Abstract—Mobile data consumption is rapidly growingfollowing the ever-increasing bandwidth-hungry applica-tions and improvements in network data rates. With theanticipated 5G right at the corner, operators are focusingon load-aware network dimensioning, optimization, andmanagement, where traffic volume prediction plays acritical role. To this end, several researchers investigateddifferent statistical and machine-learning models to exploitand predict the linear and nonlinear patterns that oftenarise due to the complexity of mobile networks andvarying users’ behaviors at different times and locations.In this paper, we propose a hybrid model composed ofDouble Seasonal ARIMA (D-SARIMA), which focuses onmodeling the multi-seasonal nature of the data traffic andexploiting the residuals of DSARIMA via Long-Short TermMemory (LSTM)-based Networks. The residues containthe nonlinear component of the data. To incorporate thespatial dependency inherent in mobile data traffic collectedfrom base stations, we used K-means clustering and consid-ered the correlation among them. Experiments conductedwith real-world data sets collected from 739 base stationsfor over four months, shows that our proposed hybridmodel outperforms both D-SARIMA and LSTM models.The improvement emanates from capturing the doubleseasonality, non-linearity, and spatial dependency inherentin data traffic.
The continued evolution of mobile network tech-nologies and the emergence of various serviceshave led to an exponential growth of mobile datatraffic [1]. From the operators’ perspective, thisgrowth is an opportunity that maximizes revenue.However, supporting such traffic demand, amongothers, requires availing infrastructure during net-
work dimensioning phase as well as allocatingsufficient network resources (e.g., bandwidth andenergy) and network management solutions duringnetwork operation phase. The mobile data trafficdemand has a dynamic nature that varies in time andspace domains. Fig. 1 (a) and (b) shows the temporaland spatial variations of data traffic collected fromthe Universal Mobile Telecommunications Service(UMTS) network operator in the city of AddisAbaba, Ethiopia. Thus, accurately understandingthe traffic dynamics in multiple dimensions andpredicting the current and future demands is critical.
Researchers, in recent years, have made effortsto propose different mobile traffic prediction tech-niques. The prediction can be performed at differentgranularities: aggregate demand of an operator [2],demand on a cell level [3], per user demand [4], onpacket level (e.g., packet arrival rate, the occurrenceof burst, packet inter-arrival rate, flow rate) [6], andapplication-level (e.g., predicting applications withsignificant contribution to generating the traffic) [5].
Inherently, mobile traffic prediction can be treatedas a time series prediction problem where modelscan be used to predict traffic demand based on avail-able historical data. One way of broadly categoriz-ing time series based models can be as linear statisti-cal models (such as Box-Jenkins variants), machinelearning-based models (such as Neural Networks),and a hybrid of the two models [6], [7]. In [8],linear auto-regressive integrated moving average(ARIMA) model, one of the Box-Jenkins variants,has been used to capture fixed temporal dependen-cies in network traffic and predict its yearly growth.To improve the ARIMA-based models on capturing
Fig. 1. (a) Temporal dynamics of data traffic decomposed to trend, and seasonal (daily and weekly) components. (b) Spatial distributionof the mobile data traffic. (c) Correlation matrix for selected neighboring base stations.
the long-term traffic repetitive patterns, [9] and [10]considered statistically decomposed components ofthe mobile data traffic (e.g., trends and seasonality)for prediction using Seasonal ARIMA (SARIMA)model. Generally, the linear statistical methods workwell in estimating the inherent linear characteristicsof the data traffic. However, due to the complexityof mobile networks and varying customers’ behav-iors at different times and locations, data trafficdynamics exhibits non-linear patterns and often non-stationarity which makes it difficult to be capturedvia those linear statistical models [3], [11].
Following advancements in machine learningtechniques, prediction of mobile traffic with ma-chine learning-based methods is proven to improvethe prediction accuracy by capturing the non-linearand complex patterns inherent in data traffic [6],[11]. In [12], the authors implemented Long ShortTerm Memory (LSTM) network-based predictionmodel to capture the temporal dependencies inmobile voice and data traffic. LSTM-based deeplearning model was applied in [13] to not onlyconsider the temporal but also the spatial cor-relation across the entire network by analyzingtraffic information from neighboring base stations.With users continuously moving within a givennetwork, traffic patterns across neighboring base sta-tions are correlated, and exploring both the spatialand temporal dimensions would improve the trafficprediction performance. The Double Spatiotempo-ral Neural Network (D-STNN) proposed in [14]used Convolutional-LSTM (ConvLSTM) and three-dimensional Convolutional Network (3D-ConvNet)structures with an encoder-decoder architecture to
jointly learn the complex spatial and temporal de-pendencies of the mobile data traffic and providelong-term network-wide prediction. Another meansto explore the spatial correlation of the data trafficby grouping together adjust and correlated base sta-tions with similar usage patterns is considered in [3].K-Means clustering was used in combination withElman Neural Network and Wavelet decompositionto provide a cell-level prediction.
