research article waiting endurance time estimation of...

Research ArticleWaiting Endurance Time Estimation ofElectric Two-Wheelers at Signalized Intersections

Mei Huan and Xiao-bao Yang

MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology Beijing Jiaotong UniversityBeijing 100044 China

Correspondence should be addressed to Xiao-bao Yang 250253752qqcom

Received 1 March 2014 Accepted 26 April 2014 Published 7 May 2014

Academic Editor Gang Ren

Copyright copy 2014 M Huan and X-b Yang This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The paper proposed a model for estimating waiting endurance times of electric two-wheelers at signalized intersections usingsurvival analysis method Waiting duration times were collected by video cameras and they were assigned as censored anduncensored data to distinguish between normal crossing and red-light running behavior A Cox proportional hazard model wasintroduced and variables revealing personal characteristics and traffic conditions were defined as covariates to describe the effectsof internal and external factors Empirical results show that riders do not want to wait too long to cross intersections As signalwaiting time increases electric two-wheelers get impatient and violate the traffic signal There are 128 of electric two-wheelerswith negligible wait time 250 of electric two-wheelers are generally nonrisk takers who can obey the traffic rules after waiting for100 seconds Half of electric two-wheelers cannot endure 490 seconds or longer at red-light phase Red phase time motor vehiclevolume and conformity behavior have important effects on ridersrsquo waiting timesWaiting endurance times would decrease with thelonger red-phase time the lower traffic volume or the bigger number of other riders who run against the red light The proposedmodel may be applicable in the design management and control of signalized intersections in other developing cities

1 Introduction

With the social and economic development and the rapidincrease of motor vehicles traffic problems become increas-ingly serious in many cities and more and more attentionsare paid to traffic research [1 2] Nonmotorized vehicles (iemainly regular bicycles and electric two-wheelers) are oneof the most popular modes of transportation in some Asiandeveloping countries such as India Vietnam Cambodiaand China Even in developed countries cycling travel isrecognized as low energy consumption healthy to the usersand does not damage the health of others The CanadianCensus indicates a 42 increase in daily bike commutesbetween 1996 and 2006 The US Census Bureau reportsalmost twice as many bike commuters in 2009 as in 2000 [3]

In recent ten years electric bike (e-bike) has enteredpeoplersquos life Due to its labor-saving and speed e-bike hasemerged as a popular mode of transportation in manylarge cities in China Electric two-wheeler use has rapidly

expanded in China in the process changing the mode split ofmany cities [4] In 2012 the number of Chinese e-bikes wasabout 140 million [5] Electric two-wheelers in China haverelatively low speeds and weights compared to a motorcycleBoth bicycle-style electric two-wheelers (with functioningpedals) and scooter-style electric two-wheelers (with manyof the features of gasoline scooters) are classified as bicyclesand are given access to bicycle infrastructure (see Figure 1)

However the growing popularity of cycling traffic alsoentails safety concerns as observed in accident and injurystatisticsWith the rapidly increasing number of electric two-wheelers more and more people pay much concern abouttraffic security problems involved with electric two-wheelersIn 2004 589 electric two-wheelers died and 5295 seriouslyinjured in road accidents [6] In 2010 the correspondingfigures increased to 4029 dead and 20 311 seriously injuredrespectively representing 62 of all traffic fatalities and 80of injuries [7]

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 702197 8 pageshttpdxdoiorg1011552014702197

2 The Scientific World Journal

(a) (b)

Figure 1 Bicycle-style in the left and scooter-style in the right

Previous research on pedestrians also points to severalvariables of interest regarding violation behaviors For exam-ple Keegan and OrsquoMahony gave reports about pedestriansrsquostreet-crossing behavior influenced by travel distance andwaiting time [8] Other researchers paid much attention tothe influences of personal features on the street-crossingbehavior [9ndash11] Some useful reviews of the existing researchon pedestrian street-crossing behavior in urban roads can befound in Ishaque and Noland [12] and Papadimitriou et al[13]

Unfortunately only a few studies have investigated theviolation behavior of riders much less to electric two-wheelers Johnson et al identified three distinct types ofviolated cyclists that are exposed to different levels of riskracers impatients and runners [14] Johnson et al usedquestionnaire survey to investigate the reasons for Australiancyclistsrsquo red-light infringement [15] Wu and Zhang usedlogistic model to study cyclist red-running behavior inChina [16 17] In addition some researchers investigatedtravel characteristics mode shift riding practices risk-takingbehavior environmental impacts and user safety perceptionsof electric two-wheelers [18ndash22] Till now however noliterature is involved with waiting endurance times of electrictwo-wheelers

Riders must apply greater caution when crossing streetsandwaiting to cross because they aremore likely to be injuredin the car-rider conflict [23] Especially the process of waitingto cross is crucial for ridersrsquo crossing Once riders terminatethe waiting processed in the red-light phase they wouldviolate the traffic rules and put themselves in danger Ridersrsquowaiting processes can be considered as time-continued stateswhich are influenced by personal characteristics and trafficconditions

