Xiaohang Zhang, Yu Du＊, Zhengren Li, Qi Wang

School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing 100876, China

I. INTRODUCTION

Telecom operators attach great importance to performance measurement [1], which is the process of collecting, analyzing and reporting information about operational performance,and one common type of it is Performance Indicator (or Key Performance Indicator) that has been used frequently by telecom operators. In this study, the operational performance refers to the operation efficiency of telecom operators, which is measured from the respective of revenue, service, network performance,investment and so on. With the help of performance measurement, managers and experts can gain insights into the operation of telecom operators, detect problems and enhance performance [2-4].

In recent years, due to the rapid development of mobile Internet [5], traditional telecom services have suffered a big hit. The revenue from voice and SMS services has been obviously reduced, while data traffic has entered a period of rapid growth. Global telecom operators are looking for new services and business models, which is a challenge as well as an opportunity for them. Currently, telecom operators pay more attention to the changes in enterprise performance [6-7], hoping to detect problems,find new market opportunities, and then adjust market strategies in time to address the increasingly drastic market competition.

In this paper, the authors propose a methodology to analyze dynamically the changing processes of telecom operators’operating states and predicting the developing trends, which based on analysis of migration patterns and trajectory patterns.

Data envelopment analysis (DEA) [8] and structural equation modeling (SEM) [9] have been the most commonly used methods of performance measurement in the telecommunications industry. Some researches [10, 12, 15,18] have used different methods to analyze the operational performance of telecom operators,but most of these methods are static, which cannot be applied to time series data. Yang and Chang [11] used DEA model and DEA window analysis to measure the efficiencies of Taiwan telecom operators over the period 2001–2005, and quarterly data are collected.Moreno and Lozano [13] used a dynamic DEA model to measure the performance of telecom operators from 1997 to 2007, and afterwards a regression was carried out to evaluate the effects. Although the above two methods are both based on DEA model, and can dynamically analyze the performance of telecom operators, they focused on the efficiency of operation, not the detail of operational performance. Moreover, the methods cannot explain the change of performance very well.

Clustering migration is an effective technique for studying time series data in customer behavior research [20, 22, 23], but it has been less widely used for operational performance[24, 25], as is the case for telecommunications. Sperandio and Coelho [24] developed a clustering migration methodology based on the Markov chain model and SOM, which has been applied to a reliability assessment of power network systems. Chen and Ribeiro[25] introduced a clustering migration method based on SOM to analyze and visualize the financial situation of companies over several years. The researches focus primarily on the causes or results of performance migrations,but less attention has been paid to the change in performance during the migration process.

In this paper, we propose a new method based on clustering migration, which can be applied to time series data, and analyze the operational performance of provincial companies with multi-dimension. More importantly, this method can describe a month-overmonth performance change of one provincial company through migration path, characterize the changing process of the operating states,and predict developing trends. Therefore, our method is different from previous works. At the end of this paper, we summarize some development models of current telecom operators through empirical research, which can help managers to forecast future performance migration.

II. LITERATURE REVIEW

2.1 Performance measurement

The performance measurement of telecom operators has been widely studied in recent years. DEA is a major tool that has been often used to calculate the relative efficiency of telecom operators. Debnath and Shankar [10]used DEA to compare the relative efficiency of Indian telecom operators and to the strongest and weakest telecom operators. Yang and Chang [11] used DEA under constant and variable returns-to-scale to measure the efficiencies of Taiwan telecom operators over the period 2001–2005. In this study, DEA window analysis was employed to increase the number of decision-making units. Kumar and Shankar[12] developed a framework to understand variables that can affect consumers’ preference in telecom operators in India. This study used a hybrid approach to assess the relative efficiency based on fuzzy AHP and DEA model.Moreno and Lozano [13] used a dynamic DEA model to measure the performance of telecom operators from 1997 to 2007, and afterwards a regression was carried out to evaluate the effects of local competition, unbundling regulation, intermodal competition, incentive regulation, and mergers on the telecom operators’ efficiency. Qu et al [14] used DEA-CCR to build a operational performance evaluation model of China’s telecom, and to measure the operational performance of different regions.

Structural equation modeling (SEM) has also been a commonly used performance measurement method in telecommunication. Gerpott and Ahmadi [15] presented a second-order composite index (TDI) for assessing the availability, adoption and use of telecommunication networks and services at the country level.The indicator and subindex weights were calculated according to the SEM technique. The weights of indicators or subindices entering into an overall TDI should vary depending on the socio-economic target criterion. Lemstra and Voogt [16] developed a performance index and a market model for broadband development in the EU. The statistically significant factors and components in the path model were determined by SEM. SEM has often been used to calculate the weight of indicators and subindices, and then one or several overall indices to measure the performance of telecom operators.

