CN104394538A - Mobile network data flow analysis and prediction method - Google Patents

Abstract

The invention relates to a mobile network data flow analysis and prediction method and belongs to the technical field of mobile communication. Based on the traditional time sequence prediction method, relevance among flow characteristics and social factors is considered in the method, and flow prediction is performed in workdays and rest days: to flow predication in any workday, two-day flow sequences with the strongest relevance to the workday are combined and averaged with the flow sequence in the day of the previous week as a final workday flow predication model; to flow predication in any rest day, after flow is compensated in the workday, the five-day flow sequences with the strongest relevance to the rest day are combined and averaged with the flow sequence in the day of the previous week as a final rest day flow predication model. Through the method, the predication accuracy isn't seriously affected by flow generated in non-relevant days and the calculated amount is lower, thus the method can reach the higher predication effect.

Description

A kind of mobile network data flow analysis and Forecasting Methodology

Technical field

The invention belongs to mobile communication technology field, relate to a kind of mobile network data flow analysis and Forecasting Methodology, particularly a kind of Mobile data flow analysis that social factor is combined with time series forecasting and Forecasting Methodology.

Background technology

In the past few decades, mobile network obtains swift and violent development with its mobility, high transfer rate, the advantage such as expansion and good cost performance that is easy to, the data service flow carried in network is increasing, and type of service gets more and more, and discharge characteristic also becomes increasingly complex.According to Cisco statistics, 2012, global Mobile data flow was 12 times of 2000, and predicted that 2012 in 2017, and global Mobile data flow is by growth by 13 times.In addition, statistics also show mobile flow by voice to multimedia development in pluralism, wherein video flow occupies 2/3rds of global Mobile data total flow.

Growing network size and user's request bring lot of challenges to mobile network, and the network traffics of wherein sharp increase cause huge pressure to current network framework, also reduce Consumer's Experience simultaneously.

Predicting network flow effectively manages network, safeguards and the important means of safety guarantee, by analyzing historical data, can the situation of the aspect such as the operating environment of awareness network and network service state, for the upgrading of network and improvement provide necessary reference.But along with developing rapidly of mobile network, being on the increase of terminal equipment, network flow data will present and significantly increase, and network traffics are about to large data age of marching toward.Under high amount of traffic amount background, the sharply increase of terminal traffic type causes flow character to change, and traditional method for predicting has not been suitable for the interpretation and application of current and even following mobile network.

At present, most of Forecasting Methodology only probes into the reason of discharge characteristic change from the angle of microcosmic point, network, and e.g., terminal data bag transmission mechanism, diversified type of service and its related protocol produced are the key factors causing discharge characteristic to change.But along with the development of mobile network, the appearance of changes in flow rate phenomenon is not limited thereto, analyze changes in flow rate for macroscopic aspect, it is also very necessary for discharge characteristic change being associated with social factor.In addition, for the method that flow analysis and prediction propose, as Forecasting Methodology, wavelet algorithm etc. based on neural net can reach higher prediction effect, but because its complex structure, parameter are numerous, cause that algorithm the convergence speed is slow, predicted time is longer and cannot be used in real network volume forecasting, therefore to network flow quantitative analysis and predict imperative.

Summary of the invention

In view of this, the object of the present invention is to provide a kind of mobile network data flow analysis and Forecasting Methodology, the method is on conventional time series prediction principle basis, consider the relevance between discharge characteristic and social factor, angle volume forecasting being divided into working day different with day off two is carried out.

For achieving the above object, the invention provides following technical scheme:

A kind of mobile network data flow analysis and Forecasting Methodology, the method is on the basis of conventional time series Forecasting Methodology, consider the relevance between discharge characteristic and social factor, angle volume forecasting being divided into working day different with day off two is carried out: for the volume forecasting of any darg day, the two day flow sequences the strongest with this day correlation are adopted to combine, and average, as volume forecasting on working day final mask with the flow sequence that upper one week this day produced; For the volume forecasting on any day off, adopt after carrying out the compensation of flow yardstick working day, get the flow sequence of five day the strongest with this day correlation to combine, and average, as volume forecasting on day off final mask with the flow sequence that upper one week this day produced.

