an:05036645
Zbl 1094.60059
Borst, Sem; N????ez-Queija, Rudesindo; Zwart, Bert
Sojourn time asymptotics in processor-sharing queues
EN
Queueing Syst. 53, No. 1-2, 31-51 (2006).
00126675
2006
j
60K25 60F10 68M20 90B18 90B22
bandwidth-sharing networks; large deviations; tail asymtotics; heavy-tailed distributions; light-tailed distributions
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.
Oleg K. Zakusilo (Ky??v)