Ghezzi and Cortimiglia [17] proposed an interpretative framework to analyze the disruptive changes in telecom operators in both the technology and business dimensions. This study focused on disruptive changes in operating states of telecom operators, and related disruptive change factors to business model dimensions, aiming to develop market strategies. This study was based on qualitative analysis and the subjective judgment of the interviewees had a great in fluence on the research results.

Shi and Du [18] proposed a methodology for measuring and analyzing the performance of telecom operators, which focused on building up a performance indicator system and discovering the characters of those performance indicators by applying complex network methods. Based on the indicators network,indicators and the relationship between them could be better understood, and the trends of operating states could be predicted. However,this method cannot be used to analyze time series data.

Yang et al [19] used the methods of hypothesis testing to examine the effects of strategic investments on business performance of telecom operators in the USA and Korea.Although the 2006–2013 time series data have been used, this research was focused on the relationship between strategic investments and performance, and they used the panel data analysis method to integrate the data, which made it difficult to have an insight into changing processes of operational performance.

DEA and SEM have been the most commonly used methods of performance measurement, but they were often used to analyze static data in previous studies. There were also some dynamic methods based on DEA,however, they were difficult to gain insights on operational details such as market, investment and network performance. Moreover, the change of performance was hard to explain.Most of the other methods of performance measurement also have similar problems. In summary, the existing studies of performance measurement have lacked quantitative methods for dynamically analyzing the changing processes of telecom operators’ operating states and predicting developing trends.

2.2 Clustering migration

Clustering migration is an effective technique to study time series data, which is mainly used in customer behavior research. Lingras and Hogo [20] proposed a method of clustering migration based on a Self-Organizing Map(SOM) and rough set to study the changes in cluster characteristics of supermarket customers within 24 weeks. Marketing managers may want to focus on specific groups of customers.This method could help marketing managers understand migrations of customers from one cluster to another, and then market strategies could be developed based on these migrations of customer behavior. Denny and Williams[21] introduced a visualization method based on a Self-Organizing Map (SOM), which used Relative Density SOM (ReDSOM) visualization to compare changes in clustering structures in time-series. With the help of ReDSOM, researchers could visually identify emerging clusters, disappearing clusters, split clusters, merged clusters, enlarging clusters,contracting clusters, the shifting of cluster centroids, and changes in cluster density. Seret and Broucke [22] proposed a method of clus-tering migration based on consumer behavior trajectories. This method combined clustering techniques and tuning sequence mining methods to discover prominent customer behavior trajectories, which could help researchers and managers understand consumer decisions and improve business processes that are influenced by customer actions. Bose and Chen [23]developed a clustering migration method for extending the standard fuzzy c-means clustering algorithm using membership functions to detect how customers move between clusters over time. This method was then applied to empirical research on telecoms. The findings of it provided insights for mobile services providers on how to detect temporal changes in customer behavior.

Table I. The performance indicators in the original dataset. They can be divided into revenue, services, network performance and investment.

Researchers have used the technique of clustering migration to analyze changes in enterprise performance. Sperandio and Coelho[24] developed a clustering migration methodology based on the Markov chain model and SOM, which has been applied to a reliability assessment of power network systems. Chen and Ribeiro [25] introduced a clustering migration method based on SOM to analyze and visualize the financial situation of companies over several years through two steps. Initially,the bankruptcy risk was characterized by a feature SOM (FSOM), and therefore the temporal sequence was converted to the trajectory vector projected on the map. Afterwards, the trajectory SOM (TSOM) clustered the trajectory vectors to a number of trajectory patterns.Analyzing these trajectory patterns could help experts and managers understand the changing law of enterprise performance.

In conclusion, the technique of clustering migration has been less widely used for the dynamic analysis of enterprise performance,as is the case for telecommunications. Most researchers have focused on the causes or results of enterprise performance migrations;less attention has been paid to the change in enterprise performance during the migration process. Moreover, few researchers have predicted the migration of enterprise performance.

III. DATA AND VARIABLES

3.1 Data description and preparation

The original dataset used in this study contains monthly operating data from 31 provincial companies of one Chinese telecom operator during the years 2013–2015. The data set contains 40 performance indicators measured in each month; they are divided into revenue,services, network performance and investment. These performance indicators are shown in Table 1.

