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In this paper, we revisit the LAPUE model with a different focus: we begin byadopting a new penalty function which gives a smooth transition of the boundarybetween lateness and no lateness and demonstrate the LAPUE model based on thenew penalty function has a unique equilibrium and is stable with respect to(w.r.t.) small perturbation of probability distribution under moderateconditions. We then move on to discuss statistical robustness of the modifiedLAPUE (MLAPUE) model by considering the case that the data to be used forfitting the density function may be perturbed in practice or there is adiscrepancy between the probability distribution of the underlying uncertaintyconstructed with empirical data and the true probability distribution infuture, we investigate how the data perturbation may affect the equilibrium. Weundertake the analysis from two perspectives: (a) a few data are perturbed byoutliers and (b) all data are potentially perturbed. In case (a), we use thewell-known influence function to quantify the sensitivity of the equilibrium bythe outliers and in case (b) we examine the difference between empiricaldistributions of the equilibrium based on perturbed data and the equilibriumbased on unperturbed data. To examine the performance of the MLAPUE model andour theoretical analysis of statistical robustness, we carry out some numericalexperiments, the preliminary results confirm the statistical robustness asdesired.

A Modified Late Arrival Penalised User Equilibrium Model and Robustness in Data Perturbation