CELLULAR NETWORK TRAFFIC PREDICTION USING EXPONENTIAL SMOOTHING METHODS

Wireless traffic prediction plays an important role in network planning and management, especially for real-time decision making and short-term prediction. Systems require high accuracy, low cost, and low computational complexity prediction methods. Although exponential smoothing is an effective method, there is a lack of use with cellular networks and research on data traffic. The accuracy and suitability of this method need to be evaluated using several types of traffic. Thus, this study introduces the application of exponential smoothing as a method of adaptive forecasting of cellular network traffic for cases of voice (in Erlang) and data (in megabytes or gigabytes). Simple and Error, Trend, Seasonal (ETS) methods are used for exponential smoothing. By investigating the effect of their smoothing factors in describing cellular network traffic, the accuracy of forecast using each method is evaluated. This research comprises a comprehensive analysis approach using multiple case study comparisons to determine the best fit model. Different exponential smoothing models are evaluated for various traffic types in different time scales. The experiments are implemented on real data from a commercial cellular network, which is divided into a training data part for modeling and test data part for forecasting comparison.


INTRODUCTION
Wireless traffic prediction is a key component of network planning, development, and management.Accurate prediction will become even more necessary with the development of 5 th generation wireless systems (5G) that contain many new service capabilities (5G PPP, 2015).The 5G system has a higher capacity and higher density of mobile broadband users than the current 4G system.It also supports device-to-device communications and massive machine-type communications (NGMN Alliance, 2015).Consequently, people are living in the age of social networks (Tyagi & Kumar, 2017) and the Internet-of-Things (Matta, Pant, & Arora, 2017).Life becomes more convenient and intelligent when everything can be connected via heterogeneous wireless networks (Qiang, Li, & Altman, 2017).Along with these advanced technologies, Yusuf-Asaju, Dahalin, and Ta'a (2018) also figured out the issues of mobile network performance and proposed a framework for modeling mobile network quality of experience using the big data analytics approach.And in fact, better network operation and management are required to ensure a robust infrastructure that includes the underlying network and supporting technologies, for example.
Analysis of wireless network traffic shows that the traffic series normally contains seasonal components and can be modeled and forecasted by time series analysis models (Tran, Ma, Li, Hao, & Trinh, 2015).Authors in these papers proposed combining statistical procedures for modeling and forecasting cellular network traffic, such as the autoregressive integrated moving average (ARIMA) and generalized autoregressive conditional heteroskedasticity (GARCH).They took advantage of the ARIMA model for capturing the conditional mean of the traffic series and the GARCH model for dealing with the conditional heteroskedasticity existing inside the traffic.They achieved better forecast results compared with the individual models, but at the cost of computational complexity.The results can be used for capacity planning and overload warning issues that are important parts of network planning.
Exponential smoothing is a simple method of adaptive forecasting in which the forecasts adjust based on past errors, unlike forecasts from regression models that use fixed coefficients.Exponential smoothing methods have been applied in several areas, such as palm oil real production forecasting (Siregar, Butar-Butar, Rahmat, Andayani, & Fahmi, 2017), power (Usaratniwart, Sirisukprasert, Hatti, & Hagiwara, 2017), revenue forecasting (Rahman, Salma, Hossain, & Khan, 2016), and solar irradiance prediction (Margaret & Jose, 2015), to name a few.These researchers all achieved good results with this low-complexity and low-cost method.In terms of wireless traffic prediction, Tikunov and Nishimura (2007) proposed the application of Holt-Winter's exponential smoothing, which is simple, low cost, does not require a without highly skilled analyst, and operates nearly automatically for GSM/GPRS network Erlang traffic prediction.The recorded data were classified into three types, namely high, medium, and low intensity traffic cells.The authors focused on cells with high and medium traffic intensity for the purposes of overload warning and capacity planning.Although good results were achieved, only voice traffic was considered.In the era of data, there is a necessity for more comprehensive studies about using exponential smoothing in cellular network traffic that includes not only voice (Erlang) but also data (megabytes or gigabytes).
Base on the mentioned requirement, more exponential smoothing methods were investigated that included not only the specific Holt-Winter's multiplicative seasonal method (HWMS), but also different types of exponential smoothing methods.They were then applied to forecast cellular network traffic that consists of not only voice (in Erlang) but also data (in megabytes or gigabytes).In this study, the simple exponential smoothing methods include single, double, Holt-Winter's no seasonal, Holt-Winter's additive seasonal, and HWMS.The methods are introduced together with an Error, Trend, Seasonal (ETS) framework.The exponential smoothing methods are considered in three cases of hourly voice, daily voice, and daily data traffic types.

