173 research outputs found
Iterative approximation of k-limited polling systems
The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out be accurate, robust and computationally efficient
Asymptotic behavior of the loss probability for an M/G/1/N queue with vacations
In this paper, asymptotic properties of the loss probability are considered
for an M/G/1/N queue with server vacations and exhaustive service discipline,
denoted by an M/G/1/N -(V, E)-queue. Exact asymptotic rates of the loss
probability are obtained for the cases in which the traffic intensity is
smaller than, equal to and greater than one, respectively. When the vacation
time is zero, the model considered degenerates to the standard M/G/1/N queue.
For this standard queueing model, our analysis provides new or extended
asymptotic results for the loss probability. In terms of the duality
relationship between the M/G/1/N and GI/M/1/N queues, we also provide
asymptotic properties for the standard GI/M/1/N model
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