3,198 research outputs found
Asymptotic optimality of maximum pressure policies in stochastic processing networks
We consider a class of stochastic processing networks. Assume that the
networks satisfy a complete resource pooling condition. We prove that each
maximum pressure policy asymptotically minimizes the workload process in a
stochastic processing network in heavy traffic. We also show that, under each
quadratic holding cost structure, there is a maximum pressure policy that
asymptotically minimizes the holding cost. A key to the optimality proofs is to
prove a state space collapse result and a heavy traffic limit theorem for the
network processes under a maximum pressure policy. We extend a framework of
Bramson [Queueing Systems Theory Appl. 30 (1998) 89--148] and Williams
[Queueing Systems Theory Appl. 30 (1998b) 5--25] from the multiclass queueing
network setting to the stochastic processing network setting to prove the state
space collapse result and the heavy traffic limit theorem. The extension can be
adapted to other studies of stochastic processing networks.Comment: Published in at http://dx.doi.org/10.1214/08-AAP522 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Stable Wireless Network Control Under Service Constraints
We consider the design of wireless queueing network control policies with
particular focus on combining stability with additional application-dependent
requirements. Thereby, we consequently pursue a cost function based approach
that provides the flexibility to incorporate constraints and requirements of
particular services or applications. As typical examples of such requirements,
we consider the reduction of buffer underflows in case of streaming traffic,
and energy efficiency in networks of battery powered nodes. Compared to the
classical throughput optimal control problem, such requirements significantly
complicate the control problem. We provide easily verifyable theoretical
conditions for stability, and, additionally, compare various candidate cost
functions applied to wireless networks with streaming media traffic. Moreover,
we demonstrate how the framework can be applied to the problem of energy
efficient routing, and we demonstrate the aplication of our framework in
cross-layer control problems for wireless multihop networks, using an advanced
power control scheme for interference mitigation, based on successive convex
approximation. In all scenarios, the performance of our control framework is
evaluated using extensive numerical simulations.Comment: Accepted for publication in IEEE Transactions on Control of Network
Systems. arXiv admin note: text overlap with arXiv:1208.297
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