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Abstract

Air passenger travel forecasting is necessary and becomes very valuable for airline company, because accurately obtaining practical requirements of air passenger, which can not only help airline company to improve air passenger satisfaction degree and enhance user experience so as to gain huge revenue, but also can help air passengers discover suitable travel plan quickly. In order to generate the air passenger travel forecasting model, this paper aims to analyze the internal driving force and social affect factor simultaneously, which was based on dynamical personal behaviors and air passenger social relationship exactly. In particular, three aspects in terms of dynamical personal behaviors, effect of fellow air passenger, and influence of similar air passenger are all considered simultaneously, and then the data from these aspects are further trained so as to obtain weight allocation in many different scenarios. Besides, workday and non-workday are separately considered in order to make the forecasting model feasible and effective.

Keywords

Heterogeneous network air passenger travel forecasting model dynamical individual behavior social influence force feasible and effective prediction

Introduction

Air passenger travel forecasting has become a hot research topic recently, for example Hofer et al.¹ measured how socio-economic mobility affects domestic passengers at U.S. airports. Except metrics such as income and population levels, socio-economic mobility has been considered as an important characteristic for the socio-economic fabric of market areas. As to the growing urbanization and subsequently increasing traffic, Becker et al.² aimed to discover future potential worldwide markets for interurban air mobility up to 300 km. Forecasting of air passenger and cargo had a major influence on the master plan of the airport infrastructure development and investment by the civil airline. Sulistyowati et al.³ aimed to obtain the most accurate forecasting value of the air passenger and cargo at three international airports named Soekarno Hatta, I Gusti Ngurah Rai, and Juanda Airport in Indonesia. Liu Huang et al.⁴ aimed to forecast number of daily passengers in an airline company for the airline from Beijing to Sanya, using the historical data from 2010 to 2016. The forecasting was conducted out by means of machine learning, such as the models of multi-variable regression, support vector regression, RMA-improved, and RBF-based neural network. Li and Sheng⁵ investigated the mode choice behavior in terms of inter-city passengers among air transport, high-speed rail, and air and high-speed rail integration services. Kim and Shin⁶ aimed to develop a forecasting model for short-term air passenger demand, which used big data from search queries to identify these short-term fluctuations. For Fatemi Ghomi and Forghani,⁷ the data belonged to a major airline company in Turkey and comprised past five years’ daily passenger data for a flight. It was used to forecast expected passenger count for that flight, servicing 355 days which were open to sale in reservation systems.

Besides, for the research about travel forecasting has been used in some practical applications. Sun et al.⁸ aimed to first use a reliability evaluation method to get the reliability of bus line, and the model of reliability forecasting proposed in this paper was tested with the data of the bus line 23 in Dalian city of China. The results showed that the random forest with the reasonable parameters could forecast the reliability of bus service accurately. Gu et al.⁹ solved the train timetabling problem of a double track high-speed railway line with heavy traffic and trains with different operational speeds. The case study showed that more trains would be scheduled when different kinds of headway time were considered.

Current researches about air passenger travel forecasting model mainly adopt the passenger name record (PNR) data to calculate travel relevancy degree between different air passengers, so as to measure the relationship of air passengers. But in fact, the implicit relationship about different ticket orders has more finding value as to one ticket order, not just the value in terms of obvious relationship. Furthermore, current methods about measuring air passengers’ values usually do not consider the interaction effect of different individuals in their social relationship networks.

Research about the air passenger values is facilitated to the travel forecasting of air passenger; Bingyu¹⁰ used generated biograph to forecast the travel probability of air passenger and calculated the potential value of air passenger; however, the proposed model only considered the relationship between air passengers and airlines, without considering the interaction effect between different air passengers. Besides, Bingyu¹⁰ proposed that the effect value in terms of social network should also be considered except for the individual values. While they calculated the air passenger network value, only the air passenger topological relationship was considered, but the individual air passenger difference was ignored, which would lead to the influence force difference eventually.

