Evaluation method on bus arrival headway reliability

Chen Qian Wang Xin Li Wenquan

(1School of Transportation, Southeast University, Nanjing 210096, China)

(2Transportation Research Institute, Old Dominion University, Norfolk, VA 23508, USA)

Improving the reliability of bus service has the potential to increase the attractiveness of public transit to the current and prospective riders. The ability of transport operators to understand and improve reliability relies on their ability to measure it[1]. The transit agencies need to know how efficiently and reliably their transit system operates by using operation data. The data can be obtained by traditional investigation (survey on vehicle, survey at stop) and advanced technologies (automatic vehicle location (AVL) and automatic passenger counters (APC)[2-3]). By analyzing the historical data, trends in service reliability and factors that contribute to service reliability can be obtained, which help a better understanding of the current transit operation system and the implementation of future improvement strategies.

This paper presents an in-depth analysis of bus arrival headway reliability service based on operational characteristics in Hefei, China. First, an improved index on bus arrival headway reliability is proposed. Then, a series of calculating formulae at the stops, routes and network levels are described. Finally, the bus arrival headway reliability is analyzed based on the bus operation data in Hefei. The analysis demonstrates that the new measures provide additional insight to the headway reliability, while the traditional measures of reliability are relatively limited.

1 Overview of Headway Reliability

As far back as the late 1960s some people were devoted to the topic of transit reliability dating and these works have continued until today, not only because the transit agencies place great importance to it, but also because it is a complicated problem that it is still far from being resolved.

1.1 Service reliability

Three types of measures of reliability have been studied in recent research. They are on-time performance (OTP), mean and excess passenger waiting time (EWT) and headway reliability (HR). These measures of reliability are widely used in the evaluation of bus operational reliability[4-5].

On-time performance, the commonly used measure, is used to describe the schedule adherence. It can be denoted as the percentage of vehicle departures that take place in a defined on-time window at a specific location.

Mean passenger waiting time and excess passenger waiting time are measures of estimating the passenger experience indirectly from vehicle location data and measures of operational performance. The excess waiting time is a relative measure that represents the extra amount of time a passenger waiting on average above the scheduled waiting time. It is the waiting time that will result from perfect adherence to schedule, and is noted for being useful[6].

For high-frequency service, often defined as headways of ten minutes or less, variation in vehicle headways becomes a more relevant measure. The headway reliability, defined as the percentage of headways that fall within a specified range from the scheduled headway, is a reliability measure frequently used by transit agencies and research studies.

1.2 Headway reliability

There are three types of measures that represent the operational quality of the transit system based on the headway reliability.

One definition is based on the variation method. The headway reliability of a stop is represented by the variation of the headway, and the headway reliability of a route is the average value of all stops on this route[7].

(1)

(2)

wherePHiis the headway reliability at stopi;PHis the headway reliability of a route;hiis the actual headway of stopi; andh0iis the scheduled headway of stopi. This definition is simple to explain and calculate. Nevertheless, the value ofPHiis probably larger than 1 or less than 0, which is not reasonable.

Another definition is based on the probability method. The headways reliability is presented as the probability that the actual headway is less than the defined headway[8].

(3)

The third definition is based on the statistics method. In the transit capacity and quality of service manual (TCQSM), the coefficient of variation (CV) of the transit headway serving a particular route arriving at a stop is calculated as

(4)

The headway deviation is measured as the actual headway minus the scheduled headway. From the definition, the coefficient of variation of the headway presents the average variation of the headway, which means unreliability, so 1 minusCvhis suggested as the headway reliability. However whenCvhis larger than 1, the headway reliability is smaller than 0.

Transit service reliability has been defined in a variety of ways. In China, almost all of the bus routes have no scheduled arrival time for each stop, and the headway reliability is a proper index with which to evaluate status of the vehicle operation and the reliability of waiting time for passengers. However, the existing studies about this index have some shortcomings, such as the value of reliability is not between 0 and 1; bunching is not considered in the definition; and there is not a series of indices for different levels such as stop, route and network, etc. Few studies notice it and carry on deep research on the definition of headway reliability. The calculation method is required to be modified to fit the evaluations for those routes with high frequency.

2 Methodology

Given the shortcomings of the existing headway reliability measures, a modified measure is proposed here.

2.1 Advanced definition

The headway reliability based on a particular vehicle is formulated in the following equations:

(5)

The headway reliability based on a particular stop is defined as

(6)

The headway reliability based on a particular route is defined as

(7)

The headway reliability based on the studied bus network is defined as

(8)

2.2 Discussion of performance parameters

2.2.1 Threshold value

There are four different situations describing whether the transit vehicle arrives accordant with the satisfaction level.

In order to ensure consistency between early arrival vehicles and late arrival vehicles, passengers’ delay is analyzed to evaluate the reliability of early arrival vehicles.

3 Case Study

3.1 Data used

Hefei is the capital and the largest city of Anhui Province in China. The operational data used in this paper cover almost all the vehicles of 97 routes of Hefei in a normal weekday, including detailed data on arrival time, passenger flow of boarding and alighting at each stop, during AM peak, PM peak, and off-peak periods. By analyzing the data, we compare the headway reliability using existing measures along with those using the definition presented in this paper.

