738 research outputs found
A Compartmental Model for Traffic Networks and its Dynamical Behavior
We propose a macroscopic traffic network flow model suitable for analysis as
a dynamical system, and we qualitatively analyze equilibrium flows as well as
convergence. Flows at a junction are determined by downstream supply of
capacity as well as upstream demand of traffic wishing to flow through the
junction. This approach is rooted in the celebrated Cell Transmission Model for
freeway traffic flow. Unlike related results which rely on certain system
cooperativity properties, our model generally does not possess these
properties. We show that the lack of cooperativity is in fact a useful feature
that allows traffic control methods, such as ramp metering, to be effective.
Finally, we leverage the results of the paper to develop a linear program for
optimal ramp metering
On resilient control of dynamical flow networks
Resilience has become a key aspect in the design of contemporary
infrastructure networks. This comes as a result of ever-increasing loads,
limited physical capacity, and fast-growing levels of interconnectedness and
complexity due to the recent technological advancements. The problem has
motivated a considerable amount of research within the last few years,
particularly focused on the dynamical aspects of network flows, complementing
more classical static network flow optimization approaches. In this tutorial
paper, a class of single-commodity first-order models of dynamical flow
networks is considered. A few results recently appeared in the literature and
dealing with stability and robustness of dynamical flow networks are gathered
and originally presented in a unified framework. In particular, (differential)
stability properties of monotone dynamical flow networks are treated in some
detail, and the notion of margin of resilience is introduced as a quantitative
measure of their robustness. While emphasizing methodological aspects --
including structural properties, such as monotonicity, that enable tractability
and scalability -- over the specific applications, connections to
well-established road traffic flow models are made.Comment: accepted for publication in Annual Reviews in Control, 201
Dynamical Systems on Networks: A Tutorial
We give a tutorial for the study of dynamical systems on networks. We focus
especially on "simple" situations that are tractable analytically, because they
can be very insightful and provide useful springboards for the study of more
complicated scenarios. We briefly motivate why examining dynamical systems on
networks is interesting and important, and we then give several fascinating
examples and discuss some theoretical results. We also briefly discuss
dynamical systems on dynamical (i.e., time-dependent) networks, overview
software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than
original version, some reorganization and also more pointers to interesting
direction
Prediction and predictability of global epidemics: the role of the airline transportation network
The systematic study of large-scale networks has unveiled the ubiquitous
presence of connectivity patterns characterized by large scale heterogeneities
and unbounded statistical fluctuations. These features affect dramatically the
behavior of the diffusion processes occurring on networks, determining the
ensuing statistical properties of their evolution pattern and dynamics. In this
paper, we investigate the role of the large scale properties of the airline
transportation network in determining the global evolution of emerging disease.
We present a stochastic computational framework for the forecast of global
epidemics that considers the complete world-wide air travel infrastructure
complemented with census population data. We address two basic issues in global
epidemic modeling: i) We study the role of the large scale properties of the
airline transportation network in determining the global diffusion pattern of
emerging diseases; ii) We evaluate the reliability of forecasts and outbreak
scenarios with respect to the intrinsic stochasticity of disease transmission
and traffic flows. In order to address these issues we define a set of novel
quantitative measures able to characterize the level of heterogeneity and
predictability of the epidemic pattern. These measures may be used for the
analysis of containment policies and epidemic risk assessment.Comment: 20 pages, 5 figure
On resilient control of dynamical flow networks
Resilience has become a key aspect in the design of contemporary infrastructure networks. This comes as a result of ever-increasing loads, limited physical capacity, and fast-growing levels of interconnectedness and complexity due to the recent technological advancements. The problem has motivated a considerable amount of research within the last few years, particularly focused on the dynamical aspects of network flows, complementing more classical static network flow optimization approaches.In this tutorial paper, a class of single-commodity first-order models of dynamical flow networks is considered. A few results recently appeared in the literature and dealing with stability and robustness of dynamical flow networks are gathered and originally presented in a unified framework. In particular, (differential) stability properties of monotone dynamical flow networks are treated in some detail, and the notion of margin of resilience is introduced as a quantitative measure of their robustness. While emphasizing methodological aspects -including structural properties, such as monotonicity, that enable tractability and scalability- over the specific applications, connections to well-established road traffic flow models are made
Some Remarks about the Complexity of Epidemics Management
Recent outbreaks of Ebola, H1N1 and other infectious diseases have shown that
the assumptions underlying the established theory of epidemics management are
too idealistic. For an improvement of procedures and organizations involved in
fighting epidemics, extended models of epidemics management are required. The
necessary extensions consist in a representation of the management loop and the
potential frictions influencing the loop. The effects of the non-deterministic
frictions can be taken into account by including the measures of robustness and
risk in the assessment of management options. Thus, besides of the increased
structural complexity resulting from the model extensions, the computational
complexity of the task of epidemics management - interpreted as an optimization
problem - is increased as well. This is a serious obstacle for analyzing the
model and may require an additional pre-processing enabling a simplification of
the analysis process. The paper closes with an outlook discussing some
forthcoming problems
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