Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 5, No. 2, 2023 

 

21 

Proportional	Estimation	Method	of	Urban	Rail	
Passenger	Flow	Transfer	Path	Selection	Based	on	IC	
Card	Data	
Xueke Zhao 

School of Traffic & Transportation, Chongqing Jiaotong University, Chongqing 400074, China 

 

Abstract: Based on the analysis of the influencing factors of urban rail transit passenger flow transfer path selection behavior 
and the components of travel time, a method of estimating the proportion of urban rail transit passenger flow transfer path 
selection based on IC card data is proposed. Firstly, the research determines the shortest interchange path algorithm as Dijkstra 
algorithm and the graph-based depth-first search algorithm as the effective interchange path search algorithm; analyzes the 
factors influencing the passenger flow interchange path selection behavior as three types of travel time, interchange cost and 
road network familiarity; constructs the generalized cost function of effective interchange path selection by combining travel 
time and interchange cost; establishes the passenger flow probability selection model by combining road network familiarity. To 
eliminate the influence of absolute difference of utility on the probability of path selection in the polynomial logit model, the 
path probability selection model is improved with the help of minimum travel cost; Bayesian estimation is used to compare the 
passenger travel time with the theoretical travel time to identify the closest effective interchange path, and the joint distribution 
probability is used to calibrate the probability selection model in terms of travel time and interchange cost. The coefficient, 
coefficient of interchange passenger flow, penalty coefficient of interchange number, familiarity of road network and other related 
parameters are combined with the joint distribution probability to calibrate the probability of selection of different effective 
interchange paths. 

Keywords: Urban rail transportation, Route selection ratio, Dijkstra algorithm, IC card data, Parameter estimation. 
 

1. Introduction 
The percentage of passenger traffic routes of urban subway 

(hereinafter referred to as urban rail) is used as the basis for 
line flow distribution. At present, the number distribution 
methods of urban rail in China and abroad mostly use the 
multi-path proportional division technology. The number of 
routes is generally set using the Logit model based on various 
forms of impedance functions (mileage, time) [1], and the 
coefficients in this model are determined by a large number 
of manual data. Because the measurement cost is relatively 
expensive, the data reliability is difficult to ensure. Both 
domestic and foreign urban rail use AFC system to record 
passenger travel information, The system can accurately 
obtain the location and time of passengers entering and 
leaving the station. 

Mengtian Leng et al. Jang W [3] established a relevant 
analysis model based on IC card data, identified the transfer 
points of each passenger in the travel path, analyzed the 
possible travel transfer modes between the passenger's 
departure and destination, and discussed the relationship 
between relevant data and traffic planning. Tianyou Liu et al. 
Zheng Yajing and Zhao Ji et al. [5] obtained the effective 
transfer path of transfer passenger flow through IC card data, 
thus strengthening the connection between OD combination 
and transfer passenger flow, and obtaining more accurate 
transfer passenger flow data. Based on the IC card data, Chen 
Yanyan et al. [6] used the passenger travel OD to match the 
IC card data of passenger travel, combined with the 
relationship between the passenger travel time in peak hours 
and the passenger travel time in non-peak hours, provided a 
calculation formula for the waiting time of passengers 
traveling in peak hours based on the IC card big data, and 

studied the characteristics of the waiting time of passengers 
going out. Zhang Yimu et al. [7] proposed a calculation 
method of getting on and off station points based on time 
matching according to the IC card of urban subway, BRT and 
bus networks, obtained the travel chain of transfer passenger 
flow, and discussed the impact of matching threshold on the 
overall matching accuracy. Liu Jianfeng and other [8] people 
studied the main influencing factors of passenger route 
selection of urban rail transit, and verified the main 
influencing factors through actual survey data. Lin Zhan et al. 
[9] gave a traffic distribution model of urban rail transit 
network based on the improved Logit model, and studied and 
proved the model and method. Sun Yan and other [10] people 
tested the rationality of the model in terms of goodness of fit 
and expected results according to the characteristics of 
travelers. 

Based on the IC card data and Bayesian estimation, this 
paper proposes an estimation method of the proportion of 
urban rail passenger flow transfer route selection based on the 
IC card data, which provides a new idea for the determination 
of passenger flow transfer. 

