27,862 research outputs found
A variational approach for continuous supply chain networks
We consider a continuous supply chain network consisting of buffering queues and processors first proposed by [D. Armbruster, P. Degond, and C. Ringhofer, SIAM J. Appl. Math., 66 (2006), pp. 896–920] and subsequently analyzed by [D. Armbruster, P. Degond, and C. Ringhofer, Bull. Inst. Math. Acad. Sin. (N.S.), 2 (2007), pp. 433–460] and [D. Armbruster, C. De Beer, M. Fre- itag, T. Jagalski, and C. Ringhofer, Phys. A, 363 (2006), pp. 104–114]. A model was proposed for such a network by [S. G ̈ottlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559] using a system of coupling ordinary differential equations and partial differential equations. In this article, we propose an alternative approach based on a variational method to formulate the network dynamics. We also derive, based on the variational method, a computational algorithm that guarantees numerical stability, allows for rigorous error estimates, and facilitates efficient computations. A class of network flow optimization problems are formulated as mixed integer programs (MIPs). The proposed numerical algorithm and the corresponding MIP are compared theoretically and numerically with existing ones [A. Fu ̈genschuh, S. Go ̈ttlich, M. Herty, A. Klar, and A. Martin, SIAM J. Sci. Comput., 30 (2008), pp. 1490–1507; S. Go ̈ttlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559], which demonstrates the modeling and computational advantages of the variational approach
Study on Energy Consumption and Coverage of Hierarchical Cooperation of Small Cell Base Stations in Heterogeneous Networks
The demand for communication services in the era of intelligent terminals is
unprecedented and huge. To meet such development, modern wireless
communications must provide higher quality services with higher energy
efficiency in terms of system capacity and quality of service (QoS), which
could be achieved by the high-speed data rate, the wider coverage and the
higher band utilization. In this paper, we propose a way to offload users from
a macro base station(MBS) with a hierarchical distribution of small cell base
stations(SBS). The connection probability is the key indicator of the
implementation of the unload operation. Furthermore, we measure the service
performance of the system by finding the conditional probability-coverage
probability with the certain SNR threshold as the condition, that is, the
probability of obtaining the minimum communication quality when the different
base stations are connected to the user. Then, user-centered total energy
consumption of the system is respectively obtained when the macro base
station(MBS) and the small cell base stations(SBS) serve each of the users. The
simulation results show that the hierarchical SBS cooperation in heterogeneous
networks can provide a higher system total coverage probability for the system
with a lower overall system energy consumption than MBS.Comment: 6 pages, 7 figures, accepted by ICACT201
Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
In this paper we are concerned with the monodromy of Picard-Fuch differential
equations associated with one-parameter families of Calabi-Yau threefolds. Our
results show that in the hypergeometric cases the matrix representations of
monodromy relative to the Frobenius bases can be expressed in terms of the
geometric invariants of the underlying Calabi-Yau threefolds. This phenomenon
is also verified numerically for other families of Calabi-Yau threefolds in the
paper. Furthermore, we discover that under a suitable change of bases the
monodromy groups are contained in certain congruence subgroups of Sp(4,Z) of
finite index whose levels are related to the geometric invariants of the
Calabi-Yau threefoldsComment: 32 pages References adde
A Link-based Mixed Integer LP Approach for Adaptive Traffic Signal Control
This paper is concerned with adaptive signal control problems on a road
network, using a link-based kinematic wave model (Han et al., 2012). Such a
model employs the Lighthill-Whitham-Richards model with a triangular
fundamental diagram. A variational type argument (Lax, 1957; Newell, 1993) is
applied so that the system dynamics can be determined without knowledge of the
traffic state in the interior of each link. A Riemann problem for the
signalized junction is explicitly solved; and an optimization problem is
formulated in continuous-time with the aid of binary variables. A
time-discretization turns the optimization problem into a mixed integer linear
program (MILP). Unlike the cell-based approaches (Daganzo, 1995; Lin and Wang,
2004; Lo, 1999b), the proposed framework does not require modeling or
computation within a link, thus reducing the number of (binary) variables and
computational effort.
The proposed model is free of vehicle-holding problems, and captures
important features of signalized networks such as physical queue, spill back,
vehicle turning, time-varying flow patterns and dynamic signal timing plans.
The MILP can be efficiently solved with standard optimization software.Comment: 15 pages, 7 figures, current version is accepted for presentation at
the 92nd Annual Meeting of Transportation Research Boar
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