SIMPLE EXPONENTIAL SMOOTHING
Simple exponential smoothing methods include: Base on the mentioned requirement, more exponential smoothing methods were investigated tha only the specific Holt-Winter's multiplicative seasonal method (HWMS), but also diffe exponential smoothing methods.They were then applied to forecast cellular network traffic that c only voice (in Erlang) but also data (in megabytes or gigabytes).In this study, the simple smoothing methods include single, double, Holt-Winter's no seasonal, Holt-Winter's additive HWMS.The methods are introduced together with an Error, Trend, Seasonal (ETS) fram exponential smoothing methods are considered in three cases of hourly voice, daily voice, and dai types.
The analysis of cellular network traffic is appropriate for the HWMS method (Val Base on the mentioned requirement, more exponential smoothing methods were investigated that only the specific Holt-Winter's multiplicative seasonal method (HWMS), but also diffe exponential smoothing methods.They were then applied to forecast cellular network traffic that c only voice (in Erlang) but also data (in megabytes or gigabytes).In this study, the simple smoothing methods include single, double, Holt-Winter's no seasonal, Holt-Winter's additive HWMS.The methods are introduced together with an Error, Trend, Seasonal (ETS) fram exponential smoothing methods are considered in three cases of hourly voice, daily voice, and dai types.
The analysis of cellular network traffic is appropriate for the HWMS method (Val Base on the mentioned requirement, more exponential smoothing methods were investigated that only the specific Holt-Winter's multiplicative seasonal method (HWMS), but also diffe exponential smoothing methods.They were then applied to forecast cellular network traffic that c only voice (in Erlang) but also data (in megabytes or gigabytes).In this study, the simple smoothing methods include single, double, Holt-Winter's no seasonal, Holt-Winter's additive HWMS.The methods are introduced together with an Error, Trend, Seasonal (ETS) fram exponential smoothing methods are considered in three cases of hourly voice, daily voice, and dai types.
The analysis of cellular network traffic is appropriate for the HWMS method (Val Base on the mentioned requirement, more exponential smoothing methods were investigated that inclu only the specific Holt-Winter's multiplicative seasonal method (HWMS), but also different exponential smoothing methods.They were then applied to forecast cellular network traffic that consis only voice (in Erlang) but also data (in megabytes or gigabytes).In this study, the simple exp smoothing methods include single, double, Holt-Winter's no seasonal, Holt-Winter's additive seaso HWMS.The methods are introduced together with an Error, Trend, Seasonal (ETS) framewo exponential smoothing methods are considered in three cases of hourly voice, daily voice, and daily da types.
The analysis of cellular network traffic is appropriate for the HWMS method (Valakev Brazenas, 2015), which is suitable for a series with a linear time trend and multiplicative s Base on the mentioned requirement, more exponential smoothing methods were investigated that inclu only the specific Holt-Winter's multiplicative seasonal method (HWMS), but also different ty exponential smoothing methods.They were then applied to forecast cellular network traffic that consist only voice (in Erlang) but also data (in megabytes or gigabytes).In this study, the simple expo smoothing methods include single, double, Holt-Winter's no seasonal, Holt-Winter's additive season HWMS.The methods are introduced together with an Error, Trend, Seasonal (ETS) framewor exponential smoothing methods are considered in three cases of hourly voice, daily voice, and daily dat types.
The analysis of cellular network traffic is appropriate for the HWMS method (Valakevic Brazenas, 2015), which is suitable for a series with a linear time trend and multiplicative se variation.If x t is the input traffic series, then the smoothed series,  � , is given by The analysis of cellular network traffic is appropriate for the HWMS method (Valakevicius & Brazenas, 2015), which is suitable for a series with a linear time trend and multiplicative seasonal variation.If x t is the input traffic series, then the smoothed series, is given by (1) where a is the permanent component (intercept), b is the trend, and c t is the multiplicative seasonal factor.These three coefficients are defined by the following recursions: (2) where are the damping factors and s is the seasonal frequency.
The forecasts are computed by: (5) where the seasonal factors are used from the last s estimates.