In this paper, forecasting about route selection of air passenger travel is abstracted to link forecasting model and influence factors of choosing airlines, then an air passenger travel forecasting model is proposed, which is based on both dynamical personal behavior and social influence force. The main contributions of this paper is to measure the strength of influence force in terms of dynamical personal behaviors and air passenger social relationship, and provide theoretical foundation to probability calculation for the airlines’ forecasting process.

Analysis about the passenger travel and influence factor

Supposing $G_{1} = (P, A, E_{1}, E_{2}, W)$ , where $P$ represents whole air passengers, and $A$ means set of all airlines. Besides, $E_{1}$ is used to describe the relationship set of different air passengers, while $E_{2}$ is adopted to represent relationship between air passengers and airlines. $W$ is weight set of all airlines. The relationship between air passenger and choice of airlines is presented in Figure 1.

Figure 1.

Heterogeneous network of air passenger travel and chosen airlines.

For the relationship $E_{2}$ , each air passenger–airline relationship includes round-trip travel dates, duration days of stay, and status identification. And the value of status identification means whether the air passenger has returned to original place. So this value can be used to forecast the return travel or the next new travel while the value is 0.

Supposing $f : (G_{1}, p_{i} \in P, a_{j} \in A) \to Pro (p_{i}, a_{j})$ , where $Pro (p_{i}, a_{j})$ is used to represent the probability that passenger $p_{i}$ chooses airline $a_{j}$ . Analysis about air passenger travel and influence factor in terms of dynamical individual behavior, fellow air passenger, and similar air passenger is presented as below.

Dynamical individual behavior impact analysis

As to air passengers and their historical airlines, we collected the time interval for these air passengers who chose the same airline twice, and calculated the period that having max travel count. The closer for the period between now and the hot cycle time, which means the bigger probability that air passenger chose the same airline.

In order to describe the probability that air passenger chooses certain airlines, hot cycle time is adopted so as to represent this value, which can be calculated by

Pro (t) = \sum_{i} Pro (t | t_{i}) = \sum_{i} e^{\frac{- λ | t - t_{0} - t_{i} |}{T}}

(1)

where

t

is the current date,

t - t_{0}

is used to describe the duration period between last travel date and current date, and

T

represents the period of max time interval, while

t_{i}

is the time interval between nearby twice travel dates i and i + 1.

Pro (t)

represents the total probability for air passenger choosing this airline, which means the closer between time

t

and the hot cycle time, the larger probability for choosing this airline.

Pro (t | t_{i})

is used to mean the probability of choosing the airline at time

t

under the effect of hot cycle time

t_{i}

In order to verify algorithm performance, we calculated historical travel data so as to describe cycle time distribution and probability distribution, respectively, as Figures 2 and 3 show.

Figure 2.

Cycle time distribution.

Figure 3.

Probability distribution.

As we can see from Figure 2, the time interval for choosing the same airline again is not irregular, there are one or two peaks, which means air passengers prefer to choose certain airlines again near the fixed time interval. Figure 3 shows the relationship between probability and circle time, which is similar with the distribution of air passengers’ actual choosing.

Supposing $L_{t}$ represents the time interval date, which is used to describe the relationship set of an air passenger and all airlines air passenger chose, then $L_{t} = [t_{1}, t_{2}, t_{3}, \dots, t_{n}]$ is considered as relational data, and $T = \max (t_{1}, t_{2}, t_{3}, \dots, t_{n})$ , finally these data should be normalized to the format of $L_{t} = [t_{1} / T, t_{2} / T, t_{3} / T, \dots, t_{n} / T]$ .

Fellow air passenger impact analysis

Though the probability about air passengers choosing certain airlines within different periods can be forecasted by the historical data of air passengers, the potential demand cannot be found for those airlines that were never be chosen by air passengers, especially while the travel data are relatively rare. So the travel plan cannot be well forecasted only according to the historical travel data. This paper aims to utilize both travel data and impact of fellow air passenger, so as to make up the shortfall of rare travel data.

The affect about fellow air passengers to the travel airlines’ choice is described as below:

The probability about fellow air passengers choosing the same airlines again is larger.

Air passengers usually have similar requirements with fellow air passengers while choosing airlines, so this can be used to discover the potential required airlines by calculating fellow relationship degree between air passengers.

