An Analysis on Commuting Travel Time Reliability: A Case study in

Bei

Lixia Lei

and Qi Zhang

School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044;

State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China

Keywords: Urban traffic, travel time, reliability evaluation index, AFC data, commute.

Abstract: Based on the AFC data of Beijing metro, this paper analyzes the travel time distribution and reliability of

subway commuter travel. This paper first analyzes the OD commuter travel time distribution by combing a

large amount of actual data. The results indicate that the OD commuter travel time distribution follows the

Lognormal distribution. Then the paper analyzes the applicability of travel time reliability evaluation index,

which shows that the Buffer time index is suitable for evaluating the reliability of subway OD travel time.

1 INTRODUCTION

With the rapid development of China's subway

industry, People's travel requirements include not

only comfort, convenience, economy and security，

but also increase the accuracy of travel time,

especially commuters. They are more demanding on

travel time reliability.

In previous works, the research on the reliability

of the travel time mainly focuses on the urban road

network, and there are relatively few studies on the

reliability of the OD between the metro stations.

Commonly, the evaluation indexes of the reliability

of the travel time of the road network include the

reserved time index, the planned time index and the

95% time. At present, there is a lack of evaluation

index suitable for evaluating the reliability of travel

time of subway OD.

Therefore, this research takes Beijing metro OD

as the research object and Combine AFC data to

study the distribution rule of OD travel time. Based

on the reliability evaluation index of road network

travel time, through the index applicability analysis,

Select the appropriate indicators for evaluating the

reliability of subway commute travel time.

2 OVERVIEW OF COMMUTER

TRAVEL TIME RELIABILITY

2.1 Definition

Subway travel time means the time passenger spend

on the process from credit card into the station into

credit card off the station. Travel time components

includes the pit stop walking time, platform waiting

time, in the car time, outbound travel time form. If

need to transfer, plus travel time, transfer station

waiting time, etc.. Commuter passengers before the

trip have the psychological expectations of the time

required, and set aside a certain period of time. The

time reserved by passengers is called planned travel

time.

Travel time reliability is the probability that a

traveler will be able to travel successfully during a

scheduled travel time and may also indicate the

percentage of passengers who have successfully

completed their travel during the planned travel

time.

2.2 Probability distribution model of

commuting travel time

OD commuter travel time probability density

distribution in the form shown below, it can be

divided into three stages, the first stage a ~ b travel

time increases, the corresponding probability

increases gradually until the probability of b

maximum. In the second stage, the probability of b ~

Lei, L. and Zhang, Q.

An Analysis on Commuting Travel Time Reliability: A Case study in Beijing.

In 3rd International Conference on Electromechanical Control Technology and Transportation (ICECTT 2018), pages 375-378

ISBN: 978-989-758-312-4

375

c gradually decreases, which is symmetrical with

that of the first stage about x = b. The third phase c ~

d probability is at a relatively low value and is still

decreasing. According to the characteristics of

probability density distribution of OD travel time,

we assume that its distribution obeys normal

distribution and logarithmic normal distribution, and

performs curve fitting and test.

Fig. 1. OD travel time actual probability density

distribution

The data source in the study is the AFC data of

full network include the morning rush hour from

March 16 to March 20, 2015. The AFC system

provides detailed passenger travel information,

extracts each passenger's arrival and departure

stations and the time of inbound and outbound credit

card.

According to the probability density function of

normal distribution and lognormal distribution

model and distribution model hypothesis testing

method, the fitting procedure of commuting travel

time distribution model is as follows:

Step1: Take a single OD pair of commuting time

as a general, data preprocessing. Draw a histogram

of commuting travel time distribution, and conduct a

preliminary analysis of the probability distribution

characteristics of OD travel time.

Step2: Using the cftool fitting toolbox in

MATLAB, we can obtain the probability density

function image and parameter μ, σ of OD commute

travel time after the commuting travel time of the

OD pair is respectively normalized and logarithm

normal distribution curve fitting.

Step3: Use the goodness of fit parameters SSE

and R2 and other statistical indicators and P-P map,

travel time empirical distribution function chart and

the probability distribution chart to compare the

differences to test the rationality of the distribution

model assumptions.

Through a large number of ODs, the actual data

of commuter travel time verifies that 98% of OD

commuting trips are logarithmically normal.

Therefore, it can be assumed that the probability

distribution model of OD commuting travel time is

lognormal distribution. which is:

ln ( , )TN



(1)

1()

() exp

InT

σπ

⎛⎞

−

=−

⎜⎟

⎝⎠

(2)

(T)Represents OD Excursion Travel Time,

where

and represent the expected

value and variance of the logarithm of travel time

respectively.