ERROR TREND SEASONAL EXPONENTIAL SMOOTHING
This framework defines an extended class of exponential smoothing methods and offers a theoretical foundation for analysis of these models using state-space based likelihood calculations.Support for model selection and calculation of forecast standard errors are also included.The standard exponential smoothing models discussed in the previous section, such as HWMS, are encompassed by this ETS framework.
In the ETS exponential smoothing method, the time series may be decomposed into three components, namely the error (E) that is the irregular unpredictable component of the series, the trend (T) that characterizes the long-term movement of the time series, and the season (S) that corresponds to a pattern with known periodicity.s of cellular network traffic is appropriate for the HWMS method (Valakevicius & 15), which is suitable for a series with a linear time trend and multiplicative seasonal x t is the input traffic series, then the smoothed series,  �  , is given by he permanent component (intercept), b is the trend, and c t is the multiplicative seasonal three coefficients are defined by the following recursions: , , and  < 1 are the damping factors and s is the seasonal frequency.
The analysis of cellular network traffic is appropriate for the HWMS method (Valakevi Brazenas, 2015), which is suitable for a series with a linear time trend and multiplicative s variation.If x t is the input traffic series, then the smoothed series,  �  , is given by where a is the permanent component (intercept), b is the trend, and c t is the multiplicative s factor.These three coefficients are defined by the following recursions: where0 < , , and  < 1 are the damping factors and s is the seasonal frequency.
The analysis of cellular network traffic is appropriate for the HWMS method (Valakevi Brazenas, 2015), which is suitable for a series with a linear time trend and multiplicative se variation.If x t is the input traffic series, then the smoothed series,  �  , is given by where a is the permanent component (intercept), b is the trend, and c t is the multiplicative se factor.These three coefficients are defined by the following recursions: where0 < , , and  < 1 are the damping factors and s is the seasonal frequency.
The analysis of cellular network traffic is appropriate for the HWMS method (Valakevi Brazenas, 2015), which is suitable for a series with a linear time trend and multiplicative se variation.If x t is the input traffic series, then the smoothed series,  �  , is given by where a is the permanent component (intercept), b is the trend, and c t is the multiplicative s factor.These three coefficients are defined by the following recursions: where0 < , , and  < 1 are the damping factors and s is the seasonal frequency.
The analysis of cellular network traffic is appropriate for the HWMS method (Valakevi Brazenas, 2015), which is suitable for a series with a linear time trend and multiplicative se variation.If x t is the input traffic series, then the smoothed series,  �  , is given by where a is the permanent component (intercept), b is the trend, and c t is the multiplicative s factor.These three coefficients are defined by the following recursions: where0 < , , and  < 1 are the damping factors and s is the seasonal frequency.The analysis of cellular network traffic is appropriate for the HWMS method (Valakevicius & Brazenas, 2015), which is suitable for a series with a linear time trend and multiplicative seasonal variation.If x t is the input traffic series, then the smoothed series,  �  , is given by where a is the permanent component (intercept), b is the trend, and c t is the multiplicative seasonal factor.These three coefficients are defined by the following recursions: where0 < , , and  < 1 are the damping factors and s is the seasonal frequency.
The forecasts are computed by: where the seasonal factors are used from the last s estimates.

ETS EXPONENTIAL SMOOTHING
This framework defines an extended class of exponential smoothing methods and offers a the foundation for analysis of these models using state-space based likelihood calculations.Sup model selection and calculation of forecast standard errors are also included.The standard expo smoothing models discussed in the previous section, such as HWMS, are encompassed by th framework.
In the ETS exponential smoothing method, the time series may be decomposed into components, namely the error (E) that is the irregular unpredictable component of the series, th (T) that characterizes the long-term movement of the time series, and the season (S) that corre to a pattern with known periodicity.
The ETS models can be described as state equations that are extended versions of those outl The ETS models can be described as state equations that are extended versions of those outlined by Hyndman et al. (2002) as in Equations ( 6), (7), and (8), respectively: (6) where l is a level term, b is a growth term, and s is a seasonal term.Variables P, R, and T are functions of the prediction error and lagged states; Q is a function of the lagged state; is the damping parameter for linear trend models; is the damping parameter for multiplicative trend models; and is prediction error.Figure 1 presents the model of ETS exponential smoothing method.

