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Sojourn time asymptotics in processor-sharing queues. (English) Zbl 1094.60059
This survey paper gives an overview of several methods used in investigating queues with processor-sharing (PS) discipline in case of heavy-tailed service requirements. In this case there exists a simple asymptotic equivalence between the sojourn time and the service requirement distribution, which is commonly referred to as a reduced service rate approximation. The paper considers Tauberian approach, sample-path large-deviations approach, and probabilistic approach using the conditional sojourn time. It also contains the generalization of the reduced service rate approximation to several extensions of the M/G/1 PS queue. In addition, it identifies a relationship between the reduced service rate approximation and a queue length distribution with a geometrically decaying tail, and extends it to so-called bandwidth-sharing networks. It also touches PS queues with light-tailed service requirements. The paper also proposes some possible avenues for further research.

##### MSC:
 60K25 Queueing theory (aspects of probability theory) 60F10 Large deviations 68M20 Performance evaluation, queueing, and scheduling in the context of computer systems 90B18 Communication networks in operations research 90B22 Queues and service in operations research
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