Similar air passenger impact analysis

Similar air passengers usually prefer to choose same airlines in certain conditions, for example air passengers having similar interests prefer to choose the same airlines. Besides, for some activities such as sport competition, academic conference, these air passengers also prefer to choose the same airlines. In order to measure the similarity of air passenger, workday travel and non-workday travel are both considered, so as to effectively obtain the similarity of air passenger under the conditions of different time types. Supporting $G_{work}$ is travel network, and air passenger workday travel matrix $O$ is generated based on $G_{work}$ . For the matrix $O$ , the row and column are used to represent the passenger and airline, respectively, and the elements in the matrix are used to describe the amount of passenger (row value) chooses airline (column value), then the matrix is generated by the statistics of all the elements from historical data.

Then finally the air passenger workday travel similarity matrix $S$ can be obtained by

S_{i k} = \frac{\sum_{j = 0}^{m} \min (O_{i j}, O_{k j})}{\sum_{j = 0}^{m} \max (O_{i j}, O_{k j})}

(2)

where

O_{i j}

represents the amount of air passenger

p_{i}

chose airlines

a_{j}

on workday, and

S_{i k}

means the similarity of travel choice on workday for air passengers

p_{i}

and

p_{k}

m

is the number of all airlines, and if

a_{j} \in A

, and

O_{i j} = O_{k j}

for all airlines, then

S_{i k} = 1

Forecasting mode of choosing airline about air passenger travel

Choosing airline is mainly affected by the personal inner driving force and social influence. The inner driving force can be obtained by the analysis of personal behavior rule, and the social influence can be obtained by the analysis of fellow air passenger and similar air passenger.

So in the process of network construction, inner driving force and social affect behave like two types: the route from air passenger to airlines directly, and the route from air passenger to airlines indirectly which means it was simultaneously influenced by other air passengers.

The travel mode and choosing airlines may have great differences during different period for air passengers, so dates are divided into workday, weekend, and holiday accordingly. Figure 4 shows that the network edge weight calculation method is based on time perception, which means network edges are generated while considering workday, weekend, and holiday simultaneously. Figure 5 shows network is generated so as to describe the relationship between different air passengers.

Figure 4.

Network edge weight calculation method based on time perception.

Figure 5.

Network description about passengers’ relationship.

Where last relation time $t^{'}$ means the period between last travel date and current date; Average cycle time $t_{0}$ represents the average period value between twice nearby travel dates

t_{0} = {\begin{array}{l} \sum_{i = 1}^{n - 1} t_{i} / (n - 1) & n > 1 \\ t_{s} & n = 1 \end{array}

(3)

where

n

represents the total travelling number of all air passengers,

t_{i}

is the time interval between two travel dates

i

and

i + 1

, and

t_{s}

is the average cycle time for all air passengers.

Closeness coefficients mean the probability of choosing travel again, which can be obtained by

R = {\begin{matrix} 1 & t^{'} \leq t_{0} \\ \frac{t_{0}}{t} & t^{'} > t_{0} \end{matrix}

(4)

While the last travel date is less than the average cycle time $t_{0}$ , the value of $R$ is 1. While $t^{'}$ is larger than $t_{0}$ , the probability of choosing travel again becomes gradually decreased, and then the $R$ is also continually reduced.

Travelling frequency $F$ is used to represent the total numbers of the relation between twice travel dates during certain period, and the edge weight can be obtained by

W = R \times F

(5)

The choosing of airlines should be considered under the conditions of workday, weekend, and holiday, respectively, so for the date type c, the weight $ω_{k}$ can be expressed as

ω_{k} = {\begin{matrix} 1 & k = c \\ 0 & k \neq c \end{matrix}

(6)

Then, membership degree is used to solve exact forecasting time. Supposing time membership degree is $ϕ$ , $P r o_{t} (i)$ means the probability of time $t$ whose membership degree to time type $i$ , and $ϕ_{i}$ means the probability of time $t$ whose membership degree to time type $i$ while considering three conditions of workday, weekend, and holiday, respectively, which can be calculated by

P r o_{t} (i) = {\begin{array}{l} \frac{T_{i} - t}{L_{i}} i = c \\ \frac{L_{i}}{T_{i} - t} \times \frac{1}{T_{i} - t - L_{i}} i \neq c \end{array}

(7)

ϕ_{i} = \frac{P r o_{t} (i)}{\sum_{i = 1}^{3} P r o_{t} (i)}

(8)

where

T_{i}

is the end time for time period

i

, and

L_{i}

represents the length of

i

. Besides,

c

means the time type of

t

, while the value of

c

is 1, 2, and 3, which means the time type is workday, weekend, and holiday, respectively.

