Fluid queues and regular variation
Performance Evaluation
Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models
Mathematics of Operations Research
On a reduced load equivalence for fluid queues under subexponentiality
Queueing Systems: Theory and Applications
Appendix: A primer on heavy-tailed distributions
Queueing Systems: Theory and Applications
Reduced-Load Equivalence and Induced Burstiness in GPS Queues with Long-Tailed Traffic Flows
Queueing Systems: Theory and Applications
Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue
Mathematics of Operations Research
Generalized processor sharing with light-tailed and heavy-tailed input
IEEE/ACM Transactions on Networking (TON)
Reduced-Load Equivalence for Queues with Gaussian Input
Queueing Systems: Theory and Applications
Performance of TCP-friendly streaming sessions in the presence of heavy-tailed elastic flows
Performance Evaluation - Long range dependence and heavy tail distributions
Sojourn time asymptotics in processor-sharing queues
Queueing Systems: Theory and Applications
Subexponential interval graphs generated by immigration–death processes
Probability in the Engineering and Informational Sciences
Reduced-load equivalence for Gaussian processes
Operations Research Letters
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The stationary workload WφA+B of a queue with capacity φ loaded by two independent processes A and B is investigated. When the probability of load deviation in process A decays slower than both in B and $\mathrm{e}^{-\sqrt{x}}$, we show that WφA+B is asymptotically equal to the reduced load queue Wφ−bA, where b is the mean rate of B. Given that this property does not hold when both processes have lighter than $\mathrm{e}^{-\sqrt{x}}$ deviation decay rates, our result establishes the criticality of $\mathrm{e}^{-\sqrt{x}}$ in the functional behavior of the workload distribution. Furthermore, using the same methodology, we show that under an equivalent set of conditions the results on sampling at subexponential times hold.