ITE Journal - January 2020 - 47

Table 2. Regression results of running time.
Coefficient

Estimate

T-value

P-value

(Intercept)

88.4

29.8

P < 0.0001

Distance

71.04

19.01

P < 0.0001

No. of stops

3.53

9.67

P < 0.0001

Lift
Ons

58.33
12.5

24.12
36.47

P < 0.0001
P < 0.0001

Offs
Ons + Offs
[Ons + Offs]2

5.7
14.08
-0.11

13.33
19.41
-7.63

P < 0.0001
P < 0.0001
P < 0.0001

Average load

2.68

4.88

P < 0.0001

TDD

3.03

33.08

P < 0.0001

Morning peak

39.12

22.63

P < 0.0001

Afternoon peak

31.08

19.07

P < 0.0001

Off-peak

-1.4

-8.04

P < 0.0001

Driver experience

-0.42

-5.14

P < 0.0001

Adjusted R2 = 0.76
N = 17,800
[Ons + Offs], [Ons + Offs]2, lift usage, driver's experience, terminal
departure delay [TDD], average passenger load [on-board]].
Each of the variables used in this model is explained in Table 1.
Table 2 presents the results of the running time regression model.
According to the results of the regression model, all the
variables are statistically significant. The running times were
measured in seconds (sec.), so that the estimated values in the table
can be interpreted as the changes in running time(s) associated
with a unit change in a given parameter. Thus, the running time is
estimated to increase by 71 sec. for every 1 kilometer (.62 miles) a
bus travels between two key stops. Almost half of the variables used
in the equation are related to events that happen at the bus stops
(such as lift, Ons and Offs). It is expected that in a stop involving a
lift operation, the running time will increase by 61.5 sec. (3.5 sec.
for the bus to stop and 58 sec. for the lift process). In addition, the
average passenger activity adds 17.5 sec. to the running time.
The estimated quadratic value of passenger activity, which
is presented as [On + Off]2, indicates that the passenger activity
becomes slightly faster after the initial stage of boarding/alighting.
A crowded bus with a large number of on-board passengers can
slow the boarding and alighting processes.10 This situation can lead
to a longer dwell time at each stop and cause variation in running
time, as shown in Figure 2.
Large gaps and bus bunching are common issues in high-frequency bus routes, especially during peak hours. Moreover, large

Figure 2. Effect of crowding on bus service reliability.
gaps and bus bunching are known to be the consequences of an
unreliable bus service.11 On average, the on-board load adds 2.6 sec.
to the running time. This number can be even higher in peak hours,
since the buses and bus stops are mostly crowded.
The results show that each late departure from the terminal
causes an increase of 3 sec. in running time. This value can be
much higher in peak hours with a heavy traffic jam. The maximum
increase in running time with a late departure from the terminal
9 minutes, 38 sec., which can be a disaster in a high-frequency
operation. Therefore, controlling the departures by a trained
supervisor can be an efficient strategy to reduce the irregularity.
Normally, it is expected that peak hours require longer running
time, but Strathman et al. (2000) argued that congestion-related
delays are limited to the evening peak hours. However, in our
study, both AM and PM peak variables show a positive effect on
running time (39 sec. and 31 sec., respectively). The inconsistency
between the results of Strathman et al. (2000) and the results of
the present study may be because of different environment under
which the studies were conducted.1 Finally, the model estimates that
an operator's relative running time decreases by 0.42 sec. for each
month of additional experience.
Coefficient of variation of running time model. This model
is used to compare the variability of distributions with different
mean values. The standard deviation of the sample is shown in the
following equation.
s=

√

1
____
N−1

ΣNi=1 [x −μ]
i

(1)

2

where N is the sample size, and xi is the ith observation. µ is the
sample mean, and is given by
1
μ= __
N

Σ Ni=1 x

(2)

i

The coefficient of variation is the standard deviation normalized
by the mean. It is given by the following equation.
s
CV= ____
|μ |

(3)
w ww .it e .or g

Ja n u ar y 2020

47


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