Generalized processor sharing with light-tailed and heavy-tailed input

Sem C. Borst · Michel Mandjes · Miranda van Uitert

64 citations0/0 files storedIEEE/ACM Transactions on Networking

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Age of Information Optimization

Abstract

We consider a queue fed by a mixture of light-tailed and heavy-tailed traffic. The two traffic flows are served in accordance with the generalized processor sharing (GPS) discipline. GPS-based scheduling algorithms, such as weighted fair queueing, have emerged as an important mechanism for achieving service differentiation in integrated networks. We derive the asymptotic workload behavior of the light-tailed traffic flow under the assumption that its GPS weight is larger than its traffic intensity. The GPS mechanism ensures that the workload is bounded above by that in an isolated system with the light-tailed flow served in isolation at a constant rate equal to its GPS weight. We show that the workload distribution is in fact asymptotically equivalent to that in the isolated system, multiplied with a certain pre-factor, which accounts for the interaction with the heavy-tailed flow. Specifically, the pre-factor represents the probability that the heavy-tailed flow is backlogged long enough for the light-tailed flow to reach overflow. The results provide crucial qualitative insight in the typical overflow scenario.

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References

1994Logarithmic asymptotics for steady-state tail probabilities in a single-server queue 1975On the tails of waiting-time distributions 1999Appendix: A primer on heavy-tailed distributions 1999Asymptotic results for multiplexing subexponential on-off processes 1989How large delays build up in a GI/G/1 queue

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2007Beyond processor sharing 2011Queue-Length Asymptotics for Generalized Max-Weight Scheduling in the Presence of Heavy-Tailed Traffic 2013Max-Weight Scheduling in Queueing Networks With Heavy-Tailed Traffic 2009Scheduling policies for single-hop networks with heavy-tailed traffic 2008The heavy traffic limit of an unbalanced generalized processor sharing model 2003Generalized processor sharing queues 2010Approximation for a two-class weighted fair queueing discipline 2008QoS Analysis of Queuing Systems with Self-Similar Traffic and Heavy-Tailed Packet Sizes

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