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Multicast networks : capacity, algorithms, and implementation
textIn this dissertation, we investigate the capacity and performance of wireless networks with an emphasis on multicast traffic. The defining characteristic of a multicast network is a network where a number of different destinations all require the information generated by a single source. The models that we explore differ in the nature of the nodes from all-mobile case where all nodes are mobile to hybrid case where some nodes are mobile and some are static. We investigate different performance measure for these wireless multicast networks: upper bounds, capacity scaling laws, and achievable rates. The understanding of these measures for such networks helps in the development of efficient algorithms for operating these networks.
In addition, we study the practical realization of algorithms for real-time streaming of rich multimedia content in the context of mobile wireless networks for embedded and cyberphysical systems. Our initial work is in the context of unicast and multiple unicast systems over an autonomous aerial vehicle (AAV) network. Bandwidth requirements and stringent delay constraints of real-time video streaming, paired with limitations on computational complexity and power consumptions imposed by the underlying implementation platform, make cross-layer and cross-domain co-design approaches a necessity. In this dissertation, we propose a novel, low-complexity rate-distortion optimized (RDO) protocol specifically targeted at video streaming over mobile embedded networks. First, we test the performance of our RDO algorithm on simulation models developed for aerial mobility of multiple wirelessly communicating AAVs. Second, we test the performance of our RDO algorithm and other proposed adaptive algorithms on a real network of AAVs and present a comparative study between these different algorithms. Note that generalizing these algorithms to multicast settings is relatively straightforward and thus is not highlighted to a great degree in this thesis.Electrical and Computer Engineerin
Neural Delay Differential Equations: System Reconstruction and Image Classification
Neural Ordinary Differential Equations (NODEs), a framework of
continuous-depth neural networks, have been widely applied, showing exceptional
efficacy in coping with representative datasets. Recently, an augmented
framework has been developed to overcome some limitations that emerged in the
application of the original framework. In this paper, we propose a new class of
continuous-depth neural networks with delay, named Neural Delay Differential
Equations (NDDEs). To compute the corresponding gradients, we use the adjoint
sensitivity method to obtain the delayed dynamics of the adjoint. Differential
equations with delays are typically seen as dynamical systems of infinite
dimension that possess more fruitful dynamics. Compared to NODEs, NDDEs have a
stronger capacity of nonlinear representations. We use several illustrative
examples to demonstrate this outstanding capacity. Firstly, we successfully
model the delayed dynamics where the trajectories in the lower-dimensional
phase space could be mutually intersected and even chaotic in a model-free or
model-based manner. Traditional NODEs, without any argumentation, are not
directly applicable for such modeling. Secondly, we achieve lower loss and
higher accuracy not only for the data produced synthetically by complex models
but also for the CIFAR10, a well-known image dataset. Our results on the NDDEs
demonstrate that appropriately articulating the elements of dynamical systems
into the network design is truly beneficial in promoting network performance.Comment: 11 pages, 12 figures. arXiv admin note: substantial text overlap with
arXiv:2102.1080
Enriching the tactical network design of express service carriers with fleet scheduling characteristics
Express service carriers provide time-guaranteed deliveries of parcels via a network consisting of nodes and hubs. In this, nodes take care of the collection and delivery of parcels, and hubs have the function to consolidate parcels in between the nodes. The tactical network design problem assigns nodes to hubs, determines arcs between hubs, and routes parcels through the network. Afterwards, fleet scheduling creates a schedule for vehicles operated in the network. The strong relation between flow routing and fleet scheduling makes it difficult to optimise the network cost. Due to this complexity, fleet scheduling and network design are usually decoupled. We propose a new tactical network design model that is able to include fleet scheduling characteristics (like vehicle capacities, vehicle balancing, and drivers' legislations) in the network design. The model is tested on benchmark data based on instances from an express provider, resulting in significant cost reductions
Jamming transition in air transportation networks
In this work we present a model of an air transportation traffic system from
the complex network modelling viewpoint. In the network, every node corresponds
to a given airport, and two nodes are connected by means of flight routes. Each
node is weighted according to its load capacity, and links are weighted
according to the Euclidean distance that separates each pair of nodes. Local
rules describing the behavior of individual nodes in terms of the surrounding
flow have been also modelled, and a random network topology has been chosen in
a baseline approach. Numerical simulations describing the diffusion of a given
number of agents (aircraft) in this network show the onset of a jamming
transition that distinguishes an efficient regime with null amount of airport
queues and high diffusivity (free phase) and a regime where bottlenecks
suddenly take place, leading to a poor aircraft diffusion (congested phase).
Fluctuations are maximal around the congestion threshold, suggesting that the
transition is critical. We then proceed by exploring the robustness of our
results in neutral random topologies by embedding the model in heterogeneous
networks. Specifically, we make use of the European air transportation network
formed by 858 airports and 11170 flight routes connecting them, which we show
to be scale-free. The jamming transition is also observed in this case. These
results and methodologies may introduce relevant decision making procedures in
order to optimize the air transportation traffic
Cross-layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks
This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc
wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints.
By dual decomposition, the resource allocation problem
naturally decomposes into three subproblems: congestion control,
routing and scheduling that interact through congestion price.
The global convergence property of this algorithm is proved. We
next extend the dual algorithm to handle networks with timevarying
channels and adaptive multi-rate devices. The stability
of the resulting system is established, and its performance is
characterized with respect to an ideal reference system which
has the best feasible rate region at link layer.
We then generalize the aforementioned results to a general
model of queueing network served by a set of interdependent
parallel servers with time-varying service capabilities, which
models many design problems in communication networks. We
show that for a general convex optimization problem where a
subset of variables lie in a polytope and the rest in a convex set,
the dual-based algorithm remains stable and optimal when the
constraint set is modulated by an irreducible finite-state Markov
chain. This paper thus presents a step toward a systematic way
to carry out cross-layer design in the framework of “layering as
optimization decomposition” for time-varying channel models
Dynamic vs Oblivious Routing in Network Design
Consider the robust network design problem of finding a minimum cost network
with enough capacity to route all traffic demand matrices in a given polytope.
We investigate the impact of different routing models in this robust setting:
in particular, we compare \emph{oblivious} routing, where the routing between
each terminal pair must be fixed in advance, to \emph{dynamic} routing, where
routings may depend arbitrarily on the current demand. Our main result is a
construction that shows that the optimal cost of such a network based on
oblivious routing (fractional or integral) may be a factor of
\BigOmega(\log{n}) more than the cost required when using dynamic routing.
This is true even in the important special case of the asymmetric hose model.
This answers a question in \cite{chekurisurvey07}, and is tight up to constant
factors. Our proof technique builds on a connection between expander graphs and
robust design for single-sink traffic patterns \cite{ChekuriHardness07}
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