The impact of autocorrelation on queuing systems
Management Science
The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Mean Waiting Time Approximations in the G/G/1 Queue
Queueing Systems: Theory and Applications
A new renewal approximation for certain autocorrelated processes
Operations Research Letters
Characterizing the variability of arrival processes with indexes of dispersion
IEEE Journal on Selected Areas in Communications
IEEE Journal on Selected Areas in Communications
Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data
IEEE Journal on Selected Areas in Communications
Queueing Systems: Theory and Applications
Autocorrelation effects in manufacturing systems performance: a simulation analysis
Proceedings of the Winter Simulation Conference
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We have proposed a three-parameter renewal approximation to analyze splitting and superposition of autocorrelated processes. We define the index of dispersion for counts of an ordinary process used in a new and more accurate technique to estimate the third parameter. Then, we express this newly defined index of dispersion for the superposition in terms of the ordinary as well as the stationary indices of dispersion of the originally autocorrelated component processes. Hence, even if the superposition data is not observable, as long as sufficient information exists on component processes, the parameters of the proposed renewal approximation can be estimated accurately. The accurate renewal approximation of a general process helps in sustaining accuracy if it is split, by-passing the need to sample from branched processes. We have tested the impact of our approximation on the accuracy of the mean waiting time, which compared favorably with simulation results of the original systems.