions. Properties of the solution are discussed.