The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Connection-wise end-to-end performance analysis of queuing networks with MMPP inputs
Performance Evaluation
Departure Processes of BMAP/G/1 Queues
Queueing Systems: Theory and Applications
Decomposition of general queueing networks with MMPP inputs and customer losses
Performance Evaluation
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 Joint Moments Based Analysis of Networks of MAP/MAP/1 Queues
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Queueing Systems: Theory and Applications
A new renewal approximation for certain autocorrelated processes
Operations Research Letters
Queueing Systems: Theory and Applications
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In two-moment decomposition approximations of queueing networks, the arrival process is modeled as a renewal process, and each station is approximated as a GI/G/1 queue whose mean waiting time is approximated based on the first two moments of the interarrival times and the service times. The departure process is also approximated as a renewal process even though the autocorrelation of this process may significantly affect the performance of the subsequent queue depending on the traffic intensity. When the departure process is split into substreams by Markovian random routing, the split processes typically are modeled as independent renewal processes even though they are correlated with each other. This cross correlation might also have a serious impact on the queueing performance. In this paper, we propose an approach for modeling both the cross correlation and the autocorrelation by a three-moment four-parameter decomposition approximation of queueing networks. The arrival process is modeled as a nonrenewal process by a two-state Markov-modulated Poisson process, viz., MMPP(2). The cross correlation between randomly split streams is accounted for in the second and third moments of the merged process by the innovations method. The main contribution of the present research is that both the cross correlation and the autocorrelation can be modeled in parametric decomposition approximations of queueing networks by integrating the MMPP(2) approximation of the arrival/departure process and the innovations method. We also present numerical results that strongly support our refinements.