In this paper a hazard-based duration approach isadopted to describe waiting endurance times of electrictwo-wheelers at signalized intersections Duration modelshave been used extensively in biometrics and reliabilityengineering for decades [24] Durationmodels can be used todetermine causality in duration data and they are also usefultools in the field of transportation [25ndash29] Hazard-baseddurationmodels of survival analysis have an advantage in thatit allows the explicit study of the relationship between dura-tion time and the explanatory variables More importantly

duration models can deal with not only uncensored data butalso censored data For example the exact waiting durationreflecting rider endurance cannot be observed if riders couldwait until the permission of traffic rules Accordingly thewaiting times of electric two-wheelers are modeled by a Coxproportional hazardmodelThe covariates related to personalfeatures and traffic conditions are investigated to capturethe influenced factors of rider behavior The results give thewaiting time when a rider is likely to cross the red lightand the significantly influential factors on waiting endurancetime

2 Method

21 Duration Model The variable of interest in durationmodel is the survival time that elapsed from the beginningof an event until its end The waiting time of an electric two-wheeler at red light can be regarded as the waiting durationthat starts when a rider arrives at the intersection at thered period and ends when the rider begins to cross theintersection

Let 119879 denote the survival time In waiting time analysisof electric two-wheelers the survival time is the waitingduration of a rider at a signalized intersection It is assumedthat the waiting duration starts when a rider of electric two-wheeler arrives at the intersection at the red period and endswhen the rider begins to cross the intersection

Then the survival function is denoted by 119878(119905) It isalso called endurance probability or survivor probabilityin duration literature It represents the probability that theduration does not elapse before time 119905 as follows

119878 (119905) = Pr (119879 gt 119905) (1)

In this paper it is defined as the probability of the adherenceto traffic rules with waiting time 119905 or the probability that arider can endure waiting for a time period 119905

The failure probability or violating probability of ridersrsquocrossing behavior is then

119865 (119905) = Pr (119879 le 119905) = 1 minus 119878 (119905) (2)

which is known as the cumulative distribution of 119879

The Scientific World Journal 3

The waiting duration time 119879 has a probability densityfunction which is defined as the limit of the probability offailure in a small interval per unit time It can be expressedas

119891 (119905) =120597119865 (119905)

120597119905= limΔ119905rarr0

119875 (119905 le 119879 lt 119905 + Δ119905)

Δ119905 (3)

The density function is also known as the unconditionalfailure rate

The hazard function ℎ(119905) of duration time 119879 gives theconditional failure rate In this study the hazard function isthe instantaneous rate at which the waiting duration will endin an infinitesimally small time period Δ119905 after time 119905 giventhat the duration time has lasted to time 119905 seconds

ℎ (119905) = limΔ119905rarr0

Pr (119905 le 119879 lt 119905 + Δ119905 | 119879 ge 119905)Δ119905

=minus119889 ln 119878 (119905)

119889119905

(4)

To accommodate the effects of exogenous variables orsystematic factors is an important characteristic of durationmodels These variables or factors are called covariatesA covariate is an independent variable not manipulatedby experiment or environment but still can influence theduration Using this hazard function the effects of covariateson the waiting duration time can be introduced To includecovariates that affect duration time the Cox proportionalhazard model is widely used [30] This is defined as

ℎ (119905) = ℎ0 (119905) exp (1205731015840Χ) (5)

where ℎ0(119905) is called the baseline hazard function and can

be interpreted as the hazard function when all covariatesare ignored exp(1205731015840Χ) is a commonly used functional formfor covariate effects where Χ = (119909

1 1199092 119909

119901)1015840 is a set of

covariates and 120573 = (1205731 1205732 120573

119901) is a vector of estimable

coefficients These coefficients can be estimated from theobserved data and indicate the magnitude of the effects oftheir corresponding covariates

Combining (4) and (5) the survival function can bewritten as

119878 (119905) = exp [minusint119905

0

ℎ (119908) 119889119908] = exp [minus1198670 (119905)]exp(1205731015840Χ)

(6)

where 1198670(119905) = int

119905

0ℎ0(119908)119889119908 represents the baseline cumula-

tive hazard functionThus the covariates can be incorporatedinto the survival function

22 Model Estimation The main interest of this paper is toidentify from the 119901 covariates a subset of variables that affectthe violation hazardmore significantly and consequently thewaiting duration time at a signalized intersection We areconcerned with the regression coefficients If 120573

119894is zero the

corresponding covariate is not related to the waiting timeIf 120573119894is not zero it represents the magnitude of the effect

of 119909119894on hazard when the other covariates are considered

simultaneously

To estimate the coefficients 1205731 1205732 120573

119901 a partial like-

lihood method is adopted Suppose that 119896 of the waitingduration times from 119899 electric two-wheelers are uncensoredand distinct and n-k are right-censored Let 119905

(1)lt 119905(2)lt

sdot sdot sdot lt 119905(119896)

be the ordered 119896 distinct duration times withcorresponding covariates x

(1) x(2) x

(119896) Let R(119905

(119894)) be the

risk set at time 119905(119894)R(119905(119894)) consists of all riders whose duration

times are at least 119905(119894) For the particular duration time 119905

(119894)

conditionally on the risk set R(119905(119894)) the probability is

exp (sum119901119895=1120573119895119909119895(119894))

sum119897isin119877(119905(119894))

exp (sum119901119895=1120573119895119909119895119897)

=exp (120573x

(119894))

sum119897isin119877(119905(119894))

exp (120573x119897) (7)

