A storage model with a two-state random environment
Operations Research - Supplement to Operations Research: stochastic processes
On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Fluid queues and regular variation
Performance Evaluation
On the M/G/1 queue with heavy-tailed service time distributions
On the M/G/1 queue with heavy-tailed service time distributions
Heavy-traffic limit theorems for the heavy-tailed GI/G/1 queue
Heavy-traffic limit theorems for the heavy-tailed GI/G/1 queue
Heavy-traffic theory for the heavy-tailed M/G/1 queue and v-stable L\''evy noise traffic
Heavy-traffic theory for the heavy-tailed M/G/1 queue and v-stable L\'''evy noise traffic
The $\'nu$-stable L\'''evy Motion in Heavy-traffic Analysis of Queueing Models with Heavy-tailed Distributions
The M/G/1 queue with heavy-tailed service time distribution
IEEE Journal on Selected Areas in Communications
ACM SIGMETRICS Performance Evaluation Review
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
An overview of Brownian and non-Brownian FCLTs for the single-server queue
Queueing Systems: Theory and Applications
Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers
Queueing Systems: Theory and Applications
Random Walk with a Heavy-Tailed Jump Distribution
Queueing Systems: Theory and Applications
Waiting Time Asymptotics in the Single Server Queue with Service in Random Order
Queueing Systems: Theory and Applications
LIMITS FOR CUMULATIVE INPUT PROCESSES TO QUEUES
Probability in the Engineering and Informational Sciences
Heavy-Traffic Limits for Loss Proportions in Single-Server Queues
Queueing Systems: Theory and Applications
Tail asymptotics for the queue length in an M/G/1 retrial queue
Queueing Systems: Theory and Applications
Heavy-tailed asymptotics for a fluid model driven by an M/G/1 queue
Performance Evaluation
Queueing approximation of suprema of spectrally positive Lévy process
Queueing Systems: Theory and Applications
Convergence of the all-time supremum of a Lévy process in the heavy-traffic regime
Queueing Systems: Theory and Applications
Heavy-traffic asymptotics for the single-server queue with random order of service
Operations Research Letters
Gaussian queues in light and heavy traffic
Queueing Systems: Theory and Applications
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We consider a GI/G/1 queue in which the service time distribution and/or the interarrival time distribution has a heavy tail, i.e., a tail behaviour like t^{-\nu} with 1, so that the mean is finite but the variance is infinite. We prove a heavy-traffic limit theorem for the distribution of the stationary actual waiting time \mathbf{W}. If the tail of the service time distribution is heavier than that of the interarrival time distribution, and the traffic load a \rightarrow 1, then \mathbf{W}, multiplied by an appropriate ‘coefficient of contraction’ that is a function of a, converges in distribution to the Kovalenko distribution. If the tail of the interarrival time distribution is heavier than that of the service time distribution, and the traffic load a \rightarrow 1, then \mathbf{W}, multiplied by another appropriate ‘coefficient of contraction’ that is a function of a, converges in distribution to the negative exponential distribution.