Bounding blocking probabilities and throughput in queueing networks with buffer capacity constraints
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
State space collapse with application to heavy traffic limits for multiclass queueing networks
Queueing Systems: Theory and Applications
Heavy traffic resource pooling in parallel-server systems
Queueing Systems: Theory and Applications
Stable scheduling policies for fading wireless channels
IEEE/ACM Transactions on Networking (TON)
Control Techniques for Complex Networks
Control Techniques for Complex Networks
Stability and Asymptotic Optimality of Generalized MaxWeight Policies
SIAM Journal on Control and Optimization
On optimal scheduling algorithms for small generalized switches
IEEE/ACM Transactions on Networking (TON)
Delay analysis and optimality of scheduling policies for multihop wireless networks
IEEE/ACM Transactions on Networking (TON)
Dynamic server allocation to parallel queues with randomly varying connectivity
IEEE Transactions on Information Theory
Dynamic power allocation and routing for time-varying wireless networks
IEEE Journal on Selected Areas in Communications
Heavy traffic optimal resource allocation algorithms for cloud computing clusters
Proceedings of the 24th International Teletraffic Congress
Heavy-traffic-optimal scheduling with regular service guarantees in wireless networks
Proceedings of the fourteenth ACM international symposium on Mobile ad hoc networking and computing
Non-derivative algorithm design for efficient routing over unreliable stochastic networks
Performance Evaluation
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The Foster---Lyapunov theorem and its variants serve as the primary tools for studying the stability of queueing systems. In addition, it is well known that setting the drift of the Lyapunov function equal to zero in steady state provides bounds on the expected queue lengths. However, such bounds are often very loose due to the fact that they fail to capture resource pooling effects. The main contribution of this paper is to show that the approach of "setting the drift of a Lyapunov function equal to zero" can be used to obtain bounds on the steady-state queue lengths which are tight in the heavy-traffic limit. The key is to establish an appropriate notion of state-space collapse in terms of steady-state moments of weighted queue length differences and use this state-space collapse result when setting the Lyapunov drift equal to zero. As an application of the methodology, we prove the steady-state equivalent of the heavy-traffic optimality result of Stolyar for wireless networks operating under the MaxWeight scheduling policy.