Data preprocessing is an indispensable step before analysis and is composed of handling missing values, eliminating seasonal effects,and normalization. (1) There are a few missing values in the dataset, which are replaced by linear interpolation [26]. (2) To improve the accuracy of the methods, eliminating seasonal effects in the dataset is necessary before analysis. In this paper, the Classical Seasonal Decomposition by Moving Averages method is used, which decomposes a time series into seasonal, trend and irregular components using moving averages [27]. (3) The indicators vary greatly in scales; therefore, we normalized them to zero mean and unit variance.

3.2 Exploring the dimensions of the performance indicators

The original dataset contains 40 performance indicators. It is difficult to analyze all of them directly, and the correlations between performance indicators can seriously affect the accuracy of the research results. Therefore,we use principal components analysis (PCA)to reduce the dimensionality of the data. A principal component can be defined as a linear combination of optimally weighted observed variables [28]. We use this method to explore the dimensions of the performance indicators.

Since we only focus on the main components, the components that have an eigenvalue significantly larger than 1 will be chosen. As shown in figure 1 and table 2, the first five components are significantly larger than 1, and they contain 74% of the total variance of the data, so we choose these components for subsequent analysis. Figure 1 is a graphical representation of the descending eigenvalues,through which the components can be selected more intuitively.

During the PCA, we use the varimax rotation to make the components orthogonal to each other. The component matrix is shown in Table 3. The variables are interpreted by the component that has the highest absolute value of loading loaded on (in gray). To facilitate component interpretation, variables do not load on multiple components and we pick the minus of the raw loadings on PC4 and PC5.When combined with the components, these variables help us to understand the underlying meaning of the components.

As shown in table 3, the first component that accounts for 62% of the total variance inthe data comprises the information on revenue, investment, and development of services.For simplicity, we consider that thefirst component mainly reflects the revenue of telecom operators. The second and third component represent the development of the cellular data services and WLAN data services of telecom operators, respectively. The performance of the 2G and 3G networks is interpreted by the fourth component. The fifth component represents the competitive position of telecom operators.

Table II. Variance can be explained by components.

Fig. 1. Graphical representation of the descending eigenvalues.

Table III. Component matrix.

There is a flaw in the original data set,which lacks indicators on 4G network performance. This Chinese telecom operator had already launched 4G services in 2014. According to operational experience, 4G network performance is strongly positively correlated with 2G and 3G networks at the beginning of 4G service: In recent years, the development of mobile data service was a key factor affecting the performance of cellular networks.After telecom operators started 4G services,the majority of mobile data traffic was carried on 4G networks. When the growth of mobile data traffic outstripped the carrying capacity of the 4G networks, the performance of 4G networks decreased significantly. Subsequently,much of the data traffic went to 3G or even 2G networks, which led to these networks’ performances decreasing. Therefore, we can infer that the fourth component can also represent the performance of the 4G networks of this Chinese telecom operator.

IV. EMPIRICAL METHODOLOGY

Performance migration of telecom operators can be analyzed across two dimensions: the migration pattern and the trajectory pattern.The analysis of migration patterns is focused on the performance migration of provincial companies per month. Migration paths are the basis of analysis in this methodology and can be calculable by using the difference method. Then the clustering method can be used to find the migration patterns of provincial companies. As these migration patterns are analyzed, we can learn the characters of patterns, and obtain the operating experience of the telecom operator. The migration trajectory is the change process of the migration patterns of one provincial company in a certain period of time. Based on the migration trajectories of provincial companies, trajectory patterns can be calculated using the clustering method and Markov chain model. Studying trajectory patterns can help us to understand the changing rules of migration patterns, and predict the performance migration of telecom operators.

4.1 Migration pattern

Letpci,k(t) denote the score of thekth principal component for provincial companyiat timet.

whereNdenotes the number of companies,Kdenotes the number of principal components andTis the length of the time series.

One migration path presents a month-overmonth performance change vector of one provincial company. LetMi(t) denote the migration path of provincial companyiat timet.

The clustering method is applied to the migration pathsMi(t), where each cluster represents one migration pattern (MP), and the characteristics of different migration pattern(MP) can be summarized.

whereMdenotes the number of clusters and Cluster(Mi(t)) assigns the migration pathMi(t) to one cluster denoted byMPi(t).

4.2 Trajectory pattern

Migration trajectoryTRi,i=1,… ,N, is the change process of the migration patterns of one provincial companyiin a certain period of timeT.

The following steps can be used to analyze the trajectory patterns.

Step 1. The similarity of the migration trajectories between provincial companiesiandjis calculated as

Step 2. The hierarchical clustering method is applied on the similarity matrixR. Let,…,denote the resulting clusters. Each migration trajectoryTRi(i=1,… ,N) belongs to one of the clusters.

Step 3. Each trajectory patternTPmcan be obtained by applying the Markov chain model[29] on,m=1,…,.