Design of proposed air passenger travel forecasting algorithm

Supposing $P_{n \cdot m}$ is the matrix of air passenger inner driving force, then accordingly path can be described as $P \overset{L_{1}}{\to} A$ . While airlines are chosen by the affect of fellow air passenger, and then the path can be expressed as $P \overset{L_{2}}{\to} P \overset{L_{1}}{\to} A$ , where $L_{2}$ means the fellow air passenger relationship. Besides, while airlines are chosen by the effect of similar air passenger, and then the path can be calculated by $P \overset{L_{3}}{\to} P \overset{L_{1}}{\to} A$ , where $L_{3}$ means the similar air passenger relationship. Besides, $C_{n \cdot n}$ is the influence force matrix of air passenger and $S_{n \cdot n}$ is the similar matrix of air passenger. The forecasting matrix can be generated by these three influence force feathers of air passenger inner driving force, fellow air passenger influence force, and similar air passenger effect force, which can be calculated by

R_{n \cdot m} = α_{1} P_{n \cdot m} + α_{2} C_{n \cdot n} P_{n \cdot m} + (1 - α_{1} - α_{2}) S_{n \cdot n} P_{n \cdot m}

(9)

where

α_{1}

means air passenger inner driving force,

α_{2}

represents those air passengers affected by fellow air passenger, and

1 - α_{1} - α_{2}

is described as those air passengers affected by similar air passengers.

Forecasting model of choosing airlines is described in Figure 6, and for forecasting date $t$ , the forecasting procedure about choosing airlines is described as below:

Figure 6.

Workflow description of proposed algorithm.

Step 1: Constructing workday and non-workday travel network separately based on historical travel data of air passenger.

Step 2: Analyzing dynamical personal behavior of air passenger, fellow relationship of air passenger, and similar relationship of air passenger separately based on the above network.

Step 3: Calculating and obtaining the inner driving force matrix $P_{n \cdot m}$ of air passenger, relationship matrix $C_{n \cdot n}$ of fellow air passenger, and relationship matrix $S_{n \cdot n}$ of similar air passenger.

Step 4: Merging air passenger inner driving force, fellow air passenger influence force, and similar air passenger effect force so as to forecast airlines based on formula (9).

Step 5: Estimating the parameters based on the above two networks, and obtaining the values $α_{1}$ , $α_{2}$ , and $α_{3}$ so as to optimize the performance of model.

Step 6: If $t$ is workday, which means workday travel network is chosen, otherwise the non-workday travel network is chosen. Obtaining the forecasting matrix $R_{n \cdot m}$ .

Step 7: Choosing totally $k$ max probability values from each row of matrix $R_{n \cdot m}$ , and the data of other places are all set to value 0, then the new probability matrix $R^{'}$ is generated.

Step 8: The airlines accordingly to the non 0 matrix are regarded as the forecasting result, generating the airlines forecasting result set $I$ . Besides $I_{i}$ is used to describe the airlines forecasting result set of $P_{i}$ .

Step 9: Sorting the probability value of each rows in order, replacing the original value by the sorted probability value, and the other places are all set to value 0, generating the sorted matrix $R_{ranked}$ .

Step 10: Airlines forecasting result set $I$ , probability choosing matrix $R^{'}$ , and sorted matrix $R_{ranked}$ about forecasting results are described as the various pattern of manifestation for air passenger travel.

