20 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
Resilience of Traffic Networks with Partially Controlled Routing
This paper investigates the use of Infrastructure-To-Vehicle (I2V)
communication to generate routing suggestions for drivers in transportation
systems, with the goal of optimizing a measure of overall network congestion.
We define link-wise levels of trust to tolerate the non-cooperative behavior of
part of the driver population, and we propose a real-time optimization
mechanism that adapts to the instantaneous network conditions and to sudden
changes in the levels of trust. Our framework allows us to quantify the
improvement in travel time in relation to the degree at which drivers follow
the routing suggestions. We then study the resilience of the system, measured
as the smallest change in routing choices that results in roads reaching their
maximum capacity. Interestingly, our findings suggest that fluctuations in the
extent to which drivers follow the provided routing suggestions can cause
failures of certain links. These results imply that the benefits of using
Infrastructure-To-Vehicle communication come at the cost of new fragilities,
that should be appropriately addressed in order to guarantee the reliable
operation of the infrastructure.Comment: Accepted for presentation at the IEEE 2019 American Control
Conferenc
Stability and phase transitions of dynamical flow networks with finite capacities
We study deterministic continuous-time lossy dynamical flow networks with
constant exogenous demands, fixed routing, and finite flow and buffer
capacities. In the considered model, when the total net flow in a cell
---consisting of the difference between the total flow directed towards it
minus the outflow from it--- exceeds a certain capacity constraint, then the
exceeding part of it leaks out of the system. The ensuing network flow dynamics
is a linear saturated system with compact state space that we analyze using
tools from monotone systems and contraction theory. Specifically, we prove that
there exists a set of equilibria that is globally asymptotically stable. Such
equilibrium set reduces to a single globally asymptotically stable equilibrium
for generic exogenous demand vectors. Moreover, we show that the critical
exogenous demand vectors giving rise to non-unique equilibria correspond to
phase transitions in the asymptotic behavior of the dynamical flow network.Comment: 7 pages, 4 figures, submitted at IFAC 202
Resilience of Dynamic Routing in the Face of Recurrent and Random Sensing Faults
Feedback dynamic routing is a commonly used control strategy in
transportation systems. This class of control strategies relies on real-time
information about the traffic state in each link. However, such information may
not always be observable due to temporary sensing faults. In this article, we
consider dynamic routing over two parallel routes, where the sensing on each
link is subject to recurrent and random faults. The faults occur and clear
according to a finite-state Markov chain. When the sensing is faulty on a link,
the traffic state on that link appears to be zero to the controller. Building
on the theories of Markov processes and monotone dynamical systems, we derive
lower and upper bounds for the resilience score, i.e. the guaranteed throughput
of the network, in the face of sensing faults by establishing stability
conditions for the network. We use these results to study how a variety of key
parameters affect the resilience score of the network. The main conclusions
are: (i) Sensing faults can reduce throughput and destabilize a nominally
stable network; (ii) A higher failure rate does not necessarily reduce
throughput, and there may exist a worst rate that minimizes throughput; (iii)
Higher correlation between the failure probabilities of two links leads to
greater throughput; (iv) A large difference in capacity between two links can
result in a drop in throughput.Comment: 17 pages, 4 figures, accepted by ACC 202
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
Compositional Synthesis via a Convex Parameterization of Assume-Guarantee Contracts
We develop an assume-guarantee framework for control of large scale linear
(time-varying) systems from finite-time reach and avoid or infinite-time
invariance specifications. The contracts describe the admissible set of states
and controls for individual subsystems. A set of contracts compose correctly if
mutual assumptions and guarantees match in a way that we formalize. We propose
a rich parameterization of contracts such that the set of parameters that
compose correctly is convex. Moreover, we design a potential function of
parameters that describes the distance of contracts from a correct composition.
Thus, the verification and synthesis for the aggregate system are broken to
solving small convex programs for individual subsystems, where correctness is
ultimately achieved in a compositional way. Illustrative examples demonstrate
the scalability of our method