Generalized processor sharing with heterogeneous traffic classes
ACM SIGMETRICS Performance Evaluation Review
Finite buffer queue with generalized processor sharing and heavy-tailed input processes
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
User-level performance of elastic traffic in a differentiated-services environment
Performance Evaluation
Heavy Tails: The Effect of the Service Discipline
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
Analysis of cycle stealing with switching cost
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
The impact of the service discipline on delay asymptotics
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Generalized processor sharing with light-tailed and heavy-tailed input
IEEE/ACM Transactions on Networking (TON)
Reduced Load Equivalence under Subexponentiality
Queueing Systems: Theory and Applications
On Stochastic Bounds for Monotonic Processor Sharing Networks
Queueing Systems: Theory and Applications
Analysis of cycle stealing with switching times and thresholds
Performance Evaluation
A sample path relation for the sojourn times in G/G/1-PS systems and its applications
Queueing Systems: Theory and Applications
GPS scheduling: selection of optimal weights and comparison with strict priorities
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
ACM SIGMETRICS Performance Evaluation Review
Computers and Operations Research
Waiting times for M/M systems under state-dependent processor sharing
Queueing Systems: Theory and Applications
Asymptotic behavior of generalized processor sharing queues under subexponential assumptions
Queueing Systems: Theory and Applications
On sojourn times in M/GI systems under state-dependent processor sharing
Queueing Systems: Theory and Applications
Insensitivity and stability of random-access networks
Performance Evaluation
Tandem queues with subexponential service times and finite buffers
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
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We analyze the queueing behavior of long-tailed traffic flows under the Generalized Processor Sharing (GPS) discipline. We show a sharp dichotomy in qualitative behavior, depending on the relative values of the weight parameters. For certain weight combinations, an individual flow with long-tailed traffic characteristics is effectively served at a constant rate. The effective service rate may be interpreted as the maximum average traffic rate for the flow to be stable, which is only influenced by the traffic characteristics of the other flows through their average rates. In particular, the flow is essentially immune from excessive activity of flows with ‘heavier’-tailed traffic characteristics. In many situations, the effective service rate is simply the link rate reduced by the aggregate average rate of the other flows. This confirms that GPS-based scheduling algorithms provide a potential mechanism for extracting significant multiplexing gains, while isolating individual flows. For other weight combinations however, a flow may be strongly affected by the activity of ‘heavier’-tailed flows, and may inherit their traffic characteristics, causing induced burstiness. The stark contrast in qualitative behavior illustrates the crucial importance of the weight parameters.