Performance verification about proposed passenger travel forecasting algorithm

Experimental data

Experimental data are the PNR data and departure data of civil aviation passenger booking system, 5000 air passengers are used as the air passenger set $A_{0}$ , and accordingly air passengers having fellow relationship with $A_{0}$ are regarded as air passenger set $A_{1}$ . Besides, accordingly air passengers having similar relationship with $A_{1}$ are regarded as air passenger set $A_{2}$ . Then finally the generated air passenger set can be described as $A = A_{0} \cup A_{1} \cup A_{2}$ , which includes totally about 230,000 air passengers and 3,880,000 travel records.

Evaluation index in terms of recall ratio, system forecasting precision rate, and sorting accuracy is described as below^11–18:

Recall ratio and system forecasting precision rate

Forecasting description about different set definition is presented in Table 1, which aims to show the comparison between forecasting travel and indeed travel, and whether the airlines forecasting is correct.

Table 1.

Forecasting description about different set definition.

Set definition	Forecasting travel	Indeed travel	Airlines forecasting is correct
$A = {p_{i} {\|U}_{i} \neq ϕ \cap A_{i} \neq ϕ \cap A_{i} \in U_{i}}$	√	√	√
$B = {p_{i} {\|U}_{i} \neq ϕ \cap A_{i} \neq ϕ \cap A_{i} \in U_{i}}$	√	√	×
$C = {p_{i} {\|U}_{i} \neq ϕ \cap A_{i} = ϕ}$	√	×	Not suitable
$D = {p_{i} {\|U}_{i} = ϕ \cap A_{i} \neq ϕ}$	×	√	Not suitable
$E = {p_{i} {\|U}_{i} \neq ϕ \cap A_{i} = ϕ}$	×	×	Not suitable

Supposing recall ratio $ρ$ is used to describe the ratio that the airline forecasting is correct. For the forecasting result set $I_{}$ , $P_{O_{i}}$ is used to represent the potential airline sets that air passenger may choose, and the actual choosing airlines set $A_{i}$ for air passenger $p_{i}$ is obtained from the experimental data, then the recall ratio can be calculated by

ρ = \frac{num (A_{i} \neq ϕ and A_{i} \in P o_{i})}{num (A_{i} \neq ϕ)}

(10)

P_{rec} = \frac{num (A_{i} \neq ϕ and A_{i} \in P c_{i})}{num (A_{i} \neq ϕ)}

(11)

where

P_{rec}

is the system forecasting precision rate. Besides,

A_{c}

represents the system forecasting accuracy rate, which means whether air passenger travels or not, the correct forecasting occupies for the total forecasting

A_{c} =_{} \frac{num (A_{i} \neq ϕ and A_{i} \in C and A_{i} \in E)}{num (A_{i} \neq ϕ)}

(12)

Supposing $F_{B}$ is harmonic average number of recall ratio and accuracy rate, and β is importance level for accuracy rate occupying for the recall ratio, then the relationship can be described as

F_{β} = (1 + β^{2}) \frac{P_{rec} \times ρ}{β^{2} \times P_{rec} + ρ}

(13)

2. Sorting accuracy $η$

Sorting accuracy is used to measure the recall ratio of forecasting system. Forecasting sorting result matrix $R_{rank}$ is generated by forecasting result $R$ , and $R_{rankij}$ is used to describe the sorting for the probability that air passenger $p_{i}$ chooses airlines $a_{j}$ , which means the larger for the probability, the better for the sorting.

Constructing the result matrix $M_{n m}$ of choosing airlines, where $M_{i j}$ is used to represent whether the air passenger $p_{i}$ chooses airlines $a_{j}$ , and the value is 1 while it is true, otherwise the value is set to 0.

The sorting score $R_{scorei}$ is defined as

R_{scorei} = M_{i j} \cdot \sum_{j = 1}^{m} R_{rankij}

(14)

And the sorting accuracy $η$ can be obtained by

η = \frac{num (R S_{i} \neq 0)}{\sum_{i = 1}^{n} R S_{i}}

(15)

Experiment design and result analysis

The influence about model affected by $k$ value

Choosing totally $k$ potential airlines for each air passenger, and then the system recall ratio and system sorting accuracy should be calculated under the condition of various $k$ values.

