IEEE/ACM Transactions on Networking (TON)
IEEE/ACM Transactions on Networking (TON)
The busy period in the fluid queue
SIGMETRICS '98/PERFORMANCE '98 Proceedings of the 1998 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Self-Similar Network Traffic and Performance Evaluation
Self-Similar Network Traffic and Performance Evaluation
Scheduling strategies and long-range dependence
Queueing Systems: Theory and Applications
Appendix: A primer on heavy-tailed distributions
Queueing Systems: Theory and Applications
Large Deviations for Small Buffers: An Insensitivity Result
Queueing Systems: Theory and Applications
Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers
Queueing Systems: Theory and Applications
Reduced-load equivalence and induced burstiness in GPS queues with long-tailed traffic flows
Reduced-load equivalence and induced burstiness in GPS queues with long-tailed traffic flows
Generalized processor sharing queues with heterogeneous traffic classes
Generalized processor sharing queues with heterogeneous traffic classes
Two coupled queues with heterogeneous traffic
Two coupled queues with heterogeneous traffic
Invited Fluid queues with long-tailed activity period distributions
Computer Communications
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)
Analysis of cycle stealing with switching times and thresholds
Performance Evaluation
ACM SIGMETRICS Performance Evaluation Review
User Association to Optimize Flow Level Performance in Wireless Systems with Dynamic Interference
NET-COOP '09 Proceedings of the 3rd Euro-NF Conference on Network Control and Optimization
IEEE/ACM Transactions on Networking (TON)
Practical adaptive user association policies for wireless systems with dynamic interference
IEEE/ACM Transactions on Networking (TON)
IEEE/ACM Transactions on Networking (TON)
Max-Weight Scheduling in Queueing Networks With Heavy-Tailed Traffic
IEEE/ACM Transactions on Networking (TON)
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We consider a system of two coupled queues Q1 and Q2. When both queues are backlogged, they are each served at unit rate. However, when one queue empties, the service rate at the other queue increases. Thus, the two queues are coupled through the mechanism for dynamically sharing surplus service capacity. We derive the asymptotic workload behavior at Q1 for various scenarios where at least one of the two queues has a heavy-tailed service time distribution. First of all, we consider a situation where the traffic load at Q1 is below the nominal unit service rate. We show that if the service time distribution at Q1 is heavy-tailed, then the workload behaves exactly as if Q1 is served in isolation at a constant rate, which only depends on the service time distribution at Q2 through its mean. In addition, we establish that if the service time distribution at Q1 is exponential, then the workload distribution is either exponential or semi-exponential, depending on whether the traffic load at Q2 exceeds the nominal service rate or not. Next, we focus on a regime where the traffic load at Q1 exceeds the nominal service rate, so that Q1 relies on the surplus capacity from Q2 to maintain stability. In that case, the workload distribution at Q1 is determined by the heaviest of the two service time distributions, so that Q1 may inherit potentially heavier-tailed characteristics from Q2.