2. Influencing Factors of Rail 
Passenger Flow Transfer Route 
Selection Behavior 

The formation of rail transit network structure, when 
passenger flow chooses an effective transfer path, it is 
affected by various factors such as travel time, transfer cost, 
road network familiarity and so on. Therefore, the selection 
of effective transfer path by passenger flow is often a 
comprehensive decision result after comprehensively 
considering the above factors. 



 

22 

2.1. Travel time 
Travel time refers to the total time spent by the passenger 

flow after selecting an effective transfer path to enter the 
starting station from the swiping card, and then swiping the 
card to exit the station after arriving at the destination station. 
Travel time is usually composed of two parts: the time for the 
passenger flow to take the bus and the waiting time. 

The travel time of transfer passenger flow at the starting 
and ending points can be expressed as: 

 

i
iji

ij i i
ij ij

t
T

t s

 


           (1) 

 

Station i is the starting point or destination station 

Where: 

——The travel time of the vehicle at the station between 
the beginning and the end of the passenger flow; 

——The dwell time of the vehicle at the station between 
the beginning and the end of the passenger flow. 

The travel time of passenger flow on an effective transfer 
path in the set of effective transfer paths can be expressed as: 

 

 ,l l
k ijT T i j K           (2) 

 
Where: 

——A collection of valid transfer paths. 

The waiting time refers to the time from the arrival of the 
passenger flow at the departure platform to the boarding time. 
The waiting time of transfer passenger flow occurs at the 
starting station or transfer station. The waiting time is 
positively correlated with the train operation schedule. 
According to the field survey, the waiting time of transfer 
passenger flow is usually 0.5 of the departure interval of the 
line. 

2.2. Transfer fee 
The main difference in transfer costs during the transfer 

process is the number of transfer times and the walking time 
of passenger flow in the transfer channel. Therefore, the 
transfer costs in different directions in the transfer station can 
be expressed as the walking time of passenger flow. 

Transfer fee: 

 
, ,=l m l m
i iw Ti               (3) 

 
Where: 

——Transfer station; 

——Transfer from line to line; 

——Walk time from line transfer to line; 

——Transfer passenger flow adjustment coefficient. 

The total transfer cost can be obtained by considering the 
waiting time of the passenger flow during the transfer: 

 

 , ,= 0.5l m l m
i i mE a w f            (4) 

Where: 

——Change passenger flow coefficient value; 

——Departure interval. 

When an effective transfer path of passenger flow requires 
multiple transfers, the impact of transfer times on transfer 
costs should be considered, and the penalty adjustment 
coefficient of transfer times of passenger flow should be 
added. And the more transfer times, the greater the penalty 
coefficient. At this time, the transfer fee can be expressed as: 

 

   , ,
, 0.5l m l m

i i k i mE a e w f


          (5) 

 
Where: 

——When the passenger flow selects an effective transfer 
path in the set of effective transfer paths, the cumulative 
number of transfers at the transfer station; 

——Penalty adjustment coefficient for transfer times of 
passenger flow. 

2.3. Familiarity with road network 
Road network familiarity is an important factor for 

passenger flow to choose an effective transfer path. Generally, 
the road network familiarity of passenger flow can be 
summarized by IC card number or issuing relevant 
questionnaires. The more familiar the transfer passenger flow 
is with the road network, the more feasible it is to choose the 
shortest transfer path. When the passenger flow is not very 
familiar with the road network, they often choose the route 
with less transfer times or shorter mileage, but the travel time 
of this route is not necessarily the least. Therefore, when the 
change passenger flow has different familiarity with the road 
network, it will not only affect the choice of the shortest 
transfer path for the change passenger flow, but also affect the 
distribution of the change passenger flow on the road network. 

3. Construction of Effective Transfer 
Route Selection Model for Rail 
Passenger Flow 

3.1. Definition of effective transfer path of 
passenger flow 

With the continuous acceleration of the rail transit network 
process, passenger flow travel from the starting point to the 
destination is often not a direct route for passengers, and 
generally requires transfer to arrive, which is the fastest time 
and the least cost. There are generally multiple travel paths to 
choose between the starting point and the ending point of the 
rail transit network. Therefore, the transfer paths for 
passenger flow in the rail network are called effective transfer 
paths. The effective transfer path has the following three 
characteristics: 

1) There are multiple effective transfer paths between the 
starting point and the ending point. Because the stations 
covered by each effective transfer path are different, the 
effective transfer paths formed are also different, which are 
called different effective transfer paths; 

2) The passenger flow will only take the same station on 
the same route and in the same direction once during the trip; 

3) When the passenger flow chooses different effective 
transfer routes, there will be no significant difference in travel 



 

23 

time. 

