The two-moment three-parameter decomposition approximation of queueing networks with exponential residual renewal processes

We propose a two-moment three-parameter decomposition approximation of general open queueing networks by which both autocorrelation and cross correlation are accounted for. Each arrival process is approximated as an exponential residual (ER) renewal process that is characterized by three parameters: intensity, residue, and decrement. While the ER renewal process is adopted for modeling autocorrelated processes, the innovations method is used for modeling the cross correlation between randomly split streams. As the interarrival times of an ER renewal process follow a two-stage mixed generalized Erlang distribution, viz., MGE(2), each station is analyzed as an MGE(2)/G/1 system for the approximate mean waiting time. Variability functions are also used in network equations for a more accurate modeling of the propagation of cross correlations in queueing networks. Since an ER renewal process is a special case of a Markovian arrival process (MAP), the value of the variability function is determined by a MAP/MAP/1 approximation of the departure process. Numerical results show that our proposed approach greatly improves the performance of the parametric decomposition approximation of open queueing networks.