Model Specification
In this section, the type of ETS model used for smoothing is specified.There are a total of 30 possible ETS models based on the various combinations of the three components, E, T, and S, as defined in Equations ( 9), ( 10) and ( 11), respectively: components, namely the error (E) that is the irregular unpredictable component of the series, (T) that characterizes the long-term movement of the time series, and the season (S) that cor to a pattern with known periodicity.
The ETS models can be described as state equations that are extended versions of those ou Hyndman et al. (2002) as in Equations ( 6), (7), and (8), respectively: where l is a level term, b is a growth term, and s is a seasonal term.Variables P, R, an functions of the prediction error and lagged states; Q is a function of the lagged state;  damping parameter for linear trend models;  2 is the damping parameter for multiplicati models; and   ~(0,  2 ) is prediction error.Figure 1 presents the model of ETS exp smoothing method.
components, namely the error (E) that is the irregular unpredictable component of the series, (T) that characterizes the long-term movement of the time series, and the season (S) that cor to a pattern with known periodicity.
The ETS models can be described as state equations that are extended versions of those ou Hyndman et al. (2002) as in Equations ( 6), (7), and (8), respectively: where l is a level term, b is a growth term, and s is a seasonal term.Variables P, R, an functions of the prediction error and lagged states; Q is a function of the lagged state;  damping parameter for linear trend models;  2 is the damping parameter for multiplicati models; and   ~(0,  2 ) is prediction error.Figure 1 presents the model of ETS exp smoothing method.
components, namely the error (E) that is the irregular unpredictable component of the series, (T) that characterizes the long-term movement of the time series, and the season (S) that cor to a pattern with known periodicity.
The ETS models can be described as state equations that are extended versions of those ou Hyndman et al. (2002) as in Equations ( 6), (7), and (8), respectively: where l is a level term, b is a growth term, and s is a seasonal term.Variables P, R, an functions of the prediction error and lagged states; Q is a function of the lagged state;  damping parameter for linear trend models;  2 is the damping parameter for multiplicati models; and   ~(0,  2 ) is prediction error.Figure 1 presents the model of ETS exp smoothing method. 4 od, the time series may be decomposed into three irregular unpredictable component of the series, the trend nt of the time series, and the season (S) that corresponds quations that are extended versions of those outlined by ), and (8), respectively: , and s is a seasonal term.Variables P, R, and T are d states; Q is a function of the lagged state;  1 is the ;  2 is the damping parameter for multiplicative trend rror.Figure 1 presents the model of ETS exponential 4 he error (E) that is the irregular unpredictable component of the series, the trend the long-term movement of the time series, and the season (S) that corresponds n periodicity.
be described as state equations that are extended versions of those outlined by ) as in Equations ( 6), (7), and (8), respectively: m, b is a growth term, and s is a seasonal term.Variables P, R, and T are iction error and lagged states; Q is a function of the lagged state;  1 is the or linear trend models;  2 is the damping parameter for multiplicative trend 0,  2 ) is prediction error.Figure 1 presents the model of ETS exponential 4 components, namely the error (E) that is the irregular unpredictable component of the series, the trend (T) that characterizes the long-term movement of the time series, and the season (S) that corresponds to a pattern with known periodicity.
The ETS models can be described as state equations that are extended versions of those outlined by Hyndman et al. (2002) as in Equations ( 6), (7), and (8), respectively: where l is a level term, b is a growth term, and s is a seasonal term.Variables P, R, and T are functions of the prediction error and lagged states; Q is a function of the lagged state;  1 is the damping parameter for linear trend models;  2 is the damping parameter for multiplicative trend models; and   ~(0,  2 ) is prediction error.Figure 1 presents the model of ETS exponential smoothing method.

Estimation Control
According to the chosen ETS model specification, the corresponding unknown parameters and the initial states x 0 may be estimated using either the maximum likelihood or average mean square error minimization (AMSE) methods.The Gaussian log likelihood for ETS specifications can be written in terms of the prediction errors, as in Equation ( 12): (12) The parameters and initial states are achieved by maximizing the likelihood in Equation ( 12) with respect to and using the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) algorithm (Fletcher, 1987).The average mean square error (AMSE) of the h-step forecasts is expressed as in Equation ( 13): (13) The parameters and initial states that minimize the AMSE using BFGS are then achieved.

Model Selection
In this step, the model can be selected based on either the comparison of a likelihood-based information criterion across the models to decide which one more closely fits the data or the forecast error, i.e., an out-of-sample AMSE to decide which one has a more accurate forecast result.The likelihood-based information criteria include Akaike information criterion (AIC), Schwarz information criterion (BIC), or the Hannan-Quinn criterion (HQ), as expressed in Equations ( 14), (15), and ( 16

Estimation Control
According to the chosen ETS model specification, the corresponding u (, , , ), and the initial states x 0 may be estimated using either the maxim mean square error minimization (AMSE) methods.The Gaussian log likelihood for ETS specifications can be written in terms of the prediction e in Equation ( 12): The parameters and initial states are achieved by maximizing the likelihood in Equation ( respect to ,  0 , and  2 using the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) a (Fletcher, 1987).
The average mean square error (AMSE) of the h-step forecasts is expressed as in Equation (13 The parameters and initial states that minimize the AMSE using BFGS are then achieved. (

