Queues with Lévy input and hysteretic control
Queueing Systems: Theory and Applications
Asymptotic behavior of the loss rate for Markov-modulated fluid queue with a finite buffer
Queueing Systems: Theory and Applications
On the dynamics of a finite buffer queue conditioned on the amount of loss
Queueing Systems: Theory and Applications
First passage times of reflected Ornstein---Uhlenbeck processes with two-sided jumps
Queueing Systems: Theory and Applications
Loss rates for stochastic fluid models
Performance Evaluation
Queueing Systems: Theory and Applications
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We consider a Lévy process that is reflected at 0 and at K K to the sum of the feeding Lévy process and an initial condition. We define the loss rate to be the expectation of the local time at K at time 1 under stationary conditions. The main result of the paper is the identification of the loss rate in terms of the stationary measure of the reflected process and the characteristic triplet of the Lévy process. We also derive asymptotics of the loss rate as K ← ∞ when the drift of the feeding process is negative and the Lévy measure is light tailed. Finally, we extend the results for Lévy processes to hold for Markov-modulated Lévy processes.