156,075 research outputs found
Existence of simultaneous route and departure choice dynamic user equilibrium
This paper is concerned with the existence of the simultaneous
route-and-departure choice dynamic user equilibrium (SRDC-DUE) in continuous
time, first formulated as an infinite-dimensional variational inequality in
Friesz et al. (1993). In deriving our existence result, we employ the
generalized Vickrey model (GVM) introduced in and to formulate the underlying
network loading problem. As we explain, the GVM corresponds to a path delay
operator that is provably strongly continuous on the Hilbert space of interest.
Finally, we provide the desired SRDC-DUE existence result for general
constraints relating path flows to a table of fixed trip volumes without
invocation of a priori bounds on the path flows.Comment: 21 page
An exact solution approach based on column generation and a partial-objective constraint to design a cellulosic biofuel supply chain
AbstractThis study provides an exact solution method to solve a mixed-integer linear programming model that prescribes an optimal design of a cellulosic biofuel supply chain. An embedded structure can be transformed to a generalized minimum cost flow problem, which is used as a sub-problem in a column generation approach, to solve the linear relaxation of the mixed-integer program. This study proposes a dynamic programming algorithm to solve the sub-problem in O(m) time, generating improving path-flows. It proposes an inequality, called the partial objective constraint, which is based on the portion of the objective function associated with binary variables, to underlie a branch-and-cut approach. Computational tests show that the proposed solution approach solves most instances faster than a state-of-the-art commercial solver (CPLEX)
Hydrodynamic equations for incompressible inviscid fluid in terms of generalized stream function
Hydrodynamic equations for ideal incompressible fluid are written in terms of
generalized stream function. Two-dimensional version of these equations is
transformed to the form of one dynamic equation for the stream function. This
equation contains arbitrary function which is determined by inflow conditions
given on the boundary. To determine unique solution, velocity and vorticity
(but not only velocity itself) must be given on the boundary. This unexpected
circumstance may be interpreted in the sense that the fluid has more degrees of
freedom, than it was believed. Besides, the vorticity is less observable
quantity as compared with the velocity. It is shown that the Clebsch potentials
are used essentially at the description of vortical flow.Comment: 31 pages, 0 figures, The paper is reduced. Consideration of
nonstationary flow has been remove
Canonical description of ideal magnetohydrodynamic flows and integrals of motion
In the framework of the variational principle the canonical variables
describing ideal magnetohydrodynamic (MHD) flows of general type (i.e., with
spatially varying entropy and nonzero values of all topological invariants) are
introduced. The corresponding complete velocity representation enables us not
only to describe the general type flows in terms of single-valued functions,
but also to solve the intriguing problem of the ``missing'' MHD integrals of
motion. The set of hitherto known MHD local invariants and integrals of motion
appears to be incomplete: for the vanishing magnetic field it does not reduce
to the set of the conventional hydrodynamic invariants. And if the MHD analogs
of the vorticity and helicity were discussed earlier for the particular cases,
the analog of Ertel invariant has been so far unknown. It is found that on the
basis of the new invariants introduced a wide set of high-order invariants can
be constructed. The new invariants are relevant both for the deeper insight
into the problem of the topological structure of the MHD flows as a whole and
for the examination of the stability problems. The additional advantage of the
proposed approach is that it enables one to deal with discontinuous flows,
including all types of possible breaks.Comment: 16 page
Robust Anomaly Detection in Dynamic Networks
We propose two robust methods for anomaly detection in dynamic networks in
which the properties of normal traffic are time-varying. We formulate the
robust anomaly detection problem as a binary composite hypothesis testing
problem and propose two methods: a model-free and a model-based one, leveraging
techniques from the theory of large deviations. Both methods require a family
of Probability Laws (PLs) that represent normal properties of traffic. We
devise a two-step procedure to estimate this family of PLs. We compare the
performance of our robust methods and their vanilla counterparts, which assume
that normal traffic is stationary, on a network with a diurnal normal pattern
and a common anomaly related to data exfiltration. Simulation results show that
our robust methods perform better than their vanilla counterparts in dynamic
networks.Comment: 6 pages. MED conferenc
Optimal pricing control in distribution networks with time-varying supply and demand
This paper studies the problem of optimal flow control in dynamic inventory
systems. A dynamic optimal distribution problem, including time-varying supply
and demand, capacity constraints on the transportation lines, and convex flow
cost functions of Legendre-type, is formalized and solved. The time-varying
optimal flow is characterized in terms of the time-varying dual variables of a
corresponding network optimization problem. A dynamic feedback controller is
proposed that regulates the flows asymptotically to the optimal flows and
achieves in addition a balancing of all storage levels.Comment: Submitted to 21st International Symposium on Mathematical Theory of
Networks and Systems (MTNS) in December 201
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