Bicyclists may cross the bicycle lane and occupy the adjacent motor lanes for some reason. The mixed traffic consisting of cars and bicycles shows very complicated dynamitic patterns and higher accident risk. To investigate the reason behind such phenomenon, the lifetime analysis method is adopted to examine the observed data for the behavior that bicycles cross the bicycle lane and occupy the adjacent motor lanes. The concepts named valid volume and probability of lanekeeping behavior are introduced to evaluate the influence of various external factors such as lane width and curb parking, and a semiparametric method is used to estimate the model with censored data. Six variables are used to accommodate the effects of traffic conditions. After the model estimation, the effects of the selected variables on the lanekeeping behavior are discussed. The results are expected to give a better understanding of the bicyclist behavior.
Our daily life and work are closely related to traffic and mobility. Nowadays, in consequence of dramatically increasing traffic demand, traffic congestion has an immense negative impact on daily life and modern society [
In an urban street without segregated facility, the bicyclists may drive in the motor lane because of the blockage in the bicycle lane. Once the bicyclists do not satisfy the traffic condition, they will arbitrarily change travel route and even occupy the motor lane. Particularly for the position near bus stop or parking area, the occupancy of motor lane has a strong impact on traffic performance and safety [
Some bicyclists are apt to travel in the adjacent motor lanes in order to get their desired driving conditions, for example, speed and space. When the bicycle lane is blocked due to some reason, the probability of the lanecrossing behavior would increase obviously. Assume that the lanecrossing behavior occurs if the bicycle volume
In this paper, the critical volume
In terms of
Survival analysis models (also called lifetime analysis) have been used extensively for several decades in biometrics and industrial engineering as a means of determining causality in lifetime data [
The traffic behavior that bicyclists travel in bicycle lanes can be considered as a valid state under particular conditions (e.g., lane widths, traffic volume, and curb parking). Such a valid state continues with an increasing bicycle volume. If the volume is greater than the valid volume, the lanecrossing behavior will occur. It means that the particular conditions are hard to satisfy the travel demands of bicyclists. The continual process of valid state is similar to the continued life. If the lanecrossing behavior is regarded as the termination of life, the methods for lifetime data analysis can be used to estimate the valid volume
Analogy between lifetime data analysis and bicyclist behavior analysis.
Lifetime analysis  Lanecrossing behavior analysis  

Parameter  Time 
bicycle volume 
Failure event  Death at time 
Lanecrossing behavior at volume 
Variable  Lifetime 
Valid volume 
Censoring  Lifetime 
Valid volume 
Survival function 


Probability distribution function 


Firstly, an important concept, hazard function, is introduced. A hazard function at specified volume
The result in the hazard function is hazard rate (or hazard), which is the instantaneous probability that the lanecrossing will occur in an infinitesimally small volume
According to the mathematical relation between the hazard function and survival function, the probability of lanekeeping can be obtained:
To accommodate the effects of external factors, the hazard function can be written as
In this study, a framework of nonparametric baseline hazard, which was proposed by Cox using
The endurance probability function combining (
The shape of
The selection of external factors takes into account the previous researches and arguments regarding the effects of the exogenous variables and human factors on bicyclist behavior. Three broad sets of variables may influence the bicyclist behavior: personal characteristics, traffic conditions, and trip characteristics. In this paper, the traffic conditions are considered. The following factors, as shown in Table
External factors and explanation.
Variable  Name  Type  Explanation 


Effective width  Continuous variable  The effective width of bicycle lane 

Travel speed  Continuous variable  The average travel speed for the survey internal 

Car volume  Continuous variable  Car volume in the adjacent lane (veh/30 s)^{a} 

Curb parking  Binary indicator  1 if there are curb parking cars along the bicycle lane, 0 otherwise 

Retrograde motion  Binary indicator  1 if there are retrograde bicycles in the lane at the 

Safe gap  Binary indicator  1 if the adjacent lane is clear of moving car, 0 otherwise 
^{ a}“veh” is the abbreviation of vehicle.
The field survey is conducted in the urban roads with no isolation facilities. The selected survey sites are monitored by video cameras. Then, the bicycle volumes in the lanes with different effective widths can be acquired. According to [
The length of the observed section is 25 m and there is no influence of bus stop and pedestrian crosswalk. In consideration of the discrete arrival of bicycles and the nonuniform volume, short observed interval may not include enough samples while long interval may influence the definition of data status. Therefore, the observed interval is 30 s. The status of each interval is defined as (a) censored data if there is no bicycle entering the motor lane in the interval and (b) distinct data if the lanecrossing behavior occurs in the interval [
Basic features of observed sections.
Effective width 
Sample size  Volume distribution (veh/30 s)  Lanecrossing ratio (%)  

Min  Max  Mean  
1.5  118  2  28  12  47 
2.5  378  4  35  17  33 
3  381  2  34  26  28 
3.5  430  3  39  19  29 
Table
Model estimation.
Variable  Estimate  Standard error 




−0.271  0.12  −2.264  0.024 

0.002  0.152  2.092  0.036 

−0.201  0.192  1.047  0.295 

0.317  0.001  −2.238  0.025 

0.414  0.001  −3.777  <0.001 

0.148  0.148  −1.014  0.303 
Figure
Distribution of the lanekeeping probability in average condition.
In the proportional hazard model, the effects of variables are multiplicative on the baseline hazard function. A negative coefficient on a variable implies that an increase in the corresponding variables decreases the hazard rate, or equivalently increases the valid volume. The greater valid volume means that the occurrence of lanecrossing behavior decreases. The effects of external factors are analyzed in the following.
Distributions of the lanekeeping probability with various lane widths.
Distributions of lanekeeping probability under infleucne of curb parking.
Effect of retrograde motion on lanekeeping behavior.
This paper proposed a model to describe the lanekeeping behavior of a bicyclist in urban street by using survival analysis. A concept of valid volume is also proposed to describe the relation between the lanecrossing behavior and the bicycle volume. The volume data are defined as censored data and uncensored data. Proportional hazard method is used to estimate the field data with censored data. In order to capture the effect of external factors involving traffic conditions, six variables are selected to construct the PH model. The results show that the effective width of bicycle lane, travel speed, curbs parking, and retrograde motion have significant effect on the lanekeeping behavior. Two variables (car volume and safe gape) show relatively low significance. It is concluded that the lanekeeping behavior results from various related factors such as personal features, traffic conditions, and environmental factors, and any change of the influential factors can modify the lanekeeping behavior. Therefore, the planning and designing of urban street should consider these influential factors apprehensively.
The future work will focus on the influential factors. More factors will be introduced into the model and the field surveys of sites will be increased to obtain more empirical data. For example, the average speed of bicycle travelling in the car lane could be an important influential factor on the lanekeeping behavior of cyclists. Also the significances of variables and their effects on bicyclist behavior will be discussed deeply.
The authors would like to thank the anonymous editor and referees for their valuable comments. This research is supported by the Programme of Introducing Talents of Discipline to Universities under Grant no. B12022 and the Programme of International Science and Technology Cooperation in the Beijing Institute of Technology.