Making $k \in [1, 10]$ , and the calculation results about recall ratio and sorting accuracy for the model under various $k$ values are presented, as Figure 7 shows.

Figure 7.

Comparison of recall ratio and sorting accuracy for different $k$ values.

From the results we can know, while $k$ becomes gradually larger, then the recall ratio continually increases and the sorting accuracy gradually decreases. But while the values reaching to 6, then the change tends to stable.

2. The effectiveness and necessary while merging various influence force factors

Three components model will be adopted to be compared as below:

(1) Personal behavior model

Only using dynamical personal behavior rule to forecast the choosing airlines, which means $R_{n \times m} = P_{n \times m}$ .

(2) Fellow air passenger relationship model

Only using the travel preference of fellow air passenger and the influence force to forecast the choosing airlines of target air passenger, which means $R_{n \times m} = C_{n \times m} P_{n \times m}$

(3) Similar air passenger relationship model

Only using the travel preference of similar air passenger and its similar extent to forecast the choosing airlines of target air passenger, which means $R_{n \times m} = S_{n \times m} P_{n \times m}$ .

While the $k$ value is 3, the proposed model, individual behavior model, fellow air passenger model, and similar relationship model are compared under the conditions of workday network and non-workday network, and the comparison results are presented in Figure 8.

Figure 8.

Comparison of recall ratio and sorting accuracy.

As the results shown in Figure 8, the random walk algorithm is based on bigraph, which considers the frequency character for each air passenger while choosing airlines, but ignores the time factor of choosing travel. In the meanwhile, it heavily considers the choosing condition of each airline based on the statistics, and ignores the difference, which make some irrelevant statistics rule disturb the forecasting result.

The proposed algorithm has relatively better performance in terms of model recall ratio and sorting accuracy while compared with other models. Especially for these single factor models, personal behavior model has better performance, because this model is designed according to the air passenger personal behavior rule, which is suitable for workday travel. In fact, air passengers usually choose to travel on workdays, so the personal behavior model has better forecasting performance. But the personal behavior model can only forecast the travel airlines, so it is difficult to discover never choosing but potential airlines; however, fellow air passenger and similar relationship can cover the shortage effectively, so the proposed model merging various influence force factors can achieve better forecasting performance. Consequently, the algorithm proposed has better performance, and it can effectively forecast the potential airlines requirement in the long run, but it cannot make real-time forecasting.

Conclusion

In this paper, impact analysis in terms of dynamical individual behavior, fellow air passenger, and similar air passenger is presented first. Then later air passenger travel forecasting model is put forward so as to mine potential air passengers and further forecast corresponding airlines. Finally, results analysis in terms of the model affected by $k$ values, the feasibility and effectiveness while merging various influence force factors, and performance comparison with current algorithm are all described so as to verify the performance of proposed algorithm. In short, an air passenger travel forecasting model based on dynamical personal behavior and social influence force is proposed in this paper, and the experimental results show that the proposed air passenger travel forecasting algorithm has better recall ratio and sorting accuracy than random walk model (based on bigraph), so this paper provides an effective and feasible solution of forecasting airlines for both airline company and air passenger.

Footnotes

Acknowledgements

The authors thank Jan Vitek, Ales Plsek, and Lei Zhao for their help while the first author studied in S3 lab at Purdue University as a visiting scholar from September 2010 to September 2012. We also thank the anonymous reviewers for their valuable comments.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Fundamental Research Funds for the Central Universities of Civil Aviation University of China (no. 3122018C025), Scientific Research Foundation of Civil Aviation University of China (no. 2014QD13X), and Major Projects of Civil Aviation Technology Innovation Funds of China (nos. MHRD 20150107 and MHRD 20160109).

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Air passenger travel forecasting model based on both dynamical individual behavior and social influence force

Abstract

Keywords

Introduction

Analysis about the passenger travel and influence factor

Dynamical individual behavior impact analysis

Fellow air passenger impact analysis

Similar air passenger impact analysis

Forecasting mode of choosing airline about air passenger travel

Design of proposed air passenger travel forecasting algorithm

Performance verification about proposed passenger travel forecasting algorithm

Experimental data

Experiment design and result analysis

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

References