Further, this Forecasting Methodology specifically comprises the following steps:

Step one: gather upper one week original data on flows, forms raw data set;

Step 2: raw data set is divided into working day data set and day off data set;

Step 3: analytical work day data set and day off data set between correlation;

Step 4: for workaday volume forecasting, first, consider the correlation between working day and day off data set, according to correlation size sequence, the flow correlations combination of using one week characterizes the flow of the time period needing prediction, and its discontinuous temporal correlation combination can be expressed as:

$y_{\mathrm{weekdays}}\left(t\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{w}_i{f}_i\left(t\right)$

Wherein, f _i(t) (t=1,2 ..., n.i=1,2 ..., m) represent the composite sequence i on time t, y _weekdays(t) (t=1,2 ..., n) represent f _ithe combined sequence of (t); The mix vector of m sequence is expressed as w=(w ₁, w ₂..., w _m), and meet condition below:

e ^Tw＝1；w≥0；e ^T＝(1,1,...,1)；

Step 5: for the volume forecasting on day off, adopt compensating factor to reduce the difference of the yardstick of the flow of working day and generation on day off, compensating factor can be obtained by following formula:

$p\left(t\right)=\frac{f_j\left(t\right)}{f_s\left(t\right)}$

$\mathrm{CF}\left(t\right)=\frac{1}{5}(p\left(1\right)+p\left(2\right)+...+p\left(n\right))$

Wherein, f _j(t) (j=1,2 ..., 5.t=1,2 ..., n), represent the sequence in jth sky in working day, f _s(t) (t=1,2 ..., n) represent the flow sequence that the week number of days that will predict produced at upper a week, p (t) is f _j(t) and f _sthe ratio of (t);

Step 6: the compensating factor obtained is used for the compensation to flow yardstick on working day, thus obtain new flow sequence, given by following formula:

f _{new_j}(t)＝CF(t)·f _j(t)

Wherein, f _{new_j}t () represents the flow sequence on working day obtained after compensating factor reparation, therefore, the discontinuous temporal correlation combination on day off is expressed as:

$y_{\mathrm{weekends}}\left(t\right)=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{w}_j{f}_{\mathrm{new}\_j}\left(t\right)$

Wherein, y _weekends(t) (t=1,2 ..., n) represent the flow correlations combination that relevant number of days produces;

Step 7: by following optimal models, obtain best of breed:

$\max R_{\mathrm{weekdays}}=\frac{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_k\left(t\right)-f_A)\·(y_{\mathrm{weekdays}}\left(t\right)-y_A)}{\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_k\left(t\right)-f_A)}\·\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(y_{\mathrm{weekdays}}\left(t\right)-y_A)}}$

$s.t.\left\{\begin{array}{c}{e}^{T}w=1\\ w\≥0\end{array}\right.$

$\max R_{\mathrm{weekends}}=\frac{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_s\left(t\right)-f_B)\·(y_{\mathrm{weekends}}\left(t\right)-y_B)}{\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_s\left(t\right)-f_B)}\·\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(y_{\mathrm{weekends}}\left(t\right)-y_B)}}$

$s.t.\left\{\begin{array}{c}{e}^{T}w=1\\ w\≥0\end{array}\right.$

Wherein, f _kt () represents that the sequence pair needing prediction answers workaday flow value last week, f _st () represents the flow value needing the sequence pair of prediction to answer day off last week, f _a, f _brepresent f respectively _k(t) and f _sthe mean value of (t), y _a, y _brepresent y respectively _weekdays(t) and y _weekendsthe mean value of (t);

Step 8: solve after obtaining optimum combination vector, by following equations volume forecasting sequence:

$P_{\mathrm{weekdays}}\left(t\right)=\frac{1}{2}(y_{\mathrm{weekdays}}\left(t\right)+f_k\left(t\right))$

$P_{\mathrm{weekends}}\left(t\right)=\frac{1}{2}(y_{\mathrm{weekends}}\left(t\right)+f_s\left(t\right))$

Wherein, P _weekdays(t), P _weekendst () represents working day and volume forecasting on day off formula respectively.

