Tesis Doctoral leída en la Universidad Rey Juan Carlos de Madrid en 2016. Directores de la Tesis: Antonio García Marqués y Francisco Javier Ramos López
Wireless networks and power distribution grids are experiencing increasing demands on their
efficiency and reliability. Judicious methods for allocating scarce resources such as power and bandwidth
are of paramount importance. As a result, nonlinear optimization and signal processing tools
have been incorporated into the design of contemporary networks. This thesis develops schemes
for efficient resource allocation (RA) in such dynamic networks, with an emphasis in stochasticity,
which is accounted for in the problem formulation as well as in the algorithms and schemes
to solve those problems. Stochastic optimization and decomposition techniques are investigated
to develop low-complexity algorithms with specific applications in cross-layer design of wireless
communications, cognitive radio (CR) networks and smart power distribution systems.
The costs and constraints on the availability of network resources, together with diverse quality
of service (QoS) requirements, render network design, management and operation challenging
tasks. Moreover, when the available network state information (NSI) is time-varying, nodes must be
capable of adapting their operation parameters to the those variations. While traditional schemes
only exploited local information, or did not take into account uncertainty in system parameters
and future events, the methodology proposed in this thesis aims at designing schemes through
the solution of rigorously formulated mathematical problems involving random variables. The
three basic elements when formulating an optimization problem are the design variables (mainly
corresponding to resources to be allocated, and sensing and control information), system and QoS
constraints, and the objective function (usually formulated as weighted sums of utility functions).
Equilibrium between problem tractability and realistic modeling is also sought.
Previous works on dynamic RA for wireless networks that take into account cross-layer information
rely on convex optimization and dual decomposition techniques, while exploiting instantaneous
fading; whereas others build upon dynamic backpressure policies based on adaptive control tools
and aim to stabilize queues of the network. Based on such a background, our first contribution
is the design of a stochastic scheme that uses instantaneous fading and queue length information
to optimally allocate resources at the transport, link and physical layers. Theoretical results allow
to establish links between the transmit queue lengths and Lagrange multipliers; these links can be
used to estimate and control queuing delays and establish delay priorities among users. Experimental
results confirm that RA feasibility and optimality are preserved when the scheme employs
window averages of multipliers and queue lengths.
In the last years, CRs have emerged as the next-generation solution to the perceived spectrum
underutilization, thanks to their capability to limit the interference inflicted to coexisting
primary users (PUs). To do so CRs must sense the spectrum and dynamically adapt their transmission
parameters according to the available resources and sensed information. Existing works
limit CR-inflicted interference either through short- and long-term transmit-power constraints; or,
by controlling the probability of interfering with PU transmissions. As the sensed information
may be imperfect (due to errors or quantization) and get outdated, implementation of stochastic
RA algorithms offers the possibility of adapting the operation of the network to varying channel
conditions and PU behaviour. Motivated by these facts, we develop stochastic RA algorithms that optimize sum-rate performance of a CR network, limit the probability of interfering with PUs, and
jointly account for outdated and noisy NSI. Additional works in this context point out the tradeoff
between the sensing and RA and deal with their joint design. Hence, we also develop a jointly
optimal sensing and RA algorithm that additionally takes into account the temporal correlation of
the primary NSI and the sensing cost by means of stochastic dynamic programming (SDP). The
proposed schemes obtain optimal performance, account for imperfections in the acquired state
information, and are able to adapt to varying channel conditions. A two-step strategy significantly
reduces the computational solution complexity without loss of optimality, and its formulation allows
developing adaptive stochastic schemes. Numerical experiments confirm a significant performance
improvement with respect to low-complexity alternatives and allow to trace sensing-decision maps.
The last part of the thesis addresses the design of RA algorithms for smart grids, where
increasing penetration of renewable energy sources (RESs) pose new challenges related to variability
and uncertainty. Previous works formulate security-constrained and risk-limiting dispatch schemes
based on stochastic optimization tools, whereas recent works demonstrate that power inverters
can be controlled to effect voltage regulation. More recent works deal with smart grid operation
schemes in different timescales, or capitalize on stochastic approximation to limit the magnitude
of sporadic component overloads. Based on this background, we consider joint dispatch of slowand
fast- timescale distribution grid resources under average or probabilistic constraints over fasttimescale
decisions. Using an approximate grid model, the expected network operation cost is
minimized under inverter and voltage constraints, and the two-stage dispatch is formulated as a
stochastic saddle-point problem. The developed dispatch algorithms account for conventional and
alternative energy resources at different timescales, which are coupled across time in a stochastic
manner. Average and probabilistic voltage constraints are tackled using dual decomposition and
convex optimization. The resulting schemes rely on random samples of stochastic generation and
demand, and converge to optimal dispatch decisions.
The experimental results throughout the thesis confirm that the proposed stochastic RA
schemes achieve optimal or near-optimal performance, are robust against non-stationary NSI,
fulfill instantaneous constraints and asymptotically fulfill long-term constraints. Average power
consumption constraints and their treatment by means of dual stochastic gradients are common
ground for the cross-layer and CRs designs undertaken. A similar strategy is followed to deal with
(nonconvex) probability of interference constraints in CRs and voltage probabilistic constraints in
smart grids with manageable complexity.