Fig. 2. BSS/TSS ratio against the number of clusters.

EachTPmis represented by a transition matrixP. If the probability of moving fromMP(i)toMP(j)in one month isPr(j|i)=Pi,j,the transition matrixPis given by usingPi,jas theithrow andjthcolumn element.

Since the total of transition probability from aMP(i)to otherMPmust be 1, this matrix is a right matrix.

V. EMPIRICAL RESULTS AND DISCUSSION

5.1 Migration pattern analysis

K-means is a commonly used clustering method. In this paper, K-means is used to cluster the migration paths (Mi) of 31 provincial companies to get the migration patterns.

5.1.1 Finding migration patterns based on the clustering method

In clustering, determining the number of clusters is always an important task. TheBSS/TSSratio has often been used to measure the effect of clustering [30].TSSstands for Total Sum of Squares, and BSS means deviance “Between”. TheBSS/TSSratio against the number of cluster is shown in figure 2. It is not difficult to see that when the number of clusters is 9, the curve appears to have an in flection point.

The DB index [31] and Dunn index [32]are commonly used to determine the number of clusters. In this analysis, the calculations of the two indices show that the number of clusters is also 9. Therefore, combining these indices and practical experience, we believe that the appropriate number of clusters is 9.

The clustering results of different methods can be compared to evaluate the stability of clustering. In this study, we choose K-means,K-medoids, SOM and hierarchical clustering to cluster the migration path. The corrected Rand indices [33] of one clustering method and the other three methods are calculated in pairs. The average of them represents the stability of this method (shown in table 4).

As shown in table 4, we can see that the clustering results of K-means are the most stable. Therefore, the K-means method is used to cluster the migration path in this study. The centers of nine clusters represent the characteristics of performance migration patterns(as shown in table 5). At-test is performed on each coordinate of the centers. It verifies that most coordinates of centers are significantly larger than 0 at the level 5%, except the data in gray. The positive coordinates in white indicates that their corresponding components are increasing during migration. Otherwise, the corresponding components are going down.

To better understand the characteristics of migration pattern and gain insight into the performance changes of provincial companies in different phases, we analyze the migration patterns along with the time dimension. This can further help us to understand the in fluences of regulatory policies and marketing solutions on the performance of telecom operators.With the help of time series analyses,figure 3 shows the number of provincial companies in each migration pattern at different times.

InMP(9), the sample size is the largest and uniformly distributed based on time. From Table 5, we can see that the performance characteristics ofMP(9)are all in stable development, except WLAN services. From 2013 to 2015, China’s telecommunications industry developed slowly. This migration pattern represents the mainstream development trend of this telecom operator over the past three years. From 3G to 4G, cellular data services have been the priority for development but also revenue growth points, while WLAN is the supplementary service of it. Therefore, the WLAN has dropped off during the accelerated development of cellular data services. Over the past three years, it appears that the mobile phone penetration rate of China has reached a high level. Thus, the competitive landscape of China’s telecommunications industry is nearly stable.

MP(8)appeared most frequently fromthe end of 2013 to the beginning of 2015. In Table 5, the cellular data services of provincial companies inMP(8)grow rapidly, but the performance of the cellular network and revenue declines. This Chinese telecom operator launched 4G service at the end of 2013,thereforeMP(8)represents the performance migration of provincial companies when 4G services are still in their infancy. In the 3G era, this Chinese telecom operator was subject to technical standards, so the competitive position declined. However, this situation was turned around when 4G launched, the competitive position of it was improved steadily.At this stage, the provincial companies of this telecom operator drove the growth of cellular data traffic through marketing activities such as slashing data fees, resulting in the phenomenon of incremental performance rise but income decline. The progress of 4G networks construction failed to match the explosion of data traffic at that time, resulting in the performance of 4G networks degrading, and a large number of data traffic was rerouted to 2G and 3G networks, leading to 2G and 3G network congestion. As a result, all cellular networks experienced a decline in performance. But the consumer demand for data traffic was stimulated by marketing activities, therefore some users preferred to choose WLAN data services, which showed a slight increase.MP(4)is similar toMP(8), but the characteristics of performance migrations are more obvious:Cellular data services are growing faster, and the performance of cellular networks and revenue also fall at a faster pace.

Table IV. The stability of each clustering method. The corrected Rand indices of one clustering method and the other three methods are calculated in pairs. The average of them represents the stability of this method.

Table V. Characteristics of performance migration patterns.

Fig. 3. Time frequency chart of migration patterns.