Each distinct duration time contributes a factor and hence thepartial likelihood function is

119871 (120573) =119896

Π119894=1

exp (120573x(119894))

sum119897isinR(119905(119894)) exp (120573x119897)

(8)

and the log-partial likelihood is

119897 (120573) = log 119871 (120573) =119896

sum

119894=1

120573x(119894)minus log[

[

sum

119897isin119877(119905(119894))

exp (120573x119897)]

]

(9)

The overall goodness-of-fit of the model estimation isdetermined by the likelihood ratio (LR) statistics which isspecified as

119883119871= 2 [119897 () minus 119897 (120573

0)] (10)

where 119897(1205730) is the log-partial likelihood for null model with

all the regression coefficients set as zero and 119897() is the log-partial likelihood at convergence with 119901 regression coeffi-cients The estimation of 119867

0(119905) and other detailed statistical

presentations of duration models can refer to Lee and Wang[24]

3 Data

31 Site Survey Design A cross-sectional observational studywas conducted at six signalized intersections in BeijingThreecriteria were used to select the observational sites First theselected sites should represent the typical intersection designcharacteristics and traffic conditions of urban areas in BeijingSecond the selected intersections should have similar char-acteristics involved with geometric traffic conditions trafficcontrol and the absence of pointsmen In addition therehave to be a reasonably high number of electric two-wheelerstraffic during the observation period

Video cameras were used to collect data of bicyclistsrsquocrossing behaviors at signalized intersections The cameraswere carefully placed so that the road users were unaware thatthey were being observedThe data collection was conductedon weekdays during daylight hours (ie 800 am to 530pm) in good weather conditions

To record the waiting durations of electric two-wheelersall road users who entered the intersection were recorded on


video but only the riders arriving in red-light phases werecoded Only the electric two-wheelers who arrived in thered-light period were defined as valid sample In additionleft turners and right turners were excluded because of thelimited field of view of the camerasThe waiting duration wasfrom the time a rider of electric two-wheeler arrived at thecrossing location to the time heshe began to cross It canbe classified into two kinds uncensored data and censoreddataTheuncensored datawas defined as thewaiting durationwhich ended within the red-light period (violating crossing)Otherwise the waiting duration was called the censored dataas long as it ended within the green-light period (normalcrossing) For censored data the exact waiting durationwhich can reflect waiting endurance times of electric two-wheelers is unknown

32 Covariate Selection The covariate selection takes intoaccount the previous researches and arguments regardingthe effects of the exogenous variables and human factorson rider violation behavior Two broad sets of variablesare considered as covariates personal characteristics andtraffic conditions Personal characteristics include age andgender The selected covariates of traffic conditions includeridersrsquo waiting positions violating number upon arrival red-phase time and crossing traffic volume The practical effectson waiting behavior and the feasibility of data acquisitionare considered in the covariate selection The followingcovariates as shown in Table 1 are adopted to construct theduration model

33 Descriptive Statistics Of the 961 valid observations 560(5827) electric two-wheelers violated the traffic regula-tions The average waiting time of all samples was 341seconds with a standard deviation of 335 seconds Theaverage waiting time of the violating crossing was 256secondswhile the averagewaiting time of the normal crossingis 467 seconds The maximum waiting duration was 174seconds while the minimum was 0 second The latter meansthat electric two-wheelers cross the intersection withoutany wait This descriptive statistic cannot reflect the exactwaiting behavior due to the neglect of the censored data Theestimation of the waiting endurance times with censored datawill be discussed later

4 Empirical Results

The results are discussed in two subsections The overallresults are presented in the first subsection including modelfit statistics and survival probability estimation The secondsubsection presents the effects of covariates

41 Overall Results (1) Model Fit Statistics The LR statisticof the estimatedmodel clearly indicates the overall goodness-of-fit (the LR statistic is 1798 which is greater than the chi-squared statistic with 8 degrees of freedom at any reasonablelevel of significance) The significant level corresponding toeach covariate is given by 119875 value in Table 2 From the resultsmost of the included covariates are statistically significant

at the 010 level of significance It means these covariatesare significantly related to waiting endurance times Onlyage and gender are identified as insignificant predictorvariables on waiting duration times The significance levelof each covariate suggests that the importance of covariateshould be interpreted carefully Furthermore the forwardselection method was used to analyze the covariatesrsquo degreeof importance The result shows that important ranking ofsignificant factors was waiting position violating numbertraffic volume and red-phase time respectively Finally theregression equation with significant variables (119875 lt 005)obtained is as follows

log ℎ (119905)ℎ0 (119905)

= 0177119909WP1 + 1004119909WP2 + 0076119909CN

minus 0159119909MV + 0004119909RT

(11)

