7,209 research outputs found
Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services
This study develops an online predictive optimization framework for
dynamically operating a transit service in an area of crowd movements. The
proposed framework integrates demand prediction and supply optimization to
periodically redesign the service routes based on recently observed demand. To
predict demand for the service, we use Quantile Regression to estimate the
marginal distribution of movement counts between each pair of serviced
locations. The framework then combines these marginals into a joint demand
distribution by constructing a Gaussian copula, which captures the structure of
correlation between the marginals. For supply optimization, we devise a linear
programming model, which simultaneously determines the route structure and the
service frequency according to the predicted demand. Importantly, our framework
both preserves the uncertainty structure of future demand and leverages this
for robust route optimization, while keeping both components decoupled. We
evaluate our framework using a real-world case study of autonomous mobility in
a university campus in Denmark. The results show that our framework often
obtains the ground truth optimal solution, and can outperform conventional
methods for route optimization, which do not leverage full predictive
distributions.Comment: 34 pages, 12 figures, 5 table
Optimizing flow rates in a queueing network with side constraints
Network Analysis;operations research
Markov Decision Processes with Applications in Wireless Sensor Networks: A Survey
Wireless sensor networks (WSNs) consist of autonomous and resource-limited
devices. The devices cooperate to monitor one or more physical phenomena within
an area of interest. WSNs operate as stochastic systems because of randomness
in the monitored environments. For long service time and low maintenance cost,
WSNs require adaptive and robust methods to address data exchange, topology
formulation, resource and power optimization, sensing coverage and object
detection, and security challenges. In these problems, sensor nodes are to make
optimized decisions from a set of accessible strategies to achieve design
goals. This survey reviews numerous applications of the Markov decision process
(MDP) framework, a powerful decision-making tool to develop adaptive algorithms
and protocols for WSNs. Furthermore, various solution methods are discussed and
compared to serve as a guide for using MDPs in WSNs
Convexity and Robustness of Dynamic Traffic Assignment and Freeway Network Control
We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA)
problem to design optimal traffic flow controls for freeway networks as modeled
by the Cell Transmission Model, using variable speed limit, ramp metering, and
routing. We consider two optimal control problems: the DTA problem, where
turning ratios are part of the control inputs, and the Freeway Network Control
(FNC), where turning ratios are instead assigned exogenous parameters. It is
known that relaxation of the supply and demand constraints in the cell-based
formulations of the DTA problem results in a linear program. However, solutions
to the relaxed problem can be infeasible with respect to traffic dynamics.
Previous work has shown that such solutions can be made feasible by proper
choice of ramp metering and variable speed limit control for specific traffic
networks. We extend this procedure to arbitrary networks and provide insight
into the structure and robustness of the proposed optimal controllers. For a
network consisting only of ordinary, merge, and diverge junctions, where the
cells have linear demand functions and affine supply functions with identical
slopes, and the cost is the total traffic volume, we show, using the maximum
principle, that variable speed limits are not needed in order to achieve
optimality in the FNC problem, and ramp metering is sufficient. We also prove
bounds on perturbation of the controlled system trajectory in terms of
perturbations in initial traffic volume and exogenous inflows. These bounds,
which leverage monotonicity properties of the controlled trajectory, are shown
to be in close agreement with numerical simulation results
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