Abstract
We consider networks where traffic is served according to the Generalised Processor Sharing (GPS) principle. GPS-based scheduling algorithms are considered important for providing differentiated quality of service in integrated-services networks. We are interested in the workload of a particular flow i at the bottleneck node on its path. Flow i is assumed to have long-tailed traffic characteristics. We distinguish between two traffic scenarios, (i) flow i generates instantaneous traffic bursts and (ii) flow i generates traffic according to an on/off process. In addition, we consider two configurations of feed-forward networks. First we focus on the situation where other flows join the path of flow i. Then we extend the model by adding flows which can branch off at any node, with cross traffic as a special case. We prove that under certain conditions the tail behaviour of the workload distribution of flow i is equivalent to that in a two-node tandem network where flow i is served in isolation at constant rates. These rates only depend on the traffic characteristics of the other flows through their average rates. This means that the results do not rely on any specific assumptions regarding the traffic processes of the other flows. In particular, flow i is not affected by excessive activity of flows with ‘heavier-tailed’ traffic characteristics. This confirms that GPS has the potential to protect individual flows against extreme behaviour of other flows, while obtaining substantial multiplexing gains.
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References
S. Aalto and W. Scheinhardt, Tandem fluid queues fed by homogeneous on-off sources, EURANDOM Report 99-022 (1999), to appear in Oper. Res. Lett.
R. Agrawal, A.M. Makowski and P. Nain, On a reduced load equivalence for fluid queues under subexponentiality, Queueing Systems 33(1-3) (1999) 5-41.
V. Anantharam, Scheduling strategies and long-range dependence, Queueing Systems 33(1-3) (1999) 73-89.
S.C. Borst, O.J. Boxma, and P.R. Jelenkovi´c, Reduced-load equivalence and induced burstiness in GPS queues with long-tailed traffic flows, CWI Report PNA-R0016 (2000), to appear in Queueing Systems.
O.J. Boxma and V. Dumas, The busy period in the fluid queue, Performance Evaluation Rev. 26 (1998) 100-110.
P.R. Jelenkovi´c and A.A. Lazar, Asymptotic results for multiplexing subexponential on-off processes, Adv. in Appl. Probab. 31 (1999) 394-421.
O. Kella and W. Whitt, A tandem fluid network with Lévy input, in: Queues and Related Models, eds. I. Basawa and U. Bhat (Oxford Univ. Press, Oxford, 1992) pp. 112-128.
W.E. Leland, M.S. Taqqu, W.Willinger and D.V.Wilson, On the self-similar nature of Ethernet traffic (extended version), IEEE/ACMTrans. Networking 2 (1994) 1-15.
A.G. Pakes, On the tails of waiting-time distributions, J. Appl. Probab. 12 (1975) 555-564.
A.K. Parekh and R.G. Gallager, A generalized processor sharing approach to flow control in integrated services networks: The single node case, IEEE/ACM Trans. Networking 1(3) (1993) 344-357.
A.K. Parekh and R.G. Gallager, A generalized processor sharing approach to flow control in integrated services networks: The multiple node case, IEEE/ACM Trans. Networking 2(2) (1994) 137-150.
V. Paxson and S. Floyd, Wide area traffic: The failure of Poisson modelling, IEEE/ACM Trans. Networking 3(3) (1995) 226-244.
K. Ramanan and P. Dupuis, Large deviation properties of data streams that share a buffer, Ann. Appl. Probab. 8(4) (1998) 1070-1129.
D. Stiliadis and A. Varma, Efficient fair queueing algorithms for packet-switched networks, IEEE/ACM Trans. Networking 6(2) (1998) 175-185.
W. Willinger, M.S. Taqqu, W.E. Leland and D.V. Wilson, Self-similarity in high-speed packet traffic: Analysis and modeling of Ethernet traffic measurements, Statist. Sci. 10 (1995) 67-85.
A.P. Zwart, Tail asymptotics for the busy period in the GI/G/1 queue, Math. Oper. Res. 26(3) (2001) 485-493.
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van Uitert, M., Borst, S. A Reduced-Load Equivalence for Generalised Processor Sharing Networks with Long-Tailed Input Flows. Queueing Systems 41, 123–163 (2002). https://doi.org/10.1023/A:1015785919268
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DOI: https://doi.org/10.1023/A:1015785919268