(2) Cumulative Surviving Proportion Figure 2 (solid line)gives the cumulative surviving proportion calculated by theduration model which represents the proportion complyingwith the traffic rules while waiting at signalized intersectionsCorrespondingly the dashed line represents the violatingproportion of electric two-wheelersThe violating proportionfor estimated model presents a general rising trend withelapsed waiting duration (dashed line in Figure 2) Theviolating proportion can be divided into three parts accordingto the gradient Firstly a sharp rise for the short durationindicates that there are a number of electric two-wheelerswho would violate to cross without any delay About 128percent of riders can be defined as risk preferences sincethey show high violation inclination and very low waitingendurance (lt1 seconds)Then the curve rises smoothly from1 second to 100 seconds This steady increase reflects thenumber of rider violations is increasing continuously Therising trend of violating proportion indicates that the red-light running behavior of most riders is time dependentIt means that riders are easy to end waiting duration andviolate the traffic rules with the elapsed duration When thewaiting duration time is larger than 100 seconds the curverises slightly It means that there are 250 percent of riderswho can endure 100 seconds or longer and they are generallynonrisk takers Finally about half of electric two-wheelersobserved cannot endure 490 seconds or longer

42 Analysis of Covariate Effects In the Cox proportionalhazard model the effects of covariates are multiplicativeon the baseline hazard function A negative coefficient ona covariate implies that an increase in the correspondingcovariate decreases the hazard rate or equivalently increasesthe waiting duration Furthermore when a covariate changesby one unit the hazard would change by [exp(120573)minus1]times100

The effect of gender (GEN) shows that male riders haveshorter waiting endurance time and higher tendency to crossagainst a red light Male riders were 1159 times more likelyto have red-light infringement behavior than female ridersZhang andWu reported that male riders are 1265 timesmorelikely than females to have shorter waiting times [17] andother qualitatively similar results in pedestrian study wereobtained by Hamed [31] and Tiwari et al [32]


Table 1 Covariates selection and explanation

Covariate Type Explanation

AG (age group) Categorical variable 0 if less than 30 (young) 1 if 30ndash50 (middle-aged) 2 if more than 50(elderly)

GEN (gender) Categorical variable 1 if male and 0 if female

WP (waiting position) Categorical variable 0 if appropriate position in nonmotorized lane (appropriate) 2 ifclose to motorized lane (nearest) and 1 if between the two (middle)

VN (violating number) Continuous variable The number of other cyclists who violate against the red light after therider arrives

MV (motor vehicle volume) Continuous variable Average motor vehicle volume per lane per min on red-light phasewhen the rider arrives

RT (red phase time) Continuous variable The period in the signal cycle during which the signal is red for riders

Table 2 Estimation in waiting duration model

Variable Coefficient (120573) Standard error Wald value 119875 value Exp (120573) 95 CI for Exp (120573)Lower Upper

GEN 0148 0118 1575 0209 1159 0920 1460AGE 1250 0535Young versus elderly 0221 0199 1243 0265 1248 0845 1842Middle-aged versus elderly 0174 0188 0865 0352 1191 0824 1720WP 95820 lt0001Middle versus appropriate 0177 0152 1345 0246 1193 0885 1609Nearest versus appropriate 1004 0134 55817 lt0001 2729 2097 3552CN 0076 0015 26369 lt0001 1079 1048 1111MV minus0159 0036 19995 lt0001 0853 0796 0915RT 0004 0002 4859 0027 1004 1000 1007

0

02

04

06

08

1

0 30 60 90 120 150 180Waiting duration time (s)

Cumulative proportion survivingViolating proportion

Figure 2 Cumulative proportion surviving versus waiting durationtime

The effect of age (AGE) indicates that older electric two-wheelers have longer waiting time Young riders were 1248times more likely to run against a red light upon approachingthe intersection than elderly riders Middle-aged riders were1191 times more likely to run against a red light comparedto elderly riders This is partly because elderly riders havestronger risk consciousness of traffic violations In addition

elderly ridersrsquo trip purposes are seldom related to work orschool so they are not in a hurry

The effect of waiting position (WP) shows that electrictwo-wheelers approaching the motorized lane have shorterwaiting time and high red-light running risk Electric two-wheelers at the position close to the motorized lane were2729 times more likely to run against a red light thanthose who waited in the appropriate position Riders in themiddle position were 1193 times more likely to violate trafficrules compared to riders in the appropriate position Thisis because ridersrsquo waiting positions to some extent reflecttheir risk preference Riders who are near to the motorizedlane are likely to have high risk tendency They may bemore anxious to cross the intersection than those who waitin the appropriate position Most of riders approaching themotorized lane were risk takers and those riders in theappropriate position were generally nonrisk takers

The effect of covariate VN (violating number) reflectsthe conformity behavior of electric two-wheelers whenapproaching the intersection Conformity psychology revealsthat people may follow otherrsquos crossing action includingtraffic violation The electric two-wheelers who are apt tobe affected by other riders have shorter waiting durationtime compared to those with low conformity psychologyMoreover a group of riders who crosses together couldincrease the risk of violation because the street-crossingbehavior shows obvious groupment and conformity [10]With the increasing number of riders in a group and longer


waiting time riders are easy to be influenced by each otherespecially the red-light running behavior

The covariate of RT (red-phase time) has a positive impacton violation risk Waiting times of electric two-wheelersincreases with the longer red-phase time Riders may becomemore impatient and they are apt to end waiting duration Inthe site survey many electric two-wheelers began to crossat the left-turn phase for vehicles and they ignored the factthat the rider signal was still red In our duration model thelower bound of the confidence interval for red phase time isonly slightly above 1This suggests that the importance of red-phase time should be interpreted carefully