Since December 2014, the frequency ofMP(7)has increased significantly, soMP(7)reflected the performance migration of provincial companies one year after 4G launched.InMP(7), the provincial companies’ cellular network performance improves significantly,while revenue and cellular data services develop steadily. At that time, users’ consumption habits of data traffic have been initially formed and marketing efforts were decreasing gradually, therefore the revenue of provincial companies were rebounding. The construction of 4G network was basically completed and the user experience was also greatly improved.Due to the substitution effect between cellular network services and the WLAN, WLAN data services declined accordingly. In early 2015,the two other Chinese telecom operators also began to develop 4G services. Therefore, the competitive landscape of China’s telecom industry returned to stability, and the growth of cellular data services was slowing down.

MP(6)is largely concentrated in October 2015, when China’s major telecom operators launched rollover data services, meaning unused data at the end of the month would no longer just disappear, soMP(6)reflects the impact of rollover data services to the performance of telecom operators. As we can see from table 5, the WLAN data services and competitive position ofMP(6)are sharply rising. In contrast, revenue, cellular data services, and the performance of the cellular network are decreasing. Rollover data services changed consumer behavior by reducing the usage of cellular data, which led to a big drop in cellular data services and revenue. A set of users tended to turn off the 4G module of phones. Therefore, the pressure on the 2G and 3G network became higher, and then the performance of them slipped. However, the users’consumption habits with data traffic had been developed, so some users would like to choose WLAN data services, which are cheaper than the cellular one. In general, low-end users are more sensitivity to data traffic, the Chinese telecom operator in our research had more high-end users than the others, so rollover data service had a relatively smaller impact on this telecom operator. Therefore, the competitive positions of these provincial companies have improved.

MP(5)andMP(1)were quite similar, and appeared most frequently in the first half of 2013: the cellular data services, performance of cellular networks, and revenue are maintaining steady growth, but the competitive position of the provincial companies is slipping.At that time, this telecom operator’s 3G services were coming to an end, and its primary focus was on the preparation of 4G (the tenders for 4G network equipment were launched in June 2013), while competitors’ 3G services were still accelerating. Therefore, the competitive position of the provincial companies dropped.

MP(3)andMP(2)were distributed loosely over time, but they were concentrated on the provincial companies of Shandong and Sichuan. As shown in table 5, the performance of cellular networks and revenue changed in the same direction, but moved in the opposite direction of WLAN data services. Cellular networks are the core competitiveness of telecom operators. Excellent cellular networks could provide a better user experience, which was driving force of revenue. WLAN data services were supplementary services of the cellular one in this Chinese telecom operator. As was shown inMP(8)andMP(4), the users tended to choose WLAN data services when the performance of the cellular network declined and vice versa.

5.1.2 Characteristics of migration patterns With the help of migration patterns, the changing processes of provincial companies’ performance can be characterized clearly, and then migration laws can be summed up.

The performance of the cellular network and the revenue of the provincial company change in the same direction.Cellular networks are the core competitiveness of telecom operators. Excellent cellular networks can provide a better user experience, which is the driving force of revenue.

The performance of cellular networks and WLAN data services have contrary changes.This means that the performance of the cellular network can greatly affect the consumption behaviors with data traffic. In general, WLAN data services is not equal to cellular services in many aspects of user experience, such as network coverage and authentication, meaning that the preferred data service of users is the cellular one. However, when the performance of the cellular network declines markedly,some users will turn to WLAN data services.

The revenue of provincial companies has an inverse relationship with WLAN data services.In other words, the development of the WLAN may reduce the revenue of telecom operators. As we have mentioned above, there is a substitutable relationship between cellular network services and the WLAN services, and the price of the WLAN data traffic is far below the former in general. Therefore, the development of WLAN data services not only hinders the cellular services but also makes the overall revenue decline.

In the early stage of 4G services, although cellular data services developed rapidly, therevenue of provincial companies was not improved significantly.The revenue could be driven by cellular data services, when they returned to steady growth. In general, telecom operators drive the growth of cellular data traffic through aggressive marketing activities such as slashing the fees for data in the early stage of 4G, therefore they could not raise income incrementally. Cellular data services begin to pull in growing revenue when they reach their steady periods and the efforts for marketing are decreasing.

The cellular data services and revenue of telecom operators begin to decline significantly when the rollover data launched.In the meantime, WLAN data services obtained more opportunities, thanks to the lower price.Additionally, rollover data services have little influence on the telecom operators with more high-end users.

5.2 Trajectory pattern analysis

5.2.1 Migration trajectory

Fig. 4. Migration trajectories of two provincial companies. Taking the provincial companies of Guangdong and Xinjiang as examples, using MP(9) as a baseline,plotted by the distance between MP(9) and other migration patterns on the vertical axis and the timeline on the horizontal.