2) Model Selection
In this step, the model can be selected based on either the comparison of a likelihoo information criterion across the models to decide which one more closely fits the data or the error, i.e., an out-of-sample AMSE to decide which one has a more accurate forecast result.
The likelihood-based information criteria include Akaike information criterion (AIC), information criterion (BIC), or the Hannan-Quinn criterion (HQ), as expressed in Equatio (15), and ( 16), respectively: The Gaussian log likelihood for ETS specifications can be written in terms of the prediction in Equation ( 12): The parameters and initial states are achieved by maximizing the likelihood in Equation ( respect to ,  0 , and  2 using the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) a (Fletcher, 1987).
The average mean square error (AMSE) of the h-step forecasts is expressed as in Equation (1 The parameters and initial states that minimize the AMSE using BFGS are then achieved. (

2) Model Selection
In this step, the model can be selected based on either the comparison of a likeliho information criterion across the models to decide which one more closely fits the data or the error, i.e., an out-of-sample AMSE to decide which one has a more accurate forecast result.
The likelihood-based information criteria include Akaike information criterion (AIC), information criterion (BIC), or the Hannan-Quinn criterion (HQ), as expressed in Equati (15), and ( 16), respectively: where are the maximized values and p is the number of parameters in plus the number of the estimated initial states in .The chosen model is the one with the minimum value of AIC (BIC, or HQ).

Smoothing/Forecasting
Using the chosen ETS model with estimated parameters, the in-sample smoothed series can be achieved by the one-step-ahead forecast function, Based on the smoothing model and the estimated parameters, as well as the in-sample data, the out-of-sample forecasted values can be obtained by implementing the dynamic forecast of the series.

EXPERIMENTAL METHODOLOGY AND RESULT
The real traffic from commercial cellular networks was collected and included voice in Erlang and data in Mbps.The first trace is 31-day hourly voice traffic collected during the New Year period from MSCID of MSC_ Hanoi1.The traffic data ranged from 00:00 December 9th, 2015 until 23:00 January 8th, 2016 and included 744 observations.The second trace is the daily voice traffic and included 236 3G traffic values that ranged from March 9th until October 30th, 2014, collected from 110 siteBs in the CauGiay district area in Hanoi.The third trace is the 3G data collected from 600 cells located within the HoanKiem district in Hanoi.The 443-value daily data traffic series ranged from September 12th, 2014 to November 28th, 2015.
Exponential smoothing methods were applied to forecast these three traces that are distinguished from each other by traffic type, namely voice vs. data and hourly vs. daily.The simple exponential smoothing methods included single, double, and Holt-Winters and were used to implement the forecasts for the three traffic traces.Then, the achieved models that gave the The parameters and initial states that minimize the AMSE using BFGS are then a (2) Model Selection In this step, the model can be selected based on either the comparison o information criterion across the models to decide which one more closely fits th error, i.e., an out-of-sample AMSE to decide which one has a more accurate forec The likelihood-based information criteria include Akaike information criter information criterion (BIC), or the Hannan-Quinn criterion (HQ), as expresse (15), and ( 16), respectively: where � � ,  � 0 � are the maximized values and p is the number of parameters in  � p estimated initial states in  � 0 .The chosen model is the one with the minimum va HQ).
The out-of-sample AMSE is given in Equation ( 17):  (15), and ( 16), respectively: where � � ,  � 0 � are the maximized values and p is the number of parameters in  � plus the numb estimated initial states in  � 0 .The chosen model is the one with the minimum value of AIC HQ).
The out-of-sample AMSE is given in Equation ( 17): (3) Smoothing/Forecasting Using the chosen ETS model with estimated parameters, the in-sample smoothed series achieved by the one-step-ahead forecast function, ℎ( −1 , ).Based on the smoothing mode The likelihood-based information criteria include Akaike information criterion (AIC), information criterion (BIC), or the Hannan-Quinn criterion (HQ), as expressed in Equatio (15), and ( 16), respectively: where � � ,  � 0 � are the maximized values and p is the number of parameters in  � plus the numb estimated initial states in  � 0 .The chosen model is the one with the minimum value of AIC HQ).
The out-of-sample AMSE is given in Equation ( 17): (3) Smoothing/Forecasting Using the chosen ETS model with estimated parameters, the in-sample smoothed series achieved by the one-step-ahead forecast function, ℎ( −1 , ).Based on the smoothing mode The likelihood-based information criteria include Akaike information criterion (AIC), information criterion (BIC), or the Hannan-Quinn criterion (HQ), as expressed in Equatio (15), and ( 16), respectively: where � � ,  � 0 � are the maximized values and p is the number of parameters in  � plus the numb estimated initial states in  � 0 .The chosen model is the one with the minimum value of AIC HQ).
The out-of-sample AMSE is given in Equation ( 17): (3) Smoothing/Forecasting Using the chosen ETS model with estimated parameters, the in-sample smoothed series achieved by the one-step-ahead forecast function, ℎ( −1 , ).Based on the smoothing model information criterion (BIC), or the Hannan-Quinn criterion (HQ), as expressed in Equa (15), and ( 16), respectively: where � � ,  � 0 � are the maximized values and p is the number of parameters in  � plus the num estimated initial states in  � 0 .The chosen model is the one with the minimum value of AI HQ).
The out-of-sample AMSE is given in Equation ( 17): (3) Smoothing/Forecasting Using the chosen ETS model with estimated parameters, the in-sample smoothed seri achieved by the one-step-ahead forecast function, ℎ( −1 , ).Based on the smoothing mod 6 e Hannan-Quinn criterion (HQ), as expressed in Equations ( 14), alues and p is the number of parameters in  � plus the number of the chosen model is the one with the minimum value of AIC (BIC, or in Equation ( 17): ith estimated parameters, the in-sample smoothed series can be recast function, ℎ( −1 , ).Based on the smoothing model and the The likelihood-based information criteria include Akaike information criterion (AIC), S information criterion (BIC), or the Hannan-Quinn criterion (HQ), as expressed in Equation ( 15), and ( 16), respectively: where � � ,  � 0 � are the maximized values and p is the number of parameters in  � plus the numbe estimated initial states in  � 0 .The chosen model is the one with the minimum value of AIC ( HQ).
The out-of-sample AMSE is given in Equation ( 17): (3) Smoothing/Forecasting Using the chosen ETS model with estimated parameters, the in-sample smoothed series achieved by the one-step-ahead forecast function, ℎ( −1 , ).Based on the smoothing model estimated parameters, as well as the in-sample data, the out-of-sample forecasted values obtained by implementing the dynamic forecast of the series.

