On Taylor series expansions for waiting times in tandem queues: an algorithm for calculating the coefficients and an investigation of the approximation error

Recently, a Taylor series expansion was developed for expected stationary waiting times in open (max,+)-linear stochastic systems with Poisson input process; these systems cover various instances of queueing networks. application, we present an algorithm for calculating the coefficients for infinite capacity tandem queueing networks with discrete service-time distributions. The algorithm works quite efficiently if the random vector of the service times of all servers is concentrated at a small number of atoms. We investigate the relative error of the Taylor approximation by simulation; in many cases, it follows very well a simple expression which holds exactly for independent, exponentially distributed servers.