Another approach to explore the complex dynam-ics of the data traffic is by implementing the hybridof linear statistical models (such as ARIMA) withArtificial Neural Network models [15] and Waveletanalysis [16] to capture the linear and non-linearparts, respectively, of the data and combine the tworesults to obtain the final mobile network trafficflow prediction. This two-step prediction approachmerges the positive traits of those models and hasthe benefit of improving computational complexity,model interpretability, and prediction accuracy.
This paper proposes a hybrid model of DoubleSeasonal ARIMA (D-SARIMA), which focuses onmodeling the multi-seasonal nature of the mobiledata traffic, and Long-short Term memory (LSTM)-based Networks to learn non-linearities by furtherexploiting the residuals of D-SARIMA. To evaluateits prediction performance, a comparative analysisis done with SARIMA models and LSTM-basednetworks at base station level with data set collectedfrom 739 UMTS base stations (eNodeB) in the cityof Addis Ababa, Ethopia. In addition, to furthercapture spatial dependecy of the data, we consid-ered a cluster-level comparison with K-means as aclustering approach.
The remainder of this paper is organized asfollows. Section II presents the mobile data trafficanalysis. The different traffic prediction techniquesand the hybrid model are discussed in SectionIII. Section IV presents the data pre-processingand demonstrates the experimental results. Finally,Section V concludes this paper.
II. MOBILE DATA TRAFFIC ANALYSIS
A. Data Set DescriptionThe mobile data traffic analyzed in this paper is
obtained from a UMTS network operator in AddisAbaba, Ethiopia. The data is collected from January2019 to April 2019 with a temporal resolutionof 1 hour. Specifically, the dataset encompasseseNodeBs‘ location information, observed cell-leveldownlink traffic, and active users with the corre-sponding timestamp. Fig. 1 illustrates the temporaland spatial characteristics of mobile data traffic.
The temporal variation in aggregated data trafficcan be observed in Fig. 1 (a) showing an increasingtrend in traffic volume and exhibiting daily peri-odical behavior with relatively high demand nearlyat midnight and lowest-demand during early morn-ings. The variation of data traffic on different daysthroughout the week also created new repetitivepatterns on a weekly basis indicating the presenceof double seasonalities in mobile traffic.
There is also significant traffic load variationon the network, as shown in Fig. 1 (b) with asignificant degree of correlation among neighboringbase stations illustrated by high values (greater than0.6) of the Pearson correlation coefficient Fig. 1 (c).To further explore the spatial dependency inherentin mobile data traffic collected from base stations,we consider a clustering approach based on theirtemporal pattern.
B. K-means ClusteringSeveral techniques can be used to map a group
of spatially distributed base stations with comple-menting traffic patterns together and also identifyunique temporal patterns [3]. Among the availablealternatives, we have selected K-means for mainreasons as it is very fast as compared to hierarchicalclustering techniques and provides less number ofhyperparameters, i.e., number of cluster K, as com-pared to model-based clustering mechanisms [17].
The K-means approach aims at dividing a datasets into K disjoint clusters centered around theirmeans or centroids. To obtain the clusters, K-meansiteratively updates cluster members, means, or cen-troids, where most of the time means or centroidsare initialized by randomly selecting one of the dataset to be a centroid or mean. On the other hand,membership in a cluster is given based on the close-ness of a data set to a cluster’s mean or centroid; i.e.,similarity of data traffic pattern of a particular basestation to the mean traffic pattern. Afterward, meansor centroids are updated by taking the average ofthe identified members. In this context, deployingK-means for time series data sets is faced with acritical question of identifying the optimal value ofK. To this end, we have utilized inter-cluster inertia,which measures the closeness of a data sets to thecluster mean or centroid. Furthermore, followingthe discussion in [18], we have acknowledged theimpact of temporal distortion on K-means withregards to cluster membership identification andthe optimal estimation of cluster average which isstill a challenge to be tackled. However, we foundincluding the proposed solutions in [18] to ourpaper to be computationally costy. Thus, even ifthe solution provides better cluster identifications,we have avoided it in this work; and we aim toinvestigate the impact of the proposed solutions in[18] on prediction accuracy in future work.
