Reliability of Stockholm Subway - Index of

words, the share of commuters, which arrive during the intervals that are longer than
regular one, will meet overcrowding at the platform according to our assumption.
3.2.2 Waiting times
Talking about irregular headways causing crowding effect in the system it is
necessary to mention that it also affects waiting time of commuters.
Let‟s suppose that passengers randomly arrive to the station. When the trains arrive at
perfect and regular intervals the average waiting time of the passengers according to
the Theory of Probability is equal to the half of the headway:
. (3.2)
However, in case of irregular service the average waiting time will increase. It can be
explained with the example of famous Bus paradox, for instance, described in
Gunther (2001).
Let‟s assume that buses arrive independently to the bus stop with average headway 10
minutes. The first case is that the waiting time will be equal 5 minutes, according to
formula (3.2). Nonetheless, we know that buses arrive independently and intervals
between them vary in length. The point is if the passengers arrive to the stop purely
randomly – it is more likely that they will arrive during the longer intervals than
during the short ones. The explanation is that the intervals with longer duration are
more frequently represented than the short intervals in the scale of the total length of
the studying period. The answer to that example is based on that the waiting time in
case of irregular service depends on the variability of headways. The more headway
varies the more considerable waiting time grows:
(3.3)
where H – is an average headway during the studying period and CV is the coefficient
of variation.
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