207 research outputs found
A Distributed Newton Method for Network Utility Maximization
Most existing work uses dual decomposition and subgradient methods to solve
Network Utility Maximization (NUM) problems in a distributed manner, which
suffer from slow rate of convergence properties. This work develops an
alternative distributed Newton-type fast converging algorithm for solving
network utility maximization problems with self-concordant utility functions.
By using novel matrix splitting techniques, both primal and dual updates for
the Newton step can be computed using iterative schemes in a decentralized
manner with limited information exchange. Similarly, the stepsize can be
obtained via an iterative consensus-based averaging scheme. We show that even
when the Newton direction and the stepsize in our method are computed within
some error (due to finite truncation of the iterative schemes), the resulting
objective function value still converges superlinearly to an explicitly
characterized error neighborhood. Simulation results demonstrate significant
convergence rate improvement of our algorithm relative to the existing
subgradient methods based on dual decomposition.Comment: 27 pages, 4 figures, LIDS report, submitted to CDC 201
Optimal Reverse Carpooling Over Wireless Networks - A Distributed Optimization Approach
We focus on a particular form of network coding, reverse carpooling, in a
wireless network where the potentially coded transmitted messages are to be
decoded immediately upon reception. The network is fixed and known, and the
system performance is measured in terms of the number of wireless broadcasts
required to meet multiple unicast demands. Motivated by the structure of the
coding scheme, we formulate the problem as a linear program by introducing a
flow variable for each triple of connected nodes. This allows us to have a
formulation polynomial in the number of nodes. Using dual decomposition and
projected subgradient method, we present a decentralized algorithm to obtain
optimal routing schemes in presence of coding opportunities. We show that the
primal sub-problem can be expressed as a shortest path problem on an
\emph{edge-graph}, and the proposed algorithm requires each node to exchange
information only with its neighbors.Comment: submitted to CISS 201
On Resource Allocation in Fading Multiple Access Channels - An Efficient Approximate Projection Approach
We consider the problem of rate and power allocation in a multiple-access
channel. Our objective is to obtain rate and power allocation policies that
maximize a general concave utility function of average transmission rates on
the information theoretic capacity region of the multiple-access channel. Our
policies does not require queue-length information. We consider several
different scenarios. First, we address the utility maximization problem in a
nonfading channel to obtain the optimal operating rates, and present an
iterative gradient projection algorithm that uses approximate projection. By
exploiting the polymatroid structure of the capacity region, we show that the
approximate projection can be implemented in time polynomial in the number of
users. Second, we consider resource allocation in a fading channel. Optimal
rate and power allocation policies are presented for the case that power
control is possible and channel statistics are available. For the case that
transmission power is fixed and channel statistics are unknown, we propose a
greedy rate allocation policy and provide bounds on the performance difference
of this policy and the optimal policy in terms of channel variations and
structure of the utility function. We present numerical results that
demonstrate superior convergence rate performance for the greedy policy
compared to queue-length based policies. In order to reduce the computational
complexity of the greedy policy, we present approximate rate allocation
policies which track the greedy policy within a certain neighborhood that is
characterized in terms of the speed of fading.Comment: 32 pages, Submitted to IEEE Trans. on Information Theor
Access-Network Association Policies for Media Streaming in Heterogeneous Environments
We study the design of media streaming applications in the presence of
multiple heterogeneous wireless access methods with different throughputs and
costs. Our objective is to analytically characterize the trade-off between the
usage cost and the Quality of user Experience (QoE), which is represented by
the probability of interruption in media playback and the initial waiting time.
We model each access network as a server that provides packets to the user
according to a Poisson process with a certain rate and cost. Blocks are coded
using random linear codes to alleviate the duplicate packet reception problem.
Users must take decisions on how many packets to buffer before playout, and
which networks to access during playout. We design, analyze and compare several
control policies with a threshold structure. We formulate the problem of
finding the optimal control policy as an MDP with a probabilistic constraint.
We present the HJB equation for this problem by expanding the state space, and
exploit it as a verification method for optimality of the proposed control law.Comment: submitted to CDC 201
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