3.2 Comparison between existing methods and advanced method

3.2.1 CV method vs. advanced method

According to the level of service grades based on the coefficient of variation of the headway established by TCQSM as shown in Tab.1, we analyze the transit survey data using the CV method.

Fig.1 demonstrates how the CV calculation and scheduled headway correlated with LOS evaluation. To be noted is that based on field data,Cvhdrops with the increase of the scheduled headway, which means that the level of service improves with the larger scheduled headway. The growth in the standard deviation of the headway deviation is less than that of the mean scheduled headway. The inconsistency of the growth of numerator and denominator leads to the fact that the value of the fractionCvhis doomed to get smaller along with the increase of headway.

Tab．1 Transit level of service by headway regularity

Fig.1 Distribution of Cvh and LOS of bus operation in Hefei

We can conclude that it is not reasonable to evaluate the reliability level of service byCvhonly. By the method proposed in this paper, the statistical average headway reliability of bus routes corresponding to different scheduled headways is shown in Fig.2. We obtain a relatively flat curve of the headway reliability. This overcomes the shortcoming of the CV method.

Fig.2 Average headway reliability of bus routes using advanced method in Hefei

3.2.2 Probability method vs. advanced method

Bus Line 1 is selected to compare the differences between the probability method and the advanced method. It has a 5-min interval headway at AM peak with 18 stops. Fig.3 shows the arrival time of vehicles at each stop on this route.

Fig.3 shows that in some segments of the line, vehicle 3 and vehicle 4 arrive at the stop as a bunch between stop 1 and stop 11. Using the probability method, the average reliability value of vehicle 4 is 1. Differently, that of vehicle 4 is 0.50 using the advanced method. Fig.4 shows the value of the headway reliability of vehicle 4 at each bus stop. From which we find that the values of headway reliability vary from 0.14 to 0.28 between bus stop 1 and stop 11 using the advanced method, while those values are 1 at each stop by the probability method. This makes more sense since the advanced method can accurately capture a less reliable situation when buses arrive like a bunch, while this situation is completely ignored by the probability method.

Fig.3 Arrival time of each bus at AM peak hour on Line 1

Fig.4 Headway reliability of vehicle 4 at each stop at AM peak hour on Line 1

3.3 Application of advanced method

3.3.1 Evaluating the transit reliability

Using the advanced method, we calculate the headway reliability values for vehicle, stop, route and network levels in Hefei. For the network level, the average values of the headway reliability of all the survey routes are 0.87 for the whole day and 0.81 for peak hours (including morning and evening peaks), which implies that the transit system is well operated at a relatively high reliability level. For the route level, Fig.5 shows the headway reliability for several routes during a whole travel day and during peak hours. It shows that the value of the headway reliability during peak hours is lower than the average value during the whole day. For the stop level, the average values of the headway reliability of each bus stop varies from 0.56 to 0.91 in peak hours, which are not related to the location of the bus stops. For the vehicle level, the average values of the headway reliability of each vehicle varies from 0.21 to 1.0 in peak hours. These values provide a general picture of the operational reliability of the transit network. For the transit management agencies, it is the basis of establishing measures to improve the operational level.

Fig.5 Headway reliability of some routes in Hefei

3.3.2 Evaluating the effect of exclusive bus lane (XBL)

Here we show a case of using the advanced method presented in this paper to evaluate the effect of adding the XBL to one route. Bus Line 4 is selected in this case study, which has a length of 12.8 km and 20 stops. Some segments on this route (Link between stop 5 and stop 10 is about 3 km) have been upgraded into an XBL since June, 2010. With the before and after survey data, we can evaluate whether adding the XBL improves the reliability of this route or not.

4 Conclusion

This study provides a comprehensively advanced method to evaluate transit headway reliability which overcomes the shortcomings of the existing methods such as the CV method and the probability method. More specifically, the advanced method presented in this study has the following advantages: 1) The value of reliability is between 0 and 1, which facilitates a better explanation of the transit headway reliability. 2) The value of headway no longer depends on scheduled headway. 3) The advanced method takes into account the situation that vehicles arrive as a bunch. Arriving as a bunch can bring uncertainty to transit operations. Ignoring this phenomenon can provide misleading information about transit reliability. This advanced method is more reasonable and practical in evaluating the transit operation. It is useful for the transit management agencies to thoroughly determine the weak points of the transit network.

Fig.6 Arrival time of each bus at AM peak hour of Line 4 before and after adding XBL

Fig.7 Headway reliability for each stop at AM peak hour of Line 4 before and after adding XBL

The limitations of the definition on the headway reliability proposed here is how to determine the value of the threshold, which is the embodiment of passengers’ acceptable level of waiting time. It is difficult to measure the acceptance level for different people accurately, because this is affected by many factors, such as family income, car ownership, trip purpose and distance, traveler’s ages and gender, etc, which are well worth studying deeply.

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