As mentioned in 3.5, migration trajectories of the telecom operators show the complete changing process of their migration pattern.Two migration trajectories are shown in figure 4. We can see that there are significant variations among the migration trajectories.

In figure 4, the horizontal axis represents Jan 2013 to Dec 2015. The vertical axis is the Euclidean distance between centers of MP(9)(shown in table 5) and the other migration patterns, the farther from MP(9), the greater difference between them. Note that, the distance between migration patterns except MP(9)in figure 4 cannot represent the difference between them. We using MP(9)as a baseline,because this migration pattern represents the mainstream development trend of this telecom operator over the past three years. The curves in figure 4 represent migration trajectories of provincial companies along the time axis.Each point in the curves represents the migration pattern with corresponding date. The top curve is for Guangdong and the bottom one is for Xinjiang (In Section 5.2.2, we cluster the migration trajectories of 31 provincial companies into Cluster A and B, Guangdong and Xinjiang are representative cases, respectively). By comparing the two curves, we canfind that the difference between migration trajectories is huge. For example, the migration trajectory of Xinjiang is relatively stable, which tends to stay on MP(9). However, Guangdong changes in a wider range than Xinjiang.

Next, we will analyze the similarity between the migration trajectories of provincial companies, based here some trajectory patterns can be summarized.

5.2.2 Trajectory pattern

The migration trajectory is the change process of the migration patterns of one provincial company in a certain period of time. Based on the migration trajectories of provincial companies, trajectory patterns can be calculated using the clustering method and Markov chain model. Studying trajectory patterns can help us to understand the changing rules of migration patterns.

The similarity matrix of 31 provincial companies’ migration trajectories is shown in Table A1 in the Appendix. We can more clearly understand the similarity among the migration trajectories using this table. High similarity of the migration trajectories is dark, while low similarity of the migration trajectories is light.

Hierarchical cluster analysis has been used to cluster the migration trajectories of 31 provincial companies. The result is shown in figure 5. We use Friedman index [34], McClain index [35] and Dunn index [32] to determine the number of clusters, which are often used to analyze the results of hierarchical clustering.In this analysis, the calculations of these three indices show that the reasonable number of clustering is 2.

Cluster A includes the provincial companies of Guangdong, Sichuan, Shandong, Jiangsu,Hainan, Guizhou, Guangxi, the other is called Cluster B. In this Chinese telecom operator,Guangdong, Sichuan, Shandong and Jiangsu are pioneer companies in revenue and user scale, but Hainan, Chongqing and Guangxi lag far behind them. We hold that these seven provincial companies are classified into the same cluster for the following reasons:

Hainan, Guizhou, Guangxi and Sichuan,Guangdong are geographical neighbors, so there are some similarities in the development model of them [36]. Beyond that, Cellular data services have been the development priority of this Chinese telecom operator from 2013 to 2016. The growth rate of DOU (average data traffic per month per user) is one of the important indices to weigh the development of cellular data services. Hainan, Guizhou and Guangxi rank high on the growth rate of DOU, so the performance of them is good from the dimension of services development.Therefore, telecom operators in Cluster A are better than Cluster B from the perspective of revenue or services development.

We use the Markov chain model to analyze the migration trajectories of Cluster A and Cluster B, respectively, and summarize the trajectory patterns of them. Based on the trajectory patterns, we can predict the possible performance changes.

The transfer matrix of Cluster A is shown in Table 6, the maximum transition probabilities of migration patterns are in gray. We can see that Cluster A tends to keep the migration pattern of last month. The provincial companies of Cluster A are leading the group in operation or marketing, they want to maintain the previous successful operating model, which leads to no changes in their migration patterns. Besides that, there are also some different transfers of the migration patterns in Cluster A as follow.

Fig. 5. Hierarchical cluster analysis of 31 provincial companies’ migration trajectories.

MP(1)→MP(7)means that in the stage of steady development, if the competitive positions of provincial companies in Cluster A declines significantly, they usually enhance the competitiveness by optimizing the network quality. It further shows that the performance of cellular network is a core competency of the telecom operator.MP(2)→MP(9)shows that the measures provincial companies in Cluster A used to address the decreasing of network quality are effective and timely.MP(4)→MP(1)tells us that although the provincial companies in Cluster A will take effective and timely measure when the performance of cellular networks degrade, still resulting in a short-term decline in competitive positions of them.MP(5)→MP(9)show that the competitive landscape of China’s telecom industry is basically stable in present, and the intense competition is only a short-term phenomenon,then it will return to stability.

