Applications of sensitivity analysis for probit stochastic network equilibrium

Abstract

-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 (postoptimisation); 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.

A Class of Efficient Algorithms for the Bi-Level Demand Adjustment Problems in Congested Traffic Networks

“…In the literature, there are two types of sensitivity analysis methods that can be used to compute the Jacobian matrix J. Te frst is Tobin and Friesz's [20] restricted network technique, which has been extensively investigated and employed since its publication. However, researchers have discovered several limitations in its application: (1) the strict complementarity condition is too strong and limits the restricted network method's application scope, (2) the method of selecting nondegenerate extreme points is not always efective, and (3) when the equilibrium solution is located at nondiferentiable points, using the restricted network method may result in incorrect results [6,28,29]. Te second method constructs an auxiliary quadratic programming problem to compute the directional derivatives for each OD pair following the results of Patriksson [30].…”

Selecting Resort Locations

“…Sensitivity analysis elucidates the implicit relationship between a solution (to an optimization problem, for example) and input parameters. Given a solution to a problem with specific input parameters, first-order sensitivity analysis is performed to identify a roughly linear relationship between changes in input parameters and the solution (Clark and Watling, 2006). Three criteria are commonly used to analyse sensitivity: change in values of various factors, changes in the relative importance of factors, and changes in the weights of these factors.…”

Brazilian airport infrastructure: Analysis using the Monte Carlo simulation and multiple regressions

“…Hence, the simulation is a structured process, with the intention of understanding the behavior of an experiment, according to the following steps: (i) describe the variables' behavior that are being studied; (ii) build hypothesizes; (iii) use theories that have been published, especially, for the Monte Carlo Simulation and (iv) to do the necessary calculus, obtaining the distribution of probabilities and frequency graphics. To the decision making exists texts, observing KLEIJNEN (2004), FICHTHORN and WEINBERG (2004), CLARK and WATLING (2005), TERVONEN and LAHDELMA (2005), ÖZDEMIR, YÜCESAN and HERER (2006), MATEOS, JIMÉNEZ and RÍOS-INSUA (2006) and SOHN, LIM (2007).…”