EXPERIMENTAL METHODOLOGY AND RESULTS
The real traffic from commercial cellular networks was collected and included voice in Erla data in Mbps.The first trace is 31-day hourly voice traffic collected during the New Year perio MSCID of MSC_Hanoi1.The traffic data ranged from 00:00 December 9th, 2015 until 23:00 J 8th, 2016 and included 744 observations.The second trace is the daily voice traffic and includ 3G traffic values that ranged from March 9th until October 30th, 2014, collected from 110 s the CauGiay district area in Hanoi.The third trace is the 3G data collected from 600 cells within the HoanKiem district in Hanoi.The 443-value daily data traffic series ranged from Sep 12th, 2014 to November 28th, 2015.
Exponential smoothing methods were applied to forecast these three traces that are distinguishe each other by traffic type, namely voice vs. data and hourly vs. daily.The simple expo smoothing methods included single, double , and Holt-Winters and were used to implem forecasts for the three traffic traces.Then, the achieved models that gave the best results were to make comparisons with the best choices by the ETS exponential smoothing framework in t information criterion (AIC), Schwarz n (HQ), as expressed in Equations ( 14 16), respectively: where � � ,  � 0 � are the maximized values and p is the number of para estimated initial states in  � 0 .The chosen model is the one with the HQ).
The out-of-sample AMSE is given in Equation ( 17): .
(3) Smoothing/Forecasting Using the chosen ETS model with estimated parameters, the in achieved by the one-step-ahead forecast function, ℎ( −1 , ).Based estimated parameters, as well as the in-sample data, the out-ofobtained by implementing the dynamic forecast of the series.

EXPERIMENTAL METHODOLOGY AND
The real traffic from commercial cellular networks was collected Exponential smoothing methods were applied to forecast these three each other by traffic type, namely voice vs. data and hourly v smoothing methods included single, double , and Holt-Winters a forecasts for the three traffic traces.Then, the achieved models that to make comparisons with the best choices by the ETS exponential best results were chosen to make comparisons with the best choices by the ETS exponential smoothing framework in terms of estimation information, in-sample forecast, and out-of-sample forecast.

Hourly Voice Traffic
The simple exponential smoothing methods were applied to hourly voice traffic.The estimation outputs are shown in Table 1, where HWMS presents the best results in terms of the 426.5057RMSE.Thus, the HWMS was chosen as the best forecasting method in the case of hourly voice traffic.In contrast, the ETS framework was also applied to this hourly voice traffic, and the estimation outputs are listed in Table 2.The numerical results indicate that this framework is not suitable for the hourly data series when both AIC-based and AMSE-based models yield abnormal RMSE values.To confirm this judgment, we further implement the in-sample and out-of-sample forecast tests for these two models and compare the results with those obtained using HWMS.The results are shown in Figures 2 and 3 which display that the HWMS out-ofsample forecasted data is very close to the original data, so we can figure out that HWMS outperforms the two ETS models in modeling and forecasting hourly cellular voice traffic.

