Stochastic ordering for Markov processes on partially ordered spaces
Mathematics of Operations Research
Analysis and simulation of a fair queueing algorithm
SIGCOMM '89 Symposium proceedings on Communications architectures & protocols
IEEE/ACM Transactions on Networking (TON)
Time-shared Systems: a theoretical treatment
Journal of the ACM (JACM)
Sharing a Processor Among Many Job Classes
Journal of the ACM (JACM)
Fair end-to-end window-based congestion control
IEEE/ACM Transactions on Networking (TON)
Impact of fairness on Internet performance
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Generalized processor sharing with heterogeneous traffic classes
ACM SIGMETRICS Performance Evaluation Review
Bandwidth sharing: objectives and algorithms
IEEE/ACM Transactions on Networking (TON)
On Stochastic Bounds for Monotonic Processor Sharing Networks
Queueing Systems: Theory and Applications
Nearly insensitive bounds on SMART scheduling
SIGMETRICS '05 Proceedings of the 2005 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Queueing Systems: Theory and Applications
A survey on discriminatory processor sharing
Queueing Systems: Theory and Applications
Heavy-traffic approximations for linear networks operating under α-fair bandwidth-sharing policies
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Flow-level stability of data networks with non-convex and time-varying rate regions
Proceedings of the 2007 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Stability of Parallel Queueing Systems with Coupled Service Rates
Discrete Event Dynamic Systems
Assessing the efficiency of resource allocations in bandwidth-sharing networks
Performance Evaluation
Comparison of bandwidth-sharing policies in a linear network
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Energy-aware capacity scaling in virtualized environments with performance guarantees
Performance Evaluation
Necessary and sufficient conditions for strong comparability of multicomponent systems
Discrete Event Dynamic Systems
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We study multi-dimensional stochastic processes that arise in queueing models used in the performance evaluation of wired and wireless networks. The evolution of the stochastic process is determined by the scheduling policy used in the associated queueing network. For general arrival and service processes, we give sufficient conditions in order to compare sample-path wise the workload and the number of users under different policies. This allows us to evaluate the performance of the system under various policies in terms of stability, the mean overall delay and the mean holding cost. We apply the general framework to linear networks, where users of one class require service from several shared resources simultaneously. For the important family of weighted 驴-fair policies, stability results are derived and monotonicity of the mean holding cost with respect to the fairness parameter 驴 and the relative weights is established. In order to broaden the comparison results, we investigate a heavy-traffic regime and perform numerical experiments. In addition, we study a single-server queue with two user classes, and show that under Discriminatory Processor Sharing (DPS) or Generalized Processor Sharing (GPS) the mean overall sojourn time is monotone with respect to the ratio of the weights. Finally we extend the framework to obtain comparison results that cover the single-server queue with an arbitrary number of classes as well.