The covariate ofMV (motor vehicle volume) has a distinctnegative effect on the risk of red-light running behaviorElectric two-wheelers are likely to wait longer times underhigh traffic flow conditions compared to those under relativelow traffic flow conditions when other factors are controlledThe average headways between successive motorized vehiclesunder low traffic flow conditions are larger than those underhigh trafficflowconditionsTherefore riders under low trafficflow conditions are likely to have more chance to cross theintersection than those under high flow conditions

5 Model Application

Themodel formulated in this paper can be applied to forecasttemporal shifts in waiting duration times of electric two-wheelers due to changes in traffic flow traffic managementand control This is particularly relevant today because ofchanges of traffic modes and traffic volumes For instancewith the social and economic development private carsincrease rapidly in recent decades in China At the same timeelectric two-wheelers are more and more prevalent in someChinese cities with the technology progress Similarly red-phase times and traffic volumes at signalized intersectionsmay be changed with the construction of a new businessdistrict or the temporal traffic control during major eventsand incidents All of these changes will have an effect onwaiting duration times of electric two-wheelers and thewaiting duration model in this paper can be used to assessthese impacts and provide reliable information regarding thetemporal distribution of waiting duration times at signalizedintersections In the next paragraphs two most importantvariables in predicting waiting duration times at red-lightphase are taken as examples to present themodel application

Firstly Figure 3(a) gives the new distributions of waitingduration times due to the change in motor vehicle volumeThe differences between the curves indicate the significanteffect of motor vehicle volume on waiting endurance timewhen other variables are controlled and their values are theaverage conditions of all samples While traffic flow increasesfrom 5 to 10 and 15 vehsdotminminus1 the medians of waitingduration time are 305 s 791 s and 1626 s the 75 quartilesare 35 s 282 s and 720 s It means that only 25 of electrictwo-wheelers can endure 35 seconds or longer when motorvehicle volume is 5 vehsdotminminus1 Meanwhile 25 of electrictwo-wheelers can endure 720 seconds or longer when motorvehicle volume is 15 vehsdotminminus1 Here the 50 quantile is

defined as the approximate waiting endurance time Waitingendurance times of electric two-wheelers would be 206 timeswith 15 vehsdotminminus1 compared to thosewith 10 vehsdotminminus1 (1626versus 791)

Analogously other variables estimated by the durationmodel can be used to predict the distribution of waitingduration time Figure 3(b) gives the effect of violating ridersafter arrival on waiting endurance times of electric two-wheelersWhile the number of violating riders increases from0 to 3 and 6 the medians of waiting duration time are 740 s567 s and 435 s 50 of electric two-wheelers can endure740 s or longerwhen there are no violating riders after arrivalThe result indicates that waiting endurance time is 170 timeswith no violating riders compared to those with 6 violatingriders (740 versus 435)

The hazard-based duration methodology can capture theeffects of covariates on waiting duration times of electric two-wheelers at intersections Before the applications howeverit is noted that the model should be estimated using thespecified field data Additionally the explanatory variablesshould be chosen flexibly according to the research objectiveand the traffic reality

6 Conclusions

This paper investigated the waiting endurance times ofelectric two-wheelers at signalized intersections through thedata acquired in Beijing China Waiting endurance timesof electric two-wheelers were estimated by using a Coxproportional hazard model

The paper provides several important insights into thedeterminants of red-light running behavior of electric two-wheelers especially the relation between waiting endurancetime and violation proportion First the results indicate thatthe violation risk of electric two-wheelers is time dependentAs signal waiting time increases electric two-wheelers getimpatient and violate the traffic signal With the longerwaiting duration times of electric two-wheelers they aremore likely to end the wait soon Second some crucial timepoints deserve our concern 1 second and 100 seconds The1 second indicates electric two-wheelers who are at highrisk of red-light running without any delay They accountfor 128 of the sample in the study The duration of 100seconds reflects the ridersrsquo endurance About 250 percentof electric two-wheelers can obey the traffic rules afterwaitingfor 100 seconds These riders are generally nonrisk takersThird red-phase time motor vehicle volume and confor-mity behavior have important effects on waiting endurancetimes of electric two-wheelers Minimizing the effects ofunfavorable condition may be an effective measure to obtainconscious cooperation and behavioral changes of electrictwo-wheelers Finally the model formulated in this papercan be applied to forecast temporal shifts in waiting durationtimes of electric two-wheelers due to changes in traffic flowtraffic management and control

In terms of the future work the behavior differencebetween electric bike and common bike at signalized inter-sections should be investigated Next the respective influence


0

02

04

06

08

1

0 30 60 90 120 150 180

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing

Waiting duration time (s)

MVMV

MV

= 5

= 10

= 15

(a)

0

02

04

06

08

1

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


VN = 0

VN = 3

VN = 6

(b)

Figure 3 Waiting endurance time distributions with different (a) traffic volumes and (b) violating riders

proportions of the factors to waiting endurance time shouldbe discussed In addition the risk preference of electric two-wheelers needs to be studied by questionnaire survey It ishoped that these findings may give better understanding ofbehavioral characteristics of electric two-wheelers and beapplicable in the traffic design management and control ofsignalized intersections under mixed traffic conditions

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the Fundamental ResearchFunds for the Central Universities (Grant no 2014YJS083)