In order to determine the effective transfer path of 
passenger flow, [7] determine the effective transfer path of 
passenger flow according to the travel cost, threshold 
correction parameters, and the transfer times of passenger 
flow under different effective transfer paths. The judgment 
formula is as follows (Formula 6-7): 

 

min min0.466 ln( 1)kb b b             (6) 

 

maxkN N                  (7) 

 
Where: 

——The travel cost of the first effective transfer path in the 
set of effective transfer paths formed by the passenger flow at 
the start and end points; 

——The minimum travel cost of the shortest effective 
transfer path in the set of effective transfer paths formed by 
the passenger flow at the start and end points; 

——The number of transfers required for the first effective 
transfer path in the set of effective transfer paths formed by 
the passenger flow at the start and end points; 

——The maximum transfer times of all effective transfer 
paths in the set of effective transfer paths formed by the 
passenger flow at the starting point and the ending point, 
usually  

Generalized cost model for efficient transfer path selection 

For an OD pair in the passenger flow, the total cost of the 
passenger flow on an effective transfer path in the set of 
effective transfer paths can be expressed as: 

 

 k k kD C k K               (8) 

 
Where: 

——Defined expenses; 

——Random error term; 

 

——A collection of valid transfer paths. 

In combination with travel time and transfer cost, the cost 
function of the shortest transfer path of passenger flow is 
expressed as: 

 

   

,

,

,
, , , ,

=

0.5

l l m
k k k k i k

l i

l
ij ij k

l

l m
i k i m i k l k m k k

i

D C T E

T

a e w f


  

 

   

   

  

       

 





  (9) 

 

, , , ,ij k i k l k m k   、 、              (10) 

 
Where: 

——Ride time coefficient; 

——The relationship between the starting and ending 
points and the shortest transfer path; 

——The relationship between the transfer station and the 
shortest transfer path; 

, - the relationship between the line and the shortest transfer 
path. 

3.2. Probability selection model of effective 
transfer route of passenger flow 

The probability that the transfer passenger flow selects an 
effective transfer route in the set of effective transfer routes 
during a trip is the lowest probability that the total cost of the 
effective transfer route in the set of effective transfer routes. 
Different effective transfer paths correspond to different 
selection probabilities. At present, when calculating the 
probability of effective transfer path selection, the most 
commonly used is the polynomial logit model (MNL model). 
Assuming that the random error term in the cost function is 
independently and identically distributed and follows the 
Gumbel distribution with a mean of 0, according to the 
distribution function and density function of the Gumbel 
distribution, the probability of passenger flow selecting the 
effective transfer path in the set of effective transfer paths can 
be expressed as: 

 

 
 

exp

exp
k

k
p K k

C
p k K

C





 


. .     (11) 

 
Where: 

——Constant, whose value represents the loyalty of 
passenger flow to an effective transfer path. The greater the 
value, the greater the probability of passenger flow choosing 
the effective transfer path. Usually, this value represents the 
familiarity of passenger flow with the traffic network. 

The choice probability of passenger flow for each effective 
transfer path calculated by the polynomial model is based on 
the utility absolute difference between passenger flow and the 
travel cost of each effective transfer path, which has an impact 
on the determination of subsequent transfer passenger flow. 
Therefore, the minimum travel cost is used to improve 
formula (11). The probability of the first effective transfer 
path selected in the improved polynomial model effective 
transfer path set can be expressed as: 

 

 
 

min

min

exp /

exp /
k

k
p K k

C C
p k K

C C





 


   (12) 

 
Where: 

——The minimum travel cost in the set of effective 
transfer paths. 

4. Estimation of Effective Transfer 
Path Selection Proportion 

4.1. Data source 
The IC card data of the networked operation rail station 

generally comes from the urban rail transit operation 
company with a certain level of networking. The information 
recorded by the IC card data of each city is almost the same. 
Take the IC card data of Chongqing rail transit for example, 
the IC card data contents are: card number (ticket_id), card 



 

24 

type (ticket_type), entry station number (ent_station_id), 
entry time (ent_txn_date_time), exit station number 
(exit_station_id) Outbound time (exit_txn_date_time). Where 
ticket_ Type refers to the type of transaction card. The main 
types are: 0 Livable ordinary card, 05 Livable monthly ticket 
card, 15 Livable employee card, 14 Livable senior citizen 
card, 03 Livable student card, 77 Livable senior citizen time 
card, 20 Love discount card, 98 rail one-way ticket. 

