Author(s): J. Yuan, R. M. P. Goverde & I. A. Hansen
This paper evaluates several commonly applied probability distribution models
for stochastic train process times based on empirical data recorded in a Dutch
railway station, The Hague Holland Spoor.
An initial guess of model parameters
is obtained by the Maximum Likelihood Estimator (MLE).
procedure is then followed, in which large delays are omitted one by one and the
distribution parameters are estimated correspondingly using the MLE method.
The parameter estimation is improved by minimizing the Kolmogorov-Smirnov
(K-S) statistic where of course the empirical distribution is still based on the
complete data set.
A local search is finally performed in the neighbourhood of
the improved model parameters to further optimize the estimation.
the distribution models, we compare the K-S statistic among the fitted
distributions with optimized parameters using the one-sample K-S goodness-offit
test at a commonly adopted significance level of α = 0.05.
It has been found
that the log-normal distribution can be generally considered as the best
approximate model among the candidate distributions for both the arrival times
of trains at the platform and at the approach signal of the station.
distribution can generally be considered as the best approximate distribution
model for non-negative arrival delays, departure delays and the free dwell times
of late arriving trains.
The shape parameter of the fitted distribution is generally
smaller than 1.0 in the first two cases, whereas it is always larger than 1.0 in the
These distribution evaluation results for train process times can be used
for accurately predicting the propagation of train delays and supporting timetable
design and rescheduling particularly in case of lack of empirical data.
train delays, running and dwell times, track occupancy times,
statistical distribution, the K-S test.
Size: 621 kb
Paper DOI: 10.2495/978-1-84564-500-7/09
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