The transfer matrix of Cluster B is shown in Table 7, the maximum transition probabilities of migration patterns are also in gray.As shown in Table 7, the objects in most of migration patterns tend to migrate toMP(9)in the next step. We can infer that the provincial companies in Cluster B favor the mainstream migration patternMP(9). They lag behind Cluster A in operation or marketing, the strategy of them is also more conservative.Therefore, most of them migrate according toMP(9), even if the other migration patterns appeared will also be re-adjusted to the mainstream immediately. Besides that,MP(5)→MP(7)shows that the provincial companies in Cluster B are more sensitive to competition than Cluster A. When their competitive positions slip only slightly, they will immediately optimize the quality of network to secure their market positions.

VI. IMPLICATIONS AND CONCLUSIONS

In this paper, we propose a methodology to analyze dynamically the changing processes of telecom operators’ operating states and predicting the developing trends, which based on analysis of migration patterns and trajectorypatterns.

Table VI. The transfer matrix of Cluster A.

Table VII. The transfer matrix of Cluster B.

Then we summarize some development rules through empirical research on one Chinese telecom operator, which can help to understand the current state of the telecom industry. The results show that migration paths can be divided into 9 migration patterns, from which we find that: (1) The performance of the cellular network and the revenue of the provincial company change in the same direction, but changes on the opposite side with WLAN data services. (2) In the early stage of 4G services, although cellular data services developed rapidly, the revenue of provincial companies was not improved significantly. (3)The cellular data services and revenue of telecom operators begin to decline significantly when the rollover data launched. Moreover,we obtain two trajectory patterns. The provincial companies (Cluster A) characterized by one pattern tends to keep the migration pattern of last month; however, the other companies(Cluster B) characterized by another pattern favor the mainstream migration pattern (the performance characteristics are all in stable development, except WLAN services). The provincial companies in Cluster A do better in revenue or services development than the companies in Cluster B.

With the help of migration patterns analysis, the changing process of the operating states can be characterized in multi-dimensions, that let managers and experts gain insight into operational performance of telecom operators. Trajectory patterns analysis can describe the changing progress during a long period. Based on the trajectory patterns, possible performance changes can be predicted and strategies of marketing and operating can be timely adjusted. Except for telecommunication industry, this methodology can be commonly used in other industries.

In future work, the stability of migration patterns needs more research, and an early warning system for telecom operators can be developed based on the methodology proposed in this paper.

Appendix

Table A1 is shown in page 154-155.

ACKNOWLEDGEMENT

This work was partially supported by NSFC(71371034 and 71372194) and Beijing Natural Science Foundation (9162011).

Table A1. The similarity matrix of 31 provincial companies’ migration trajectories. High similarity of the migration trajectories is dark,while low similarity of the migration trajectories is light.

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[1] B. Upadhayaet al., “Association between performance measurement systems and organisational effectiveness,”International Journal of Operations & Production Management, vol. 47,no. 34, 2014, pp. 853-875.

[2] S.K Majumdar, “Performance in the US telecommunication services industry,”Telecommunications Policy, vol. 16, no. 4, 1992, pp. 327-338.

[3] T.J Gerpottet al., “The degree of internationalization and the financial performance of European mobile network operators,”Telecommunications Policy, vol. 29, no. 8, 2005, pp. 635-661.

[4] L. Woodet al., “On the design of performance measurement plans in the telecommunications industry,”Telecommunications Policy, vol. 28,no. 11, 2004, pp. 801-820.

[5] X. Tuet al., “China Internet industry state analysis and prosperity indexes,”China Communications, vol. 13, no. 10, 2016, pp. 245-252.

[6] C.G Yanget al., “Effects of telecom service providers’ strategic investments on business performance,”Industrial Management & Data Systems, vol. 116, no. 5, 2016, pp. 960-977.

[7] Q. Liuet al., “Research on Services Modeling in LTE Networks,”China Communications, vol. 13,no. 2, 2016, pp. 109-120.

[8] A. Charnes, “Measuring the efficiency of decision-making units,”European Journal of Operational Research, vol. 2, 1978, pp. 429-444.

[9] P.M Bentleret al., “Practical Issues in Structural Equation Modeling,”Sociological Methods & Research, vol. 16, no. 1, 1987, pp. 187-196.

[10] R.M Debnathet al., “Benchmarking telecommunication service in India,”Benchmarking, vol. 15,no. 5, 2008, pp. 584-598.

[11] H.H Yanget al., “Using DEA window analysis to measure efficiencies of Taiwan’s integrated telecommunication firms,”Telecommunications Policy, vol. 33, no. 1-2, 2009, pp. 98-108.