4.2. Parameter calibration of effective transfer 
path probability selection model based on 
Bayesian estimation 

Bayesian estimation method is based on the IC card data, 
which contains the information of the inbound and outbound 
stations of the passenger flow, the travel time, and so on. It 
compares the travel time with the theoretical travel time of the 
effective transfer path calculated by the model, identifies the 
closest effective transfer path, and determines the effective 
transfer path of the passenger flow. The cost of this method is 
small and convenient. Therefore, this study uses Bayesian 
estimation method to calibrate the relevant parameters in the 
effective transfer path probability selection model. 

The set of effective transfer routes includes the information 
of inbound and outbound stops and travel time of transfer 
passenger flow; The relevant parameter set of the effective 
transfer path probability selection model includes the 
theoretical travel time of different effective transfer paths, the 
relevant parameters of the generalized cost model of effective 
transfer path selection, the interval operation data set of the 
rail transit network (train interval operation time, train arrival 
and stop time, train departure interval and passenger flow 
walking time in the transfer channel, etc.), the time allowable 
deviation coefficient, and the travel time coefficient, 
Coefficient value of transfer passenger flow and penalty 
adjustment coefficient of transfer times of transfer passenger 
flow. 

Because the above parameters have the original 
distribution before sampling, the edge probability of the joint 
distribution is usually expressed in the form of normal 
distribution; Is the conditional probability in the effective 
transfer path set given the values of the relevant parameter set 
of the effective transfer path probability selection model; Is 
the conditional distribution of each parameter, and the above 
probability is expressed as: 

 

     , , , , , , , , , , , ,C p C C                   (13) 

 
Assuming that the parameters in formula (13) are 

independent of each other, the joint edge distribution can be 
converted into: 

 

           , , , , =C C                   (14) 
 

Given each parameter value, the probability of occurrence 
of an effective transfer path is equal to the likelihood function 
of all unknown parameter values when the effective transfer 
path is known, namely: 

 

   , , , , =L , , , ,p C C            (15) 

 

The passenger flow under different effective transfer routes 
is calculated according to the selection probability of effective 
transfer routes, and the likelihood function can be rewritten as 
follows: 

 

   L , , , , = , , , ,W
w W

C p C       


     (16) 

 
Where: 

——All pairs; 

——A pair; 

——The probability that an effective transfer path is 
selected when each parameter value is given 

——The likelihood function of all unknown parameter 
values when the effective transfer path is known. 

Different effective transfer paths correspond to different 
travel costs of passenger flow, and only one effective transfer 
path can be selected for one trip of passenger flow. Therefore, 
the sample probability generated when the passenger flow 
chooses an effective transfer path is the sum of the 
probabilities of each effective transfer path between the start 
and end points, which can be expressed by the total 
probability formula: 

 

     , , , , , , , , , , , ,
W

w w
r R

p C h C f r C           


    (17) 

 
Where: 

——The sum of the probabilities of the corresponding 
pairs when an effective transfer path is selected; 

——The corresponding probability of selecting effective 
transfer paths in the set of effective transfer paths; 

——The probability of passenger flow generating 
corresponding travel time samples on the effective transfer 
path. 

The relevant data of passenger flow in the transfer channel, 
such as walking time, inbound and outbound time, travel time, 
etc., are obtained through field survey. The above survey data 
are basically subject to normal distribution, and the sum of the 
data should also conform to normal distribution. The 
theoretical travel time distribution of the effective transfer 
path is obtained by integrating the mean and variance of each 
survey time: 

 

 2 2, , , , , ,
r rr r O Dt r C N E c O D              ∼ (18) 

 
Match the travel time of passenger flow with the theoretical 

travel time: 

 

    
 

2

2 22 2

1
, , , , exp

22
r rr r

r r

O DO D

t E c O D
h t C    

     

       
     

   


(19) 

 
Use Logit model to calculate the probability of effective 

transfer path being selected: 

 