3 COMMUTER TRAVEL TIME

RELIABILITY EVALUATION

INDEX SYSTEM

Travel time reliability evaluation indicators can be

divided into mathematical statistics based on

indicators, and based on probability travel time class

indicators. The evaluation index based on

mathematical statistics mainly describes the degree

of variation of travel time and the degree of

dispersion of distribution. Based on the historical

travel time data, the evaluation index based on the

probabilistic travel time class describes the

uncertainty of travel time and is relatively close to

the actual feelings of passengers.

3.1 Travel time reliability evaluation

index

The evaluation indexes based on mathematical

statistics include the mean value, standard deviation,

variance and the like. The evaluation indexes based

on probabilistic travel time class include planned

travel time (PT), planned travel time index (PTI),

buffer time (BT), and buffer time index (BTI).

Planned travel time (PT) indicates the estimated

travel time for the passenger when traveling.

General 95% travel time said. Reflects the vast

majority of passenger travel time required. The

planned travel time index (PTI) is a measure of the

ratio of planned travel time to median to assess the

planned travel time for different OD pairs. The

larger PTI is, the lower the reliability of travel time

is. Where:

95TT

Represents 95% of travel time;

50TT

Represents the median travel time.

95PT TT=

(3)

PTI

(4)

The buffer time (BT) indicates the amount of

time a passenger must reserve in order to travel on

ICECTT 2018 - 3rd International Conference on Electromechanical Control Technology and Transportation

376

time. The buffer time exponent (BTI) expresses the

ratio of buffer time to median as a percentage to

evaluate the buffer time for different OD pairs. The

greater BT and BTI are, the lower the reliability of

travel time is.

95 50BT TT TT=−

(5)

95 50

TT TT

BTI

−

(6)

In Section 2.2, it has proved that OD commuting

travel time obeys lognormal distribution, so all the

reliability evaluation indicators of travel time are

based on lognormal distribution. The following is a

derivation based on the logarithmic normal

distribution of travel time reliability formula:

exp( 0.5 )Mean

(7)

PT exp(μ 1.645σ)=+

(8)

PTI exp(1.645σ)=

(9)

[

]

BT exp( ) exp(1.645 ) 1

μσ

=−

(10)

BTI exp(1.645σ)-1=

(11)

3.2 Commuter Travel Time Reliability

Evaluation Index Applicability

Analysis

(1) Evaluation of reliability of each travel time in

different periods of evaluation results

In the process of selecting the appropriate

evaluation index of the reliability of the travel time

of the subway, although the indexes have different

measurement scales, the reliability of the travel time

should be consistent. The figure below shows the

travel time of one OD in each day of the day Travel

time reliability evaluation bar chart As can be seen

from the figure, the trend of all the reliability

indexes are basically the same, only some indexes

magnify the reliability of time periods with less

reliable reliability and reduce the reliability

measures with better reliability periods so that the

reliability of different time periods The level of

reliability is more obvious.

Fig. 2. reliability evaluation index of different travel time

in a certain day of OD

Obviously, the average travel time of the same

OD changed more smoothly and the variance

changed a lot. The planned travel times and indices

have also been changing steadily during the day. The

buffer time and index can be very intuitive to reflect

the reliability of travel time changes over different

periods of time.

(2) Comparison of reliability evaluation index of

different travel time for different OD evaluation

The purpose of this chapter is to select all of the

reliability evaluation indicators that can objectively

evaluate the reliability of different OD travel time.

Randomly select a number of OD, according to the

average travel time from small to large sorting OD

traffic weekday travel time data obtained from the

calculation of the reliability of travel time bar chart.

As can be seen from the figure, when the mean and

planned travel time are used to evaluate the

reliability of multiple OD commuter travel times, it

is impossible to directly compare the reliability

levels and is used to describe the reliability of OD

travel time alone. The standard deviation, the

planned travel time index, the buffer time and the

buffer time index can all be used to compare the

reliability of OD travel time, but the effect is

obviously different. Among them, the planned travel

time index fluctuated less, and the evaluation result

was slightly worse. Therefore, choosing the buffer

time and buffer time index as the evaluation index of

commuting time reliability can directly compare the

reliability of different OD commuter travel time.

Considering the influence of avoiding the mean

value of travel time on the reliability evaluation, this

paper chooses the buffer time index as the

An Analysis on Commuting Travel Time Reliability: A Case study in Beijing

377

evaluation index of commuting time reliability

finally.

Fig. 3. reliability evaluation index of different OD

commuter travel time and travel time

4 CONCLUSIONS

In this paper, According to the index applicability

analysis, we select the indexes that are suitable for

the evaluation of the subway commuter travel time

reliability and finally choose the BTI as the

evaluation index of the subway commuter travel

time reliability.

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