With that, the optimal number of clusters, K,value is estimated by iteratively observing the inter-cluster inertia, and 5 clusters were obtained. Thetraffic pattern for the respective five clusters isshown in Fig. 2, indicating a presence of diversityand similarity of traffic usage among them. Simi-larly, the spatial correlation of the five clusters ispresented in Fig. 3. In a city where the differentfunctional areas (residential, business, or entertain-ment areas) are mixed, a low correlation amongthe clusters is expected; however, the close to zerocorrelation in Fig. 3 might imply peculiar usagebehaviors or the sparse population distribution inthe network load.
III. TRAFFIC PREDICTION TECHNIQUES
A. Double Seasonal ARIMAARIMA is a popular statistical model used to
capture the stationarity property of time-series data
Fig. 2. Clustered base stations with their corresponding centroids.
as a function of its sequentially lagged variablesas well as error terms. When there exist seasonalcomponents in the data, it is possible to treat theseasonal and non-seasonal parts with a generalmultiplicative SARIMA model [19].
To capture the double (daily and weekly) sea-
Fig. 3. Correlation matrix for the five clusters.
sonalities explained in Section II of the mobile datatraffic, the SARIMA model can be expressed asSARIMA(p, d, q)× (P1, D1, Q1)s1 × (P2, D2, Q2)s2where the order of regression (φ) and movingaverage (Θ) coefficients for the non-seasonal andseasonal parts of the model are represented by(p, P(.)) and (q,Q(.)), respectively. The parametersd and D are also used to represent the differencingthat can be applied one or more times to eliminatethe trend, and s(.) seasonalities, and make the time
series data stationary.Assuming a polynomial that has a factor (1−L)
of multiplicity, the Double SARIMA (D-SARIMA)model is formulated as [19]:
(1−p∑
i=1
φiLi)(1−
P1∑j=1
φjLjs1)(1−
P2∑k=1
φkLks2)
((1− L)d(1− Ls1)D1(1− Ls2)D2(Xt − µ))
= (1+
q∑i=1
θiLi)(1−
Q1∑j=1
ΘjLjs1)(1−
Q2∑k=1
ΘkLks2)εt
(1)where Xt is the aggregated traffic consumptionrepresenting the non-stationary time-series and εtis the error term at time t.
In order to incorporate the impact of spatialdependency with SARIMA models, we can considerthe aggregated traffic from different cluster as ex-ogenous variables (independent variables). Evaluat-ing the cross-correlation among clusters will helpto identify which cluster data to be considered asexternal variable.
B. LSTM
Another predictor that is widely considered tolearn and estimate complex multi-dimensional char-acteristics of the mobile data traffic is a RecurrentNeural Network (RNN). As one variant of RNN,LSTM is suitable for time series prediction andis capable of capturing the long-range temporal
information by using memory cells [20]. Whichinput to process, whether to update the memorycell, and whether to create an output is controlledby three gates in LSTM memory block, namely theinput gate, forget gate and output gate, respectively.
For a given sequential inputs pt, hidden layerht−1 and previous memory cell state ct−1, the LSTMoutput for time step t is given as [20]
Ot = σ[Wopt + Uoht−1 + V o(ft� ct−1) +
(σ(Wipt + Uiht−1 + Vict−1 + bi)�
g(Wipt + Ucht−1 + bi)) + bo] (2)
where � denotes element-wise multiplication andforget gate ft is equated as σ(Wfpt + Ufht−1 +Vfct−1 + bf ). For a given data traffic consumptionobserved at base station level for a time inter-val T , the input sequence is a 2-D dataset (i.e.,P = p1, p2, p3, ..., pT ), and for mobile data trafficmeasured over N base stations or represented interms of K clusters, the input sequence will be3-D (i.e., P = P1, P2, P3, ..., PN ). The nonlinearactivation functions are represented by g(.) and σ(.)usually denoting the Relu/tanh and sigmoid func-tions, respectively. W(.), U(.), and V(.) are weightmatrices that are adjusted during model training byminimizing the square loss function (in this paper)and b(.) are bias vectors.
