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Given a set of service requests (events), a set of guided servers (units),
and a set of unguided service contractors (conts), the vehicle dispatching problem
VDP is the task to find an assignment of events to units and conts as well as tours
for all units starting at their current positions and ending at their home positions
(dispatch) such that the total cost of the dispatch is minimized.
The cost of a dispatch is the sum of unit costs, cont costs, and event costs. Unit
costs consist of driving costs, service costs and overtime costs; cont costs consist of
a fixed cost per service; event costs consist of late costs linear in the late time, which
occur whenever the service of the event starts later than its deadline.
The program ZIBDIP based on dynamic column generation and set partitioning
yields solutions on heavy-load real-world instances (215 events, 95 units) in less
than a minute that are no worse than 1% from optimum on state-of-the-art personal
computers.
We consider a particle constrained to a submanifold ? of the configuration space
Rm. Using that the notion of holonomic constraints coincides with integrability of the corresponding
vector field, we show how this property naturally determines local coordinates on ? . We give a
rigorous justification for the calculation of the mean force along the constrained coordinates, and
we provide a concise geometrical interpretation of the different contributions to the mean force.
Our approach gives rise to a generalisation of the Fixman Theorem which is well known and widely
used in molecular dynamics applications. It further allows for working out a Hybrid Monte-Carlo
based algorithm that can be used to compute arbitrary statistical quantities from constrained
simulations such as the mean force in the context of thermodynamic free energy statistics.
Models for physical systems often take the form of implicit or behavioral models. One important problem is the
identification of which combinations of variables are good candidtates for control variables. This paper first provides one
solution to this problem for linear time varying systems. The solution is shown to be related to a general optimization
problem. It is then shown how these same algorithms can be extended to a large and important class of nonlinear systems.
In this paper the numerical approximation of solutions of Itô stochastic differential
equations is considered, in particular for equations with a small parameter ? in the noise coex-
cient. We construct stochastic linear multi-step methods and develop the fundamental numerical
analysis concerning their mean-square consistency, numerical stability in the mean-square sense and
mean-square convergence. For the special case of two-step Maruyama schemes we derive conditions
guaranteeing their mean-square consistency. Further, for the small noise case we obtain expansions
of the local error in terms of the stepsize and the small parameter ?. Simulation results using several
explicit and implicit stochastic linear k-step schemes, k = 1; 2, illustrate the theoretical findings.
A strategy for controlling the stepsize in the numerical integration of stochastic
differential equations (SDEs) is presented. It is based on estimating the p-th mean of
local errors. The strategy leads to deterministic stepsize sequences that are identical
for all paths. For the family of Euler schemes for SDEs with small noise we derive
computable estimates for the dominating term of the p-th mean of local errors
and show that the strategy becomes efficient for reasonable stepsizes. Numerical
experience is reported for test examples including scalar SDEs and a stochastic
circuit model.
Single-hop WDM networks with a central Passive Star Coupler (PSC), as well as single-hop networks with
a central Arrayed-Waveguide Grating (AWG) and a single transceiver at each node, have been extensively
studied as solutions for the quickly increasing amounts of unicast and multicast traffic in the metropolitan
area. The main bottlenecks of these networks are the lack of spatial wavelength reuse in the studied PSC
based networks and the single transceiver in the studied AWG based metro WDM networks. In this paper
we develop and evaluate the FT EE ???? FREE AWG network, which is based on a central AWG and has arrays
of fixed-tuned transmitters and receivers at each node. Transceiver arrays are a mature technology, making
the proposed network practical. In addition, the transmitter arrays allow for high speed signaling over the
AWG while the receiver arrays relieve the receiver bottleneck arising from multicasting in conjunction with
spatial wavelength reuse on the AWG. Our results from probabilistic analysis and simulation indicate that
the FTEE ???? FREE AWG network gives particularly good throughput-delay performance for a mix of unicast
and multicast traffic.
Metastability in reversible diffusion processes I. Sharp asymptotics for capcities and exit times
(2004)
We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form +rF ( )r on R or subsets of , where F is a smooth function with finitely many local minima. In analogy to previous work in discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of F can be related, up to multiplicative errors that tend to one as # 0, to the capacities of suitably constructed sets. We show that this capacities can be computed, again up to multiplicative errors that tend to one, in terms of local characteristics of F at the starting minimum and the relevant saddle points. As a result, we are able to give the first rigorous proof of the classical Eyring-Kramers formula in dimension larger than 1. The estimates on capacities make use of their variational representation and monotonicity properties of Dirichlet forms. The methods developed here are extensions of our earlier work on discrete Markov chains to continuous diffusion processes.
We continue the analysis of the problem of metastability for reversible diffusion processes,
initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator.
Recall that we are considering processes with generators of the form 1+rF()r on Rd or subsets
of Rd , where F is a smooth function with finitely many local minima. Here we consider only
the generic situation where the depths of all local minima are different. We show that in general
the exponentially small part of the spectrum is given, up to multiplicative errors tending to one, by
the eigenvalues of the classical capacity matrix of the array of capacitors made of balls of radius
centered at the positions of the local minima of F. We also get very precise uniform control on the
corresponding eigenfunctions. Moreover, these eigenvalues can be identified with the same precision
with the inverse mean metastable exit times from each minimum. In [BEGK3] it was proven
that these mean times are given, again up to multiplicative errors that tend to one, by the classical
Eyring–Kramers formula.