Daily Voice Traffic
The same experimental procedure was implemented for the case of daily voice traffic.Table 3 illustrates the estimation outputs of the simple exponential smoothing methods.The HWMS again presents the best results among other methods in term of RMSE, which is 531.6792.Thus, HWMS was chosen as the best forecasting method for the case of daily voice traffic.The ETS framework was also applied to the daily voice traffic, and the estimation outputs are illustrated in Table 4. Based on the results, the AIC-based ETS model, i.e. {A, N, M}, should be chosen due to the better RMSE.(

2) Daily Voice Traffic
The same experimental procedure was implemented for the case of daily voice traffic.The comparison between the HWMS and ETS models was done next for the case of daily voice traffic.It can be seen from Table 5 that the achieved ETS model shows the same parameters as HWMS.In addition, there appears to be no difference between the HWMS and ETS{A,N,M} in terms of in-sample forecasts in Figures 4 and 5, and the out-of-sample forecast in Figure 6.Figure4.In-sample forecast by HWMS and ETS in case of daily voice traffic.

Daily Data Traffic
The HWMS again is the best choice among other the simple exponential smoothing methods in the case of daily data traffic due to the best RMSE of 48.03080, as presented in Table 6.Besides, AIC-based ETS {A,N,M} was also the chosen model with the lower RMSE of 48.03521, as shown in Table 7.The same results were achieved in the case of daily data traffic in which the HWMS and ETS{A,N,M} have almost the same parameters, as in Table 8.The same is true for the same in-sample forecasts in Figures 7 and 8 and the same out-of-sample forecast in Figure 9.

CONCLUSIONS
In network planning and management, short-term prediction and real-time decisions are best served by simple and low-cost prediction methods with a high accuracy.Therefore, exponential smoothing methods, such as HWMS, were applied to forecast GSM/GPRS network Erlang traffic.However, a

CONCLUSION
In network planning and management, short-term prediction and real-time decisions are best served by simple and low-cost prediction methods with a high accuracy.Therefore, exponential smoothing methods, such as HWMS, were applied to forecast GSM/GPRS network Erlang traffic.However, a more comprehensive study was required to evaluate the usage of various exponential smoothing methods in more types of wireless traffic, such as data, which is becoming more important along with the development of communication technology.This research applied different exponential smoothing methods that were categorized as a simple exponential smoothing method and ETS framework, to forecast cellular network traffic that included voice and data.
The experiments on hourly and daily traffic collected from commercial cellular networks showed that HWMS was the best fit for cellular network traffic among other simple exponential smoothing methods that included single, double, Holt-Winters No Seasonal, and Holt-Winters Additive Seasonal.It was unsuitable for the ETS framework to forecast hourly voice traffic.However, in the case of daily voice and data traffic, the ETS found that the {A,N,M} models provided nearly the same results as the HWMS.The HWMS forecast series was close to the original series in both hourly and daily voice traffic cases and showed a good ability to forecast daily data traffic as well.Due to the low complexity and low cost, HWMS can be applied effectively to cellular network traffic prediction.Moreover, the evaluation of HWMS can be further implemented based on the specific requirements of cellular networks.
MD = multiplicative g unknown parameters  = ximum likelihood or average ) Smoothing/Forecasting Using the chosen ETS model with estimated parameters, the in-sample smo achieved by the one-step-ahead forecast function, ℎ( −1 , ).Based on the smoo 6 imize the AMSE using BFGS are then achieved.d based on either the comparison of a likelihood-based o decide which one more closely fits the data or the forecast ide which one has a more accurate forecast result.ria include Akaike information criterion (AIC), Schwarz nan-Quinn criterion (HQ), as expressed in Equations (14), the number of parameters in  � plus the number of the model is the one with the minimum value of AIC (the in-sample smoothed series can be function, ℎ( −1 , ).Based on the smoothing model and the The likelihood-based information criteria include Akaike information criterion (AIC), information criterion (BIC), or the Hannan-Quinn criterion (HQ), as expressed in Equatio � plus the number of the ith the minimum value of AIC(BIC, or   (17)    , the in-sample smoothed series can be ).Based on the smoothing model and the out-of-sample forecasted values can be .Y AND RESULTSllected and included voice inErlang and ollected during the New Year period from December 9th, 2015 until 23:00 January is the daily voice traffic and included 236 30th, 2014, collected from 110 siteBs in 3G data collected from 600 cells located data traffic series ranged from September se three traces that are distinguished from ourly vs. daily.The simple exponential inters and were used to implement the els that gave the best results were chosen The likelihood-based information criteria include Akaike inform information criterion (BIC), or the Hannan-Quinn criterion (HQ) (15), and ( data in Mbps.The first trace is 31-day hourly voice traffic collected MSCID of MSC_Hanoi1.The traffic data ranged from 00:00 Decem 8th, 2016 and included 744 observations.The second trace is the da 3G traffic values that ranged from March 9th until October 30th, 2 the CauGiay district area in Hanoi.The third trace is the 3G data within the HoanKiem district in Hanoi.The 443-value daily data tra 12th, 2014 to November 28th, 2015.