Beneficial effect of the present invention is: the method for the invention combines Socio-behavioral factors with time series forecasting, volume forecasting be divided into predict and predict that two angles are carried out day off working day, obtain predictor formula by optimization, thus reduce irrelevant number of days produce flow on the impact of forecasting accuracy.This method amount of calculation is lower, and can reach higher prediction effect.

Accompanying drawing explanation

In order to make object of the present invention, technical scheme and beneficial effect clearly, the invention provides following accompanying drawing and being described:

Fig. 1 is Chongqing Mobile data flow obtain manner and volume forecasting system structural framework;

Fig. 2 is the one week flow diagram in Chongqing region;

Fig. 3 is conventional time series volume forecasting general principle;

Fig. 4 is for improving time series volume forecasting general principle;

Fig. 5 is mobile volume forecasting flow chart;

Fig. 6 is discontinuous sequential combination schematic diagram;

Fig. 7 is the correlation between one week actual flow;

Fig. 8 is for prediction Monday, tests the best initial weights parameter obtained respectively for six kinds;

Fig. 9 is the correlation after compensating one week actual flow;

Figure 10 is for prediction on Sunday, tests the best initial weights parameter obtained respectively for six kinds;

Figure 11 is for prediction Monday, tests the MAPE obtained respectively for six kinds;

Figure 12 is for prediction on Sunday, tests the MAPE obtained respectively for six kinds;

Figure 13 contrasts figure with the one week flow prediction effect obtained based on neural net method for the present invention;

Figure 14 is the present invention and the volume forecasting Monday effect comparison figure obtained based on neural net method;

Figure 15 is the present invention and all forecast of daily discharge effect comparison figure obtained based on neural net method;

Figure 16 is that the present invention contrasts with the MAPE based on neural net method.

Embodiment

Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described in detail.

The data traffic that the present invention adopts moves existing network from Chongqing, and data set takes from DPI analytical system as shown in Figure 1, and data set covers all data from Access Network to backbone aggregation layer, thus ensures integrality and the reliability of data.Based on existing network data on flows, the present invention fully excavates the relevance between discharge characteristic and social factor, concrete as shown in Figure 2, in one week, user will apparently higher than working day (Mon-Fri) at ordinary times for the time of mobile terminal and mobile applications on day off (Friday is to Saturday).Meanwhile, in working day, the data traffic that the flow that every day produces correlation each other will produce apparently higher than day off.

For achieving the above object, take following technical scheme, this invention, on the conventional time series prediction principle basis shown in Fig. 3, considers the relevance between discharge characteristic and social factor, angle volume forecasting being divided into working day different with day off two is carried out, and its principle as shown in Figure 4.Fig. 5 discloses concrete prediction flow chart of the present invention:

1. consider working day and day off, the flow that every day produces has extremely strong correlation respectively.The angle that volume forecasting is divided into working day different with day off two by the present invention is carried out, thus improves overall prediction effect.

2., for workaday volume forecasting, as shown in Fig. 6 (a), the flow correlations combination of first using a week characterizes the flow of the time period needing prediction.Its discontinuous temporal correlation combination can be expressed as:

$y_{\mathrm{weekdays}}\left(t\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{w}_i{f}_i\left(t\right)$

Wherein, f _i(t) (t=1,2 ..., n.i=1,2 ..., m) represent the composite sequence i on time t.Y _weekdays(t) (t=1,2 ..., n) represent f _ithe combined sequence of (t).The mix vector of m sequence is expressed as w=(w ₁, w ₂..., w _m), and meet condition below:

e ^Tw＝1

w≥0

e ^T＝(1,1,...,1).

3. for the volume forecasting on day off, consider that the flow number of days related to day off is limited, as shown in Fig. 6 (b), this invention proposes the difference that the using compensation factor reduces the yardstick of the flow of working day and