The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Mean Waiting Time Approximations in the G/G/1 Queue
Queueing Systems: Theory and Applications
ETAQA Truncation Models for the MAP/MAP/1 Departure Process
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Taking Account of Correlations Between Streams in Queueing Network Approximations
Queueing Systems: Theory and Applications
Merging and splitting autocorrelated arrival processes and impact on queueing performance
Performance Evaluation
A new renewal approximation for certain autocorrelated processes
Operations Research Letters
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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.