References

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[2] C C Onn R K Mohamed and Y Sumiani ldquoMode choicebetween private and public transport in KlangValleyMalaysiardquoThe Scientific World Journal vol 2014 Article ID 394587 14pages 2014

[3] httpwwwlandzeppelincominvestors-pre-orders

[4] J X Weinert The rise of electric two-wheelers in China factorsfor their success and implications for the future [PhD thesis]University of California Davis Berkeley Calif USA 2007

[5] httpwwwcebikecomnewshtml2012042012042908414362htm

[6] CRTASRChinaRoadTrafficAccidents Statistics Report TrafficAdministration Bureau of China State Security Ministry Bei-jing China 2010 (Chinese)


[8] O Keegan and M OrsquoMahony ldquoModifying pedestrianbehaviourrdquo Transportation Research A Policy and Practice vol37 no 10 pp 889ndash901 2003

[9] K Lipovac M Vujanic B Maric and M Nesic ldquoThe influenceof a pedestrian countdown display on pedestrian behaviorat signalized pedestrian crossingsrdquo Transportation Research FTraffic Psychology and Behaviour vol 20 pp 121ndash134 2013

[10] T Rosenbloom ldquoCrossing at a red light behaviour of individ-uals and groupsrdquo Transportation Research F Traffic Psychologyand Behaviour vol 12 no 5 pp 389ndash394 2009

[11] Z P Zhou Y S Liu W Wang and Y Zhong ldquoMultinomiallogit model of pedestrian crossing behaviors at signalizedintersectionsrdquo Discrete Dynamics in Nature and Society vol2013 Article ID 172726 8 pages 2013

[12] M M Ishaque and R B Noland ldquoBehavioural issues in pedes-trian speed choice and street crossing behaviour a reviewrdquoTransport Reviews vol 28 no 1 pp 61ndash85 2008

[13] E Papadimitriou G Yannis and J Golias ldquoA critical assessmentof pedestrian behaviour modelsrdquo Transportation Research FTraffic Psychology and Behaviour vol 12 no 3 pp 242ndash2552009

[14] M Johnson S Newstead J Charlton and J Oxley ldquoRidingthrough red lights the rate characteristics and risk factors ofnon-compliant urban commuter cyclistsrdquoAccident Analysis andPrevention vol 43 no 1 pp 323ndash328 2011

[15] M Johnson J Charlton J Oxley and S Newstead ldquoWhy docyclists infringe at red lights An investigation of Australiancyclistsrsquo reasons for red light infringementrdquo Accident Analysisand Prevention vol 50 no 1 pp 840ndash847 2013

[16] C XWu L Yao andK Zhang ldquoThe red-light running behaviorof electric bike riders and cyclists at urban intersections in


China an observational studyrdquo Accident Analysis and Preven-tion vol 49 no 11 pp 186ndash192 2012

[17] Y Q Zhang andC XWu ldquoThe effects of sunshields on red lightrunning behavior of cyclists and electric-bike ridersrdquo AccidentAnalysis and Prevention vol 52 pp 210ndash218 2013

[18] J X Weinert M Chaktan X Yang and C R Cherry ldquoElectrictwo-wheelers in China effect on travel behavior mode shiftand user safety perceptions in amedium-sized cityrdquoTransporta-tion Research Record no 2038 pp 62ndash68 2007

[19] C R Cherry J XWeinert and Y Xinmiao ldquoComparative envi-ronmental impacts of electric bikes in Chinardquo TransportationResearch D Transport and Environment vol 14 no 5 pp 281ndash290 2009

[20] L Yao and Z X Wu ldquoTraffic safety of e-bike riders in Chinasafety attitudes risk perception and aberrant riding behaviorsrdquoTransportation Research Record vol 2314 pp 49ndash56 2012

[21] L Bai P Liu Y Q Chen X Zhang andWWang ldquoComparativeanalysis of the safety effects of electric bikes at signalizedintersectionsrdquo Transportation Research D vol 20 pp 48ndash542013

[22] W Dua J Yang B Powisd et al ldquoUnderstanding on-roadpractices of electric bike riders an observational study in adeveloped city of Chinardquo Accident Analysis and Prevention vol59 pp 319ndash326 2013

[23] RO Phillips T Bjoslashrnskau RHagman and F Sagberg ldquoReduc-tion in car-bicycle conflict at a road-cycle path intersectionevidence of road user adaptationrdquo Transportation Research FTraffic Psychology and Behaviour vol 14 no 2 pp 87ndash95 2011

[24] E T Lee and J W Wang Statistical Methods for Survival DataAnalysis John Wiley amp Sons New York NY USA 2003

[25] C R Bhat S Srinivasan and K W Axhausen ldquoAn analysis ofmultiple interepisode durations using a unifying multivariatehazard modelrdquo Transportation Research B Methodological vol39 no 9 pp 797ndash823 2005

[26] B Lee and H J P Timmermans ldquoA latent class acceleratedhazard model of activity episode durationsrdquo TransportationResearch B Methodological vol 41 no 4 pp 426ndash447 2007

[27] X B YangMHuan B F Si L Gao andHWGuo ldquoCrossing ata red light behavior of cyclists at urban intersectionsrdquo DiscreteDynamics in Nature and Society vol 2012 Article ID 490810 12pages 2012

