Waiting time at bus stops is one of the most onerous attributes of transit that users experience. Reducing waiting time, especially the component that is most characterised by uncertainty would be of considerable value to passengers. Excess Waiting Time is defined as “the measure of the additional wait experienced by transit users due to irregular spacing of buses or those that failed to run” (London Bus, 2007). EWT, as used by London Buses, is a measure of perceived regularity, measuring the average additional waiting time passengers experience compared to the waiting time they expect. EWT is a standard metric used to measure the quality of services on high frequency routes of public transport systems. The lower the EWT, the more likely it is that passengers will not wait longer than scheduled and will perceive the service as regular, e.g., a 10-min headway route has a scheduled waiting time (SWT) of 5 minutes. A EWT of 1 minute means customers are likely to
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wait 6 minutes instead of the expected 5 minutes. (Shalaik, B and Winstanley, A.C, 2009). The greater the EWT value, the less reliable is the transit service.
The advantage of measuring EWT is that it is an objective measurement, easy to understand (expressed in minutes) and it focuses more on the passengers point of view. However, it has disadvantages such as an irregular headway that can affect the results. EWT works best with longer periods of observation, shorter periods can show artificially good results if the last bus in the sample arrives early. The EWT indicator is examined from the perspective of the transit operator and calculated for each line, taking into account the outcome of the operator’s scheduling process (scheduled headways) and the actual measurements on site (actual headways).EWT is not designed to be used with irregular scheduled headways.In theory, this could result in a negative EWT score when the service is in fact perfectly regular, and will be zero when the service operates exactly according to the irregular schedule.
Mathematically, EWT can be calculated by subtracting the SWT from the average waiting time (AWT).
EWT AWT SWT ( 4-1) n 1 i n 1 i AHway * 2 AHway AWT ( 4-2) n 1 i 2 n 1 i 2 i SHway i SHway SWT ( 4-3) Where:
AHway the actual headway
SHway the schedules headway
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For example, a ten minutes headway route has a SWT of five minutes (i.e. half the headway). For a bus service with a scheduled frequency of 6 buses per hour, the scheduled headway is ten minutes. Average Waiting Time can be calculated by dividing the total of (sum of square of headway/2) over time between 1st and last observed bus, then the EWT can be calculated by subtracting SWT from AWT as mentioned in equation (4-1). For example a 4 minutes value of EWT means passengers had to wait 4 minutes additional to scheduled waiting time SWT. The
EWT methodology assumes a uniform arrival of passengers. The EWT is the only
method tested that truly incorporates the experience of all passengers as its output is a result of all data in the dataset. Figure (4-3) presents EWT values calculated for bus route 5 of the Blackpool transport system. The EWT values are visualised on a map using colour codes for a specific threshold. Values of EWT are shown in bar graph as well as in tabular format. On the transit map, EWT values are displayed in the icon’s pop up window associated with bus stop.
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Figure 4-3 EWT values for Bus Route 5 of Blackpool transport system
In Figure 4-3, bus stop numbers can be used as links for detailed information such as bus departure times, actual headways or average waiting times. We note the high values of EWT, indicating irregularities in bus services at the time of measurement.
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Figure 4-4 Bus departure times and headways for bus stop 6.
As we can see in Figure (4-4), bus departure times and headways for bus stop 6 are shown. The sum of square headway/2 is equal to 2308 minutes, while the time between 1st and last observed bus is equal to 220 minutes. The AWT=10.49 minutes. EWT= 10-5=5 minutes.
To help operators to maintain QoS and comply with license rules and conditions, EWT can be measured on daily, weekly or monthly bases. As we see in Figure (4- 5), EWT values have been calculated for a month and are shown in both tabular and graphical format. The Table shows the values of EWT calculated for the time points on a particular day from that month.
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Figure 4-5 EWT values calculated for time points for month
EWT values can be visualised in a way that enables the transit operator to easily detect any irregularity in services. As shown in Figure (4-5) the values of EWT are different and indicate the service regularity or irregularity, for example the value of EWT of stop number 62 in the ninth day of the month is 3 which is an acceptable value for service regularity, while the value of 28 could be considered and shows irregularity in the transit services at that time.
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Figure 4-6 EWT values calculated and visualised for a bus stop (13) in a month
In Figure (4-6) the EWT values are calculated and visualised for one month (August 2008). As we can see from the Figure bus departure times are depicted as points on the y-axis where we can see convergence and divergence between these points indicating the regularity in bus services .X-axis, shows date of EWT.
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Similarly, EWT is calculated for each time point. Figure (4-7) shows EWT values for fourteen time points calculated at the end of a working day (15-08-2008).
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Figure 4-7 EWT values calculated and visualised for fourteen timing points
As we can see in Figure (4-7), bus departure times are depicted on the y-axis while the stop numbers are depicted on the x-axis. The gap that appears between the buses
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departure times on the y-axis shows convergence and divergence between the services. The representation and calculation of EWT in this way may help to visualise the performance of the transport system and allow operators to detect any bad symptoms of transit service. The purpose always is to help the transportation system operator to manage their transit fleet more effectively, where it is easy to note that any long gap between bus departure times (headways) is an indication of a simultaneous extension of in length of passengers waiting times.