A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Approximations for waiting time in GI/G/1 systems
Queueing Systems: Theory and Applications
The impact of autocorrelation on queuing systems
Management Science
The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Stochastic modeling of traffic processes
Frontiers in queueing
On variations of queue response for inputs with the same mean and autocorrelation function
IEEE/ACM Transactions on Networking (TON)
An Overview of Tes Processes and Modeling Methodology
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Merging and splitting autocorrelated arrival processes and impact on queueing performance
Performance Evaluation
Queueing Systems: Theory and Applications
A new renewal approximation for certain autocorrelated processes
Operations Research Letters
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It is known that correlations in an arrival stream offered to a single-server queue profoundly affect mean waiting times as compared to a corresponding renewal stream offered to the same server. Nonetheless, this paper uses appropriately constructed GI/G/1 models to create viable approximations for queues with correlated arrivals. The constructed renewal arrival process, called PMRS (Peakedness Matched Renewal Stream), preserves the peakedness of the original stream and its arrival rate; furthermore, the squared coefficient of variation of the constructed PMRS equals the index of dispersion of the original stream. Accordingly, the GI/G/1 approximation is termed PMRQ (Peakedness Matched Renewal Queue). To test the efficacy of the PMRQ approximation, we employed a simple variant of the TES+ process as the autocorrelated arrival stream, and simulated the corresponding TES+/G/1 queue for several service distributions and traffic intensities. Extensive experimentation showed that the proposed PMRQ approximations produced mean waiting times that compared favorably with simulation results of the original systems. Markov-modulated Poisson process (MMPP) is also discussed as a special case.