[28] P van den Berg T Arentze and H Timmermans ldquoA latentclass accelerated hazard model of social activity durationrdquoTransportation Research A Policy and Practice vol 46 no 1 pp12ndash21 2012

[29] K M Habib ldquoModeling commuting mode choice jointly withwork start time and work durationrdquo Transportation Research APolicy and Practice vol 46 no 1 pp 33ndash47 2012

[30] D R Cox ldquoRegression models and life tablesrdquo Journal of theRoyal Statistical Society B vol 34 no 2 pp 187ndash220 1972

[31] M M Hamed ldquoAnalysis of pedestriansrsquo behavior at pedestriancrossingsrdquo Safety Science vol 38 no 1 pp 63ndash82 2001

[32] G Tiwari S Bangdiwala A Saraswat and S Gaurav ldquoSurvivalanalysis pedestrian risk exposure at signalized intersectionsrdquoTransportation Research F Traffic Psychology and Behaviourvol 10 no 2 pp 77ndash89 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation



DistributedSensor Networks



(a) (b)

Figure 1 Bicycle-style in the left and scooter-style in the right

Previous research on pedestrians also points to severalvariables of interest regarding violation behaviors For exam-ple Keegan and OrsquoMahony gave reports about pedestriansrsquostreet-crossing behavior influenced by travel distance andwaiting time [8] Other researchers paid much attention tothe influences of personal features on the street-crossingbehavior [9ndash11] Some useful reviews of the existing researchon pedestrian street-crossing behavior in urban roads can befound in Ishaque and Noland [12] and Papadimitriou et al[13]

Unfortunately only a few studies have investigated theviolation behavior of riders much less to electric two-wheelers Johnson et al identified three distinct types ofviolated cyclists that are exposed to different levels of riskracers impatients and runners [14] Johnson et al usedquestionnaire survey to investigate the reasons for Australiancyclistsrsquo red-light infringement [15] Wu and Zhang usedlogistic model to study cyclist red-running behavior inChina [16 17] In addition some researchers investigatedtravel characteristics mode shift riding practices risk-takingbehavior environmental impacts and user safety perceptionsof electric two-wheelers [18ndash22] Till now however noliterature is involved with waiting endurance times of electrictwo-wheelers

Riders must apply greater caution when crossing streetsandwaiting to cross because they aremore likely to be injuredin the car-rider conflict [23] Especially the process of waitingto cross is crucial for ridersrsquo crossing Once riders terminatethe waiting processed in the red-light phase they wouldviolate the traffic rules and put themselves in danger Ridersrsquowaiting processes can be considered as time-continued stateswhich are influenced by personal characteristics and trafficconditions

In this paper a hazard-based duration approach isadopted to describe waiting endurance times of electrictwo-wheelers at signalized intersections Duration modelshave been used extensively in biometrics and reliabilityengineering for decades [24] Durationmodels can be used todetermine causality in duration data and they are also usefultools in the field of transportation [25ndash29] Hazard-baseddurationmodels of survival analysis have an advantage in thatit allows the explicit study of the relationship between dura-tion time and the explanatory variables More importantly

duration models can deal with not only uncensored data butalso censored data For example the exact waiting durationreflecting rider endurance cannot be observed if riders couldwait until the permission of traffic rules Accordingly thewaiting times of electric two-wheelers are modeled by a Coxproportional hazardmodelThe covariates related to personalfeatures and traffic conditions are investigated to capturethe influenced factors of rider behavior The results give thewaiting time when a rider is likely to cross the red lightand the significantly influential factors on waiting endurancetime

2 Method

21 Duration Model The variable of interest in durationmodel is the survival time that elapsed from the beginningof an event until its end The waiting time of an electric two-wheeler at red light can be regarded as the waiting durationthat starts when a rider arrives at the intersection at thered period and ends when the rider begins to cross theintersection

Let 119879 denote the survival time In waiting time analysisof electric two-wheelers the survival time is the waitingduration of a rider at a signalized intersection It is assumedthat the waiting duration starts when a rider of electric two-wheeler arrives at the intersection at the red period and endswhen the rider begins to cross the intersection

Then the survival function is denoted by 119878(119905) It isalso called endurance probability or survivor probabilityin duration literature It represents the probability that theduration does not elapse before time 119905 as follows

119878 (119905) = Pr (119879 gt 119905) (1)

In this paper it is defined as the probability of the adherenceto traffic rules with waiting time 119905 or the probability that arider can endure waiting for a time period 119905

The failure probability or violating probability of ridersrsquocrossing behavior is then

119865 (119905) = Pr (119879 le 119905) = 1 minus 119878 (119905) (2)

which is known as the cumulative distribution of 119879



119891 (119905) =120597119865 (119905)

120597119905= limΔ119905rarr0

119875 (119905 le 119879 lt 119905 + Δ119905)

Δ119905 (3)



ℎ (119905) = limΔ119905rarr0

Pr (119905 le 119879 lt 119905 + Δ119905 | 119879 ge 119905)Δ119905

=minus119889 ln 119878 (119905)

119889119905

(4)


ℎ (119905) = ℎ0 (119905) exp (1205731015840Χ) (5)