C. Proposed Hybrid Model
To improve prediction accuracy and effectivelyhandle the linear and non-linear dynamics of themobile data traffic, we propose a hybridize model byleveraging the benefits of both SARIMA and LSTM.Fig. 4 illustrates the proposed model consisting thedata processing part and a hybrid predictor part.The model’s first part includes pre-processing partfor ”clean-up”, clustering part as well as clustercorrelation analyzing part.Whereas, hybrid predictorpart blends the prediction output from D-SARIMAand LSTM-based network to provide combined pre-diction as illustrated in Fig. 4.
While conducting a prediction for a particularcluster, its correlation with the remaining four clus-ters is analyzed. The clusters with correlation co-efficient greater than 0.5 value are assumed to bemoderately correlated and are taken as external (ex-ogenous) variables to D-SARIMA model. With that
the spatial correlation among different clusters isconsidered as a means of improving the prediction.
The complex non-linearities that couldn’t be fittedwith D-SARIMA are reflected on the model resid-uals. For a time series data yt the residual, rt, fromlinear statistical models can be expressed as:
rt = yt − Lt (3)
where Lt is the estimated linear component of thedata.
While keeping the temporal structure of theresidual errors, LSTM-based network then usedto learn additional information and provide futurepredictions.
Combining the outputs from the two models mod-els depends on the different predictors consideredand can be done through weighted or straightfor-ward addition, multiplication or by ensemble av-eraging the prediction output or model coefficients[15]. In the proposed model, straightforward addi-tion is considered to integrate the results from thetwo predictions as:
yt = rt + Lt + εt (4)
where yt represented the final prediction, rt indicat-ing the estimation from LSTM-based network andεt is the error that is not captured by the hybridmodel.
Fig. 4. Proposed hybrid model.
IV. EXPERIMENTAL RESULTS
A. Data set Pre-processing and Experiment Set upFew number of data traffic measurement values
were missing due to improper data storage andretrial. Thus, we applied linear interpolation usingKalman filters prior to prediction to impute themissing values; as Kalman filter is used to find opti-mal estimates of the missing values by computing itsconditional mean and variance up on the observeddata traffic. Furthermore, to speeds up learning andfaster convergence for based predictor, the trafficvalues are normalized into range of [0, 1] usingMin-Max normalization.
To obtain the model parameters for D-SARIMA,i.e., to determine the autoregression (p, P (.)), mov-ing average (q, Q(.)) and differencing orders (d,D(.)), it is necessary to investigate Auto CorrelationFunction (ACF) and Partial Auto Correlation Func-tion (PACF) of the the time series. Removing thenon-stationarity exhibited on the mobile data trafficas a form of increasing trend, and daily and weeklyseasonalities (in Fig. 1) is essential prior to usingthe D-SARIMA . The ACF plot in Fig. 5 showsstationarity of the data traffic in the mean value aftergoing through a second order differentiation processto remove the trend and seasonality. The significantsparks at lag (24, 48, ....) and at 168 on the ACFplot also confirm the daily (s1 = 24) and weekly(s2 = 168) seasonalities discussed in Section II.
After considering the correlated clusters as exoge-nous variables on the model, the best-fit model isidentified as SARIMA(1, 0, 2)(2, 1, 0)24(0, 1, 1)168
Fig. 5. ACF and PACF plot
based on minimum values of the Corrected Akaike’sInformation Criterion (AICc).
To capture the non-linearity on the mobile datatraffic by exploiting the residuals from D-SARIMA,the LSTM-based network within the hybrid modelconsiders 2-layers of LSTM units each with 128 and64 hidden nodes, respectively, to form a stackedLSTM network, and Time distributed dense layerat the output to apply a layer to every temporalslice of an input. The ReLU activation functionis considered for the two LSTM layers and thesigmoid activation function to restrict the predic-tion output within range of [0, 1]. For 80/10/10partitioned residual data for training, validation andtesting, optimizing the square loss is done withAdaptive Moment Estimation (ADAM) optimizer,which is widely used in Neural Networks domain.the key point to note is, the values of these param-eters including additional hyper-parameters such asbatch size (24), epoch (100) and number of pastobservations (48 or 2 days) are determined basedon experiment requirements as optimizing them wasnot the intent of the work. Thus, the parameters canalso take different value which can impact the trade-off between the prediction accuracy and the timeneeded to train the network.
B. Evaluation MetricsFor the purpose of evaluating the prediction
performance of the hybrid model and compare itagainst D-SARIMA and LSTM models, two stan-dard prediction metrics are used: Root Mean SquareError (RMSE) and Mean Absolute Error (MAE);calculated for prediction error ei over n measure-ment points of the data traffic over space and time.
