A trip chain comprises a series of trips made by a rider on a daily basis, and the entailed sequence of trips demonstrates the rider’s traveling behavior [9]. The transit chaining method is normally applied by connecting a passenger’s trip legs [8]. Some public transportation riders may arrive directly at their shopping or work destinations, whereas others may make transfers immediately after alighting at their stops. Still others may commence their transit after reaching a stop as a result of taxi rides or simple walks. Regardless of the commuting behaviors of riders, transit chains comprise single transits connected by breaks. AFC systems record the boarding and alighting times of transit riders in some cities, thereby generating geo-tagged transit data that enable the calculation of displacements and trip durations, which are important attributes of Transit Chaining Breaks (TCBs). Fig. (1) depicts a cardholder’s transit chain. Point A denotes the first boarding station; point B denotes the first alighting station, and so forth. Displacements occur between the previous stop at which the rider alights and next boarding stop. All three breaks have particular durations, but the third break does not entail a displacement.

Fig. (1). An illustration of a transit chaining break.

A key issue addressed in this study focuses on whether TCBs are transfers or actual destinations. Transfers are treated as an unnecessary demand generated by an imperfect transportation system. TCBs have specified durations, and displacements are not accounted for in estimations of demands for transportation.

TCB duration is defined as the time that lapses between the swiping of a rider’s smart card when boarding at a stop and his or her previous alighting. It includes the duration of the following activities of the rider: checking out, walking between stations, and finally getting into the public transport system and checking in with his/her smart card. The duration of transit number n of a cardholder is calculated as follows:

(1)

where boarding_time_n+1 denotes the boarding time for transit number n and alighting_time_n denotes the alighting time for transit number n+1.

Many dimensions need to be considered to determine the purposes of transit. However, an analysis can be performed using the threshold time of transfer within a public transport system to determine whether a TCB is a transfer. The time required to make transfers varies, and it is difficult to ascertain the required transfer times using the smart card data alone [6]. Previous studies have shown that the threshold transfer time may vary, usually ranging from 30 minutes to 60 minutes, and even extending up to 90 minutes [10-12].

TCB displacement is defined as the distance between the boarding station and the previous station at which the rider alights. Because the lengths of actual routes are complex and difficult to ascertain, here great-circle distances between boarding stations and previous alighting stations are treated as TCB displacements, and the displacements are calculated using the following haversine formula:

(2)

where ϕ₁, λ₁, and ϕ_2, λ₂ denote the respective geographical latitude and longitude, in radians, of the boarding station and the previous alighting station, Δλ is the absolute difference between λ₁ and λ, and r is the radius of the Earth.

Previous studies have shown that the transfer type TCB distance can range from 400 m to 1,100 m [8, 13]. On its own, the TCB displacement does not indicate whether it is a transfer point. Displacements in combination with TCB durations are more effective in identifying transfer activities.

Here, we introduce the duration-displacement matrix of TCBs. Based on this matrix, the following criteria were used to determine transfer activity relating to TCBs: (i) the TCB duration is too short for implementing activities other than transfers and (ii) the displacement occurs within a walkable distance.

A residential population zone is considered to be positively related to the demand for public transport [14]. The test criterion was the consistency of the demand estimation with regard to the distribution of the population investigated in this study. The demand estimation of zone number i can be expressed as:

(3)

where demand_i and count_j denote the outcome of the demand estimation for zone i and the assumed demand of transit station number j. The value of w_ij is 0 or 1 depending on whether station number j is located in zone i.

Control group: Daily boarding volumes at stations were treated as public demand, and the counts were projected into cell zones based on a population survey. Array X_control = [demand₁, demand₂, demand₃, … demand_i]_control, where demand_i denotes the need for public transportation in zone i.

Test group: After excluding transfer TCBs, the counts were projected on to population survey zones. Array X_test = [demand₁, demand₂, demand₃, … demand_i]_test.

Pearson product-moment correlation coefficients (Pearson) were calculated for population arrays in relation to the demand arrays to measure how the estimations generated by new method were in relation to the population. The formula used for calculating Pearson was:

(4)

where cov denotes covariance and σ_X and σ_Y are standard deviations of X and Y.

Y = [population₁, populaton₂, … population_i], where population_i is a population in zone i.

If Pearson_(control) < Pearson_(test), then the TCB method can be considered to be more objective than the non-TCB approaches.

An assessment of transit data for Beijing’s bus and metro systems revealed that there was very little change in traffic volumes at each station on workdays. For example, fluctuations in card checking counts at the 100 busiest stations in Beijing were less than 5% during the period August 15^–19, 2016. For this study, the transit logs for Beijing’s bus and metro systems were obtained for August 17, 2016, as they yielded typical data for workdays. Each entry contains card numbers, boarding stations, boarding times, alighting stations, and alighting times. A total of 13,000 bus stations and 345 metro stations were covered in the study. Analysis of the data indicated that there were 3,586,286 transit chains with 6,351,735 TCBs.

Of the 6.35 million TCB displacements that were identified, 1.7 million were 0 km in distance, indicating that riders’ boarding stations were also their final alighting stations. A graphic depiction of the duration-displacement matrix (Fig. 2) clearly reveals the relation between TCB displacements and durations. Fig. (2) shows that most transfers were made within a displacement distance of 2 km and durations were less than 15 minutes (breaks with displacements of 0 km were not depicted).

Fig. (2). Distribution of the TCB duration-displacement.

A total of 6.3 million displacements were less than 2 km. Consequently, we set a TCB displacement of 2 km as the transfer threshold distance. Fig. (3) indicates that 20 minutes was a reasonable transfer threshold time for identifying transfer activities.

Fig. (3). TCB duration count.

Table 1 shows the 10 stations where the most transfers took place. Those stations were generally treated as major demand sources. However, not all transfer activities occurring at those stations should be considered to indicate a demand for public transport.

Beijing was divided into 306 sub-district zones in China’s sixth national population census implemented in 2010. A traditional estimation method basing on transit OD pairs (X_control) as well as a method entailing the use of TCBs (X_test) were conducted. Calculated Pearson product-moment correlation coefficients of Pearson_control and Pearson_test indicated that the transit chaining approach generated higher correlations between X (transport demand estimation) and Y (population distribution), especially in the most active zones (Table 2). The use of the transit chaining approach reduced the occurrence of false demand, resulting in the estimation being more objective in relation to the population (Fig. 4).

Fig. (4). Non-chaining approach (a) and discernable improvement using the chaining approach (b).