1 1199092 119909

119901)1015840 is a set of

covariates and 120573 = (1205731 1205732 120573




119878 (119905) = exp [minusint119905

0

ℎ (119908) 119889119908] = exp [minus1198670 (119905)]exp(1205731015840Χ)

(6)

where 1198670(119905) = int

119905




119894is zero the



simultaneously




(1)lt 119905(2)lt



(1) x(2) x

(119896) Let R(119905

(119894)) be the



(119894)


exp (sum119901119895=1120573119895119909119895(119894))

sum119897isin119877(119905(119894))

exp (sum119901119895=1120573119895119909119895119897)

=exp (120573x

(119894))

sum119897isin119877(119905(119894))

exp (120573x119897) (7)


119871 (120573) =119896

Π119894=1

exp (120573x(119894))

sum119897isinR(119905(119894)) exp (120573x119897)

(8)


119897 (120573) = log 119871 (120573) =119896

sum

119894=1

120573x(119894)minus log[

[

sum

119897isin119877(119905(119894))

exp (120573x119897)]

]

(9)


119883119871= 2 [119897 () minus 119897 (120573

0)] (10)





3 Data








4 Empirical Results




log ℎ (119905)ℎ0 (119905)

= 0177119909WP1 + 1004119909WP2 + 0076119909CN

minus 0159119909MV + 0004119909RT

(11)
















0

02

04

06

08

1












5 Model Application






6 Conclusions





0

02

04

06

08

1

0 30 60 90 120 150 180

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


MVMV

MV

= 5

= 10

= 15

(a)

0

02

04

06

08

1

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


VN = 0

VN = 3

VN = 6

(b)





Acknowledgment


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119891 (119905) =120597119865 (119905)

120597119905= limΔ119905rarr0

119875 (119905 le 119879 lt 119905 + Δ119905)

Δ119905 (3)



ℎ (119905) = limΔ119905rarr0

Pr (119905 le 119879 lt 119905 + Δ119905 | 119879 ge 119905)Δ119905

=minus119889 ln 119878 (119905)

119889119905

(4)


ℎ (119905) = ℎ0 (119905) exp (1205731015840Χ) (5)



1 1199092 119909

119901)1015840 is a set of

covariates and 120573 = (1205731 1205732 120573




119878 (119905) = exp [minusint119905

0

ℎ (119908) 119889119908] = exp [minus1198670 (119905)]exp(1205731015840Χ)

(6)

where 1198670(119905) = int

119905




119894is zero the



simultaneously




(1)lt 119905(2)lt



(1) x(2) x

(119896) Let R(119905

(119894)) be the



(119894)


exp (sum119901119895=1120573119895119909119895(119894))

sum119897isin119877(119905(119894))

exp (sum119901119895=1120573119895119909119895119897)

=exp (120573x

(119894))

sum119897isin119877(119905(119894))

exp (120573x119897) (7)


119871 (120573) =119896

Π119894=1

exp (120573x(119894))

sum119897isinR(119905(119894)) exp (120573x119897)

(8)


119897 (120573) = log 119871 (120573) =119896

sum

119894=1

120573x(119894)minus log[

[

sum

119897isin119877(119905(119894))

exp (120573x119897)]

]

(9)


119883119871= 2 [119897 () minus 119897 (120573

0)] (10)





3 Data








4 Empirical Results




log ℎ (119905)ℎ0 (119905)

= 0177119909WP1 + 1004119909WP2 + 0076119909CN

minus 0159119909MV + 0004119909RT

(11)
















0

02

04

06

08

1












5 Model Application






6 Conclusions





0

02

04

06

08

1

0 30 60 90 120 150 180

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


MVMV

MV

= 5

= 10

= 15

(a)

0

02

04

06

08

1

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


VN = 0

VN = 3

VN = 6

(b)





Acknowledgment


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













4 Empirical Results




log ℎ (119905)ℎ0 (119905)

= 0177119909WP1 + 1004119909WP2 + 0076119909CN

minus 0159119909MV + 0004119909RT

(11)
















0

02

04

06

08

1












5 Model Application






6 Conclusions





0

02

04

06

08

1

0 30 60 90 120 150 180

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


MVMV

MV

= 5

= 10

= 15

(a)

0

02

04

06

08

1

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


VN = 0

VN = 3

VN = 6

(b)





Acknowledgment


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















0

02

04

06

08

1












5 Model Application






6 Conclusions





0

02

04

06

08

1

0 30 60 90 120 150 180

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


MVMV

MV

= 5

= 10

= 15

(a)

0

02

04

06

08

1

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


VN = 0

VN = 3

VN = 6

(b)





Acknowledgment


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













5 Model Application






6 Conclusions





0

02

04

06

08

1

0 30 60 90 120 150 180

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


MVMV

MV

= 5

= 10

= 15

(a)

0

02

04

06

08

1

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


VN = 0

VN = 3

VN = 6

(b)





Acknowledgment


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

02

04

06

08

1

0 30 60 90 120 150 180

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


MVMV

MV

= 5

= 10

= 15

(a)

0

02

04

06

08

1

Cum

ulat

ive p

ropo

rtio

n su

rviv

ing


VN = 0

VN = 3

VN = 6

(b)





Acknowledgment


References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article waiting endurance time estimation of...

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