RMSE =
√√√√ 1
n
n∑i=1
e2i (5)
MAE =1
n
n∑i=1
|ei| (6)
C. Prediction Results and ComparisonThe mobile data traffic prediction performance of
aforementioned hybrid model is done consideringtwo cases/approaches: Base Station-Level predictionapproach where data traffic from a single base sta-tion is analyzed, and Cluster-level approach where
the data traffic from other clusters that are mod-erately correlated are considered to incorporate thespatial dependency.Table 1 shows comparison (based on average RMSEand MAE) of the hybrid, D-SARIMA, and LSTM-based models. Key observations from the base sta-tion level results are:• The proposed hybrid model performs poorly,
whereas D-SARIMA provides relatively bettershort-time prediction. The results also indicatethe double seasonality and trend componentsare the dominant patterns in mobile data trafficthat were better captured by the linear model.
• The LSTM model was not able to sufficientlylearn the patterns (i.e., trend, seasonalities, andnon-linearities) inherent both in the data orthe D-SARIMA residuals to the extent that itcontributes negatively in the hybrid model. Thisshows that linear models are good at capturingshort-term dependency in the data. Possibleremedies to improve the LSTM model include:increasing the data size (from the current fourmonths), hyper-parameter optimization, or ex-tracting additional features from other basestations are; the latter approach is used in thecluster-level prediction explained next.
As argued repeatedly, the cluster-level approach hasthe potential to exploit the temporal and spatialdimensions of the mobile data. The addition ofthe spatial dimension will, undoubtedly, add to thenonlinearity of the data but also provides moreinformation for the LSTM to learn more. Key ob-servations from the clusters-level results in Table 1are:• All three models perform better than their
TABLE ICOMPARING THE PREDICTION PERFORMANCE ON BASE
STATION-LEVEL AND CLUSTER-LEVEL APPROACH IN TERMS OFRMSE AND MAE
Approaches Models Evaluation MetricsMAE RMSE
Base station level D-SARIMA 1.385 1.229Hybrid 1.667 1.517LSTM 1.408 1.237
Fig. 6. Double Seasonal ARIMA model fitting and 120 hours aheadprediction considering single base station in (a) and multiple cross-correlated clusters in (b).
Fig. 7. 48 hours of mobile data traffic prediction performanceconsidering base station and cluster-level approaches
counterparts in base station level investigationas they exploit cluster correlation and extractmultiple temporal patterns. The improvementis as high as 60%, which is significant.
• By comparison, the proposed hybrid modelperforms better while the D-SARIMA’s perfor-mance is inferior to the two models. The LSTMcaptures the dynamics (the non-linearity) inthe mobile data which is manifested on theimproved prediction performance of the hybridand LSTM model.
The cluster-level approach benefited the linearmodel like D-SARIMA as the other correlated clus-ters’ data traffic is taken as exogenous variables forthe prediction of a particular cluster. See Fig. 6 tofurther learn the improvements in these models.
The mobile data traffic prediction for next 48hours with the models considering both approachesis illustrated in Fig. 7. Results show that for bothbase station and cluster-level approaches, the pre-diction during low traffic load (in early morning)is comparable. However, there exists a significancedifference during day-time that can associated to auser activity and spatial mobility. In addition, as theprediction time increases, despite the performancedegradation of D-SARIMA, the performance hybridmodel prediction remains relativity constant.
V. CONCLUSIONS
As mobile networks become more complex, andusers’ data traffic consumption behaviors vary overspace and time, providing accurate predictions ofthe traffic volume gets particularly tricky. In thispaper, we propose the use of hybrid model ofD-SARIMA and LSTM-based network to exploitboth the linear and non-linearity on the data trafficand provide accurate predictions. We consideredthe double (daily and weekly) seasonal patterns inour D-SARIMA and exploiting the residuals withLSTM to learn non-linearities that the linear modelfailed to capture. Furthermore, to explore spatialdependency inherent in mobile data traffic collectedfrom base stations, we used k-means clusteringto group base stations with complementing trafficpatterns together and also identified unique temporalpatterns. By evaluating the correlation among them,we considered multiple clusters together as multiplevaluables to provide cluster-level prediction. Theresults reveal the benefits of using hybrid modeland exploiting the spatial correlation. Possible ex-tensions to this work are investigating the impactof temporal distortion on the cluster averaging,computational overhead of the hybrid model, or theimpact of optimizing the hyper-parameters of theLSTM-based network on the prediction accuracy.
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