   
 

min

min

exp /
, , , ,

exp /
k

w k
p K k

C C
f r C p

C C


   




 

 (20) 

 



 

25 

The cumulative probability of the pair is: 

 

   , , , , = , , , ,
w

w w
T

p C p C       


  (21) 

 
Namely: 

 

     , , , , , , , , , , , ,
Ww

W w
r RT

p C h C f r C           


 
   

 
 (22) 

 
Expand to all pairs in the whole network: 

 

     , , , , = , , , , , , , ,
Ww

w
r Rw W T

p C h C f r C           
 

  
      

  (23) 

 
The conditional probability of each parameter is obtained 

according to the parameter proportion relationship: 

 
 

             

, , , ,

, , , , , , , ,
Ww

w
r Rw W T

C

h C f r C C

    

                
 

 

  
      

   (24) 

 
The multiple parameters in the effective transfer path 

selection model can be updated and iterated in turn during 
estimation, including the operation time of each section. 
Assume that there are a total of parameters and time allowable 
deviation coefficient, travel time coefficient, coefficient value 
of transfer passenger flow, penalty adjustment coefficient of 
transfer times of transfer passenger flow, and road network 
familiarity parameter, which are converted into multi-
dimensional vector and expressed as: 

 

   1 2 3 5, , , , , , , , mX C x x x x      …      (25) 

 
The parameter value for the second time is: 

 

          1 3 52, , , ,
t t t t

m

tX x x x x


 …          (26) 

 
Multiple parameters are updated successively in the 

iteration. When updated, all variables before the second 
variable are updated. The joint distribution probability can be 
expressed as: 

 

          
 

                   
 

5

5 5

1 1 1
1 2 3

1 1 1 1
1 2 3 1

, , , ,

, , , ,

t

m

t t

m m

t t t
i i

i

t t t t t
i i

x x x x x x T

x

P T x x x x x x x x

P T

 



  



 

   



    

 





… …

… … … …
 (27) 

 
The joint distribution probability of parameters before 

updating can be expressed as: 

 

  
                   

 
5 5

1 1 1 1
1 2 3 1, , , ,

t t

m m

t
i

t t t t t t
i i

x

P T x x x x x x x x

P T



  
 

   




… … … …  (28) 

 
The acceptance probability of dividing formula (27) and 

formula (28) is: 

 

 
  

             
             

5

5

1 1 1
1 2 3

1 1 1
1 2 3

, , , ,
=

, , , ,

t

m

t

m

t t t
i ii

t t t t t t
i i i

P T x x x x x xx

x P T x x x x x x



 





    

  





… …

… …
(29) 

 

5. Example Verification 
Figure 2 shows the simplified road network structure, in 

which the six nodes represent the rail transit stations in the 
simplified road network structure, the four nodes represent 
the rail transit transfer stations, and the common rail stations. 
The numbers on the connecting stations represent the time 
required between the two stations. It is assumed that the 
departure and destination of passenger flow are the same, and 
the transfer time is the same throughout the transfer process, 
and the maximum number of transfers allowed is 2. Dijkstra 
algorithm is used to search the shortest transfer path between 
the two, and the graph-based depth-first search algorithm is 
used to search the effective transfer path between the two. 
There are 3 valid paths between the ODs. 

The sample parameter calibration refers to Bayesian 
estimation method, and is solved by MCMC method. The 
effective path selection results are shown in Table 1, and the 
sample parameter assignment is shown in Table 2: 

It can be seen from Table 3 that when the passenger flow 
reaches the balance and the train runs according to the 
diagram 

When driving, the proportion deviation of the effective 
transfer route of passenger flow estimated by the method in 
this paper is relatively low, which can meet the passenger 
demand. 

6. Conclusion 
Based on the IC card data, this paper uses Bayesian 

estimation to compare the travel time of passenger flow with 
the theoretical travel time to identify the closest effective 
transfer path, and uses the joint distribution probability to 
calibrate the relevant parameters in the path probability 
selection model, such as the travel time coefficient, the value 
of the transfer passenger flow coefficient, the penalty 
coefficient of the transfer times, and the familiarity of the road 
network; The MCMC algorithm is used to solve the 
theoretical solution of unknown parameters to determine the 
probability of different effective transfer paths being selected. 
The results show that the deviation of parameter estimation 
results of this method is less than 1%. 

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