8,959 research outputs found
Applications of sensitivity analysis for probit stochastic network equilibrium
Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported
Modelling network travel time reliability under stochastic demand
A technique is proposed for estimating the probability distribution of total network travel time, in the light of normal day-to-day variations in the travel demand matrix over a road traffic network. A solution method is proposed, based on a single run of a standard traffic assignment model, which operates in two stages. In stage one, moments of the total travel time distribution are computed by an analytic method, based on the multivariate moments of the link flow vector. In stage two, a flexible family of density functions is fitted to these moments. It is discussed how the resulting distribution may in practice be used to characterise unreliability. Illustrative numerical tests are reported on a simple network, where the method is seen to provide a means for identifying sensitive or vulnerable links, and for examining the impact on network reliability of changes to link capacities. Computational considerations for large networks, and directions for further research, are discussed
Inference for dynamics of continuous variables: the Extended Plefka Expansion with hidden nodes
We consider the problem of a subnetwork of observed nodes embedded into a
larger bulk of unknown (i.e. hidden) nodes, where the aim is to infer these
hidden states given information about the subnetwork dynamics. The biochemical
networks underlying many cellular and metabolic processes are important
realizations of such a scenario as typically one is interested in
reconstructing the time evolution of unobserved chemical concentrations
starting from the experimentally more accessible ones. We present an
application to this problem of a novel dynamical mean field approximation, the
Extended Plefka Expansion, which is based on a path integral description of the
stochastic dynamics. As a paradigmatic model we study the stochastic linear
dynamics of continuous degrees of freedom interacting via random Gaussian
couplings. The resulting joint distribution is known to be Gaussian and this
allows us to fully characterize the posterior statistics of the hidden nodes.
In particular the equal-time hidden-to-hidden variance -- conditioned on
observations -- gives the expected error at each node when the hidden time
courses are predicted based on the observations. We assess the accuracy of the
Extended Plefka Expansion in predicting these single node variances as well as
error correlations over time, focussing on the role of the system size and the
number of observed nodes.Comment: 30 pages, 6 figures, 1 Appendi
Hybrid Pathwise Sensitivity Methods for Discrete Stochastic Models of Chemical Reaction Systems
Stochastic models are often used to help understand the behavior of
intracellular biochemical processes. The most common such models are continuous
time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of
expectations of model output quantities with respect to model parameters, are
useful in this setting for a variety of applications. In this paper, we
introduce a class of hybrid pathwise differentiation methods for the numerical
estimation of parametric sensitivities. The new hybrid methods combine elements
from the three main classes of procedures for sensitivity estimation, and have
a number of desirable qualities. First, the new methods are unbiased for a
broad class of problems. Second, the methods are applicable to nearly any
physically relevant biochemical CTMC model. Third, and as we demonstrate on
several numerical examples, the new methods are quite efficient, particularly
if one wishes to estimate the full gradient of parametric sensitivities. The
methods are rather intuitive and utilize the multilevel Monte Carlo philosophy
of splitting an expectation into separate parts and handling each in an
efficient manner.Comment: 30 pages. The numerical example section has been extensively
rewritte
- …