[12] A. Kumaret al., “Analyzing customer preference and measuring relative efficiency in telecom sector: A hybrid fuzzy AHP/DEA study,”Telematics & Informatics, vol. 32, no. 3, 2015, pp. 447-472.

[13] P. Morenoet al., “Dynamic performance analysis of U.S. wireline telecommunication companies,”

Telecommunications Policy, vol. 37, no. 6-7,2013, pp. 469-482.

[14] Y. Quet al., “Empirical Study of the Telecommunication Operation Performance Evaluation of Regional China,”P(pán)roc. International Conference on Education, Management, Computer and Society, 2016, pp. 183.

[15] T.J Gerpottet al., “Advancement of indices assessing a nation’s telecommunications development status: A PLS structural equation analysis of over 100 countries,”Telecommunications Policy, vol. 39, no. 2, 2015, pp. 93-111.

[16] W. Lemstraet al., “Measuring broadband in Europe: Development of a market model and performance index using structural equations modelling,”Telecommunications Policy, vol. 39,no. 3-4, 2015, pp. 253-268.

[17] A. Ghezziet al., “Strategy and business model design in dynamic telecommunications industries: A study on Italian mobile network operators,”Technological Forecasting & Social Change, vol. 90, 2015, pp. 346-354.

[18] W. Shiet al., “Exploring Enterprise Performance Indicators Network: A Case Study of China Telecommunication Industry,”China Communications, vol. 9, no. 12, 2012, pp. 153-163.

[19] C.G Yanget al., “Effects of telecom service providers’ strategic investments on business performance,”Industrial Management & Data Systems, vol. 116, no. 5, 2016, pp. 960-977.

[20] P. Lingraset al., “Temporal analysis of clusters of supermarket customers: conventional versus interval set approach,”Information Sciences, vol.172, no. 1-2, 2005, pp. 215-240.

[21] Dennyet al., “Visualizing temporal cluster changes using Relative Density Self-Organizing Maps,”Knowledge and Information Systems, vol.25, no. 2, 2010, pp. 281-302.

[22] A. Seretet al., “A dynamic understanding of customer behavior processes based on clustering and sequence mining,”Expert Systems with Applications, vol. 41, no. 10, 2014, pp. 4648-4657.

[23] I. Boseet al., “Detecting the migration of mobile service customers using fuzzy clustering,”Information & Management, vol. 52, no. 2, 2015,pp. 227-238.

[24] M. Sperandioet al., “Constructing Markov Models for Reliability Assessment with Self-Organizing Maps,”P(pán)roc. International Conference on Probabilistic Methods Applied To Power Systems,2006, pp. 1-5.

[25] N. Chenet al., “Clustering and visualization of bankruptcy trajectory using self-organizing map,”Expert Systems with Applications, vol. 40,no. 1, 2013, pp. 385-393.

[26] C. Arriagaet al., “A chronology of interpolation:from ancient astronomy to modern signal and image processing,”P(pán)roceedings of the IEEE, vol.90, no. 3, 2002, pp. 319-342.

[27] M.G Kendallet al., “The advanced theory of statistics,”Journal of the Royal Statistical Society,vol. 147, no. 3, 1984, pp. 410-414.

[28] B. Chenet al., “Openness and trade policy in China: an industrial analysis,”China Economic Review, vol. 11, no. 4, 2001, pp. 323-341.

[29] D. Gamermanet al., “Markov Chain Monte Carlo: Stochastic simulation for bayesian inference,”Chapman & Hall, London, 2006.

[30] J.A Hartiganet al., “A K-means clustering algorithm,”Applied Statistics, vol. 28, no. 1, 1979, pp.100-108.

[31] D.L Davieset al., “A Cluster Separation Measure,”IEEE Computer Society, vol. 1, no. 2, 1979,pp. 224.

[32] J.C Dunn, “Well-Separated Clusters and Optimal Fuzzy Partitions,”Journal of Cybernetics, vol. 4,no. 1, 2008, pp. 95-104.

[33] N.X Vinhet al., “Information theoretic measures for clusterings comparison: is a correction for chance necessary,”P(pán)roc. ACM International Conference on Machine Learning, 2009, pp. 1073-1080.

[34] H.P Friedmanet al., “On Some Invariant Criteria for Grouping Data,”Journal of the American Statistical Association, vol. 62, no. 320, 1967, pp.1159-1178.

[35] J.O Mcclainet al., “CLUSTISZ: A Program to Test for the Quality of Clustering of a Set of Objects,”Journal of Marketing Research, vol. 12, no. 4,1975, pp. 456-460.

[36] G. Durantonet al., “Handbook of regional and urban economics,”Elsevier, Oxford, 2015.