1,196 research outputs found
Reducing Revenue to Welfare Maximization: Approximation Algorithms and other Generalizations
It was recently shown in [http://arxiv.org/abs/1207.5518] that revenue
optimization can be computationally efficiently reduced to welfare optimization
in all multi-dimensional Bayesian auction problems with arbitrary (possibly
combinatorial) feasibility constraints and independent additive bidders with
arbitrary (possibly combinatorial) demand constraints. This reduction provides
a poly-time solution to the optimal mechanism design problem in all auction
settings where welfare optimization can be solved efficiently, but it is
fragile to approximation and cannot provide solutions to settings where welfare
maximization can only be tractably approximated. In this paper, we extend the
reduction to accommodate approximation algorithms, providing an approximation
preserving reduction from (truthful) revenue maximization to (not necessarily
truthful) welfare maximization. The mechanisms output by our reduction choose
allocations via black-box calls to welfare approximation on randomly selected
inputs, thereby generalizing also our earlier structural results on optimal
multi-dimensional mechanisms to approximately optimal mechanisms. Unlike
[http://arxiv.org/abs/1207.5518], our results here are obtained through novel
uses of the Ellipsoid algorithm and other optimization techniques over {\em
non-convex regions}
Dynamic Server Allocation over Time Varying Channels with Switchover Delay
We consider a dynamic server allocation problem over parallel queues with
randomly varying connectivity and server switchover delay between the queues.
At each time slot the server decides either to stay with the current queue or
switch to another queue based on the current connectivity and the queue length
information. Switchover delay occurs in many telecommunications applications
and is a new modeling component of this problem that has not been previously
addressed. We show that the simultaneous presence of randomly varying
connectivity and switchover delay changes the system stability region and the
structure of optimal policies. In the first part of the paper, we consider a
system of two parallel queues, and develop a novel approach to explicitly
characterize the stability region of the system using state-action frequencies
which are stationary solutions to a Markov Decision Process (MDP) formulation.
We then develop a frame-based dynamic control (FBDC) policy, based on the
state-action frequencies, and show that it is throughput-optimal asymptotically
in the frame length. The FBDC policy is applicable to a broad class of network
control systems and provides a new framework for developing throughput-optimal
network control policies using state-action frequencies. Furthermore, we
develop simple Myopic policies that provably achieve more than 90% of the
stability region. In the second part of the paper, we extend our results to
systems with an arbitrary but finite number of queues.Comment: 38 Pages, 18 figures. arXiv admin note: substantial text overlap with
arXiv:1008.234
Slow Adaptive OFDMA Systems Through Chance Constrained Programming
Adaptive OFDMA has recently been recognized as a promising technique for
providing high spectral efficiency in future broadband wireless systems. The
research over the last decade on adaptive OFDMA systems has focused on adapting
the allocation of radio resources, such as subcarriers and power, to the
instantaneous channel conditions of all users. However, such "fast" adaptation
requires high computational complexity and excessive signaling overhead. This
hinders the deployment of adaptive OFDMA systems worldwide. This paper proposes
a slow adaptive OFDMA scheme, in which the subcarrier allocation is updated on
a much slower timescale than that of the fluctuation of instantaneous channel
conditions. Meanwhile, the data rate requirements of individual users are
accommodated on the fast timescale with high probability, thereby meeting the
requirements except occasional outage. Such an objective has a natural chance
constrained programming formulation, which is known to be intractable. To
circumvent this difficulty, we formulate safe tractable constraints for the
problem based on recent advances in chance constrained programming. We then
develop a polynomial-time algorithm for computing an optimal solution to the
reformulated problem. Our results show that the proposed slow adaptation scheme
drastically reduces both computational cost and control signaling overhead when
compared with the conventional fast adaptive OFDMA. Our work can be viewed as
an initial attempt to apply the chance constrained programming methodology to
wireless system designs. Given that most wireless systems can tolerate an
occasional dip in the quality of service, we hope that the proposed methodology
will find further applications in wireless communications
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