On a numerical method for calculating state probabilities for queueing systems with more than one waiting line

Keane, Hooghiemstra and Van de Ree have proposed a new numerical method for calculating state probabilities for queueing systems with more than one waiting line in parallel. The method is based on power series expansions of state probabilities as functions of the traffic intensity of a system. The coefficients of these power series can be recursively calculated. The coefficients of the power series expansions of moments of queue length distributions can be derived from those of the state probabilities in a straightforward manner. The above method is discussed for a rather general class of exponential queueing systems. The asymptotic behaviour of moments in heavy traffic is used to obtain extrapolations of the coefficients of their power series expansions at the origin. The calculation of moments is strongly improved by means of these extrapolations.