Figure 2 .
Figure 2. In-sample forecast by HWMS and ETS models in case of hourly voice traffic (2-day view window)

Figure 2 .
Figure 2. In-sample forecast by HWMS and ETS models in case of hourly voice traffic (2-day view window) 8

Figure 2 .Figure 3 .
Figure 2. In-sample forecast by HWMS and ETS models in case of hourly voice traffic (2-day view window)

Figure 5 .
Figure 5. In-sample forecast by HWMS and ETS for 3 weeks in case of daily voice traffic.

Figure 6 .
Figure 6.Out-of-sample forecast by HWMS and ETS for 3 weeks in case of daily voice traffic.

Figure 6 .
Figure 6.Out-of-sample forecast by HWMS and ETS for 3 weeks in case of daily voice traffic.(3) Daily Data Traffic The HWMS again is the best choice among other the simple exponential smoothing methods in the case of daily data traffic due to the best RMSE of 48.03080, as presented in Table 6.Besides, AICbased ETS {A,N,M} was also the chosen model with the lower RMSE of 48.03521, as shown in

Figure 5 .
Figure 5. In-sample forecast by HWMS and ETS for 3 weeks in case of daily voice traffic.

Figure 7 .
Figure 7. In-sample forecast by HWMS and ETS in case of daily data traffic.

Figure 8 .
Figure 8. In-sample forecast by HWMS and ETS for 3 weeks in case of daily data traffic.

Figure 9 .
Figure 9. Out-of-sample forecast by HWMS and ETS for 3 weeks in case of daily data traffic.

Figure 8 .
Figure 8. In-sample forecast by HWMS and ETS for 3 weeks in case of daily data traffic.

Figure 9 .
Figure 9. Out-of-sample forecast by HWMS and ETS for 3 weeks in case of daily data traffic.CONCLUSIONSIn network planning and management, short-term prediction and real-time decisions are best served by simple and low-cost prediction methods with a high accuracy.Therefore, exponential smoothing methods, such as HWMS, were applied to forecast GSM/GPRS network Erlang traffic.However, a more comprehensive study was required to evaluate the usage of various exponential smoothing methods in more types of wireless traffic, such as data, which is becoming more important along with the development of communication technology.This research applied different exponential smoothing

Figure 9 .
Figure 9. Out-of-sample forecast by HWMS and ETS for 3 weeks in case of daily data traffic.

Table 1
Hourly Voice Traffic Estimation Outputs of Simple Exponential SmoothingMethods.

Table 2
Hourly Voice Traffic Estimation Outputs of AIC and AMSE Based ETS ChosenModels.

Table 3
Daily Voice Traffic Estimation Outputs of Simple Exponential SmoothingMethods.

Table 3
illustrates the estimation outputs of the simple exponential smoothing methods.The HWMS again presents the best results among other methods in term of RMSE, which is 531.6792.Thus, HWMS was chosen as the best forecasting method for the case of daily voice traffic.The ETS framework was

Table 4
Daily Voice Traffic Estimation Output of AIC and AMSE Based ETS ChosenModels.

Table 5
Comparison of HWMS and ETS Methods in Case ofDaily Voice Traffic.

Table 6
Daily Data Traffic Estimation Outputs of Simple Exponential SmoothingMethods.

Table 7
Daily Data Traffic Estimation Output of AIC and AMSE Based ETS ChosenModels.

Table 8
Comparison of HWMS and ETS Methods in Case ofDaily Data Traffic.
Figure 7. In-sample forecast by HWMS and ETS in case of daily data traffic.

Table 8
Comparison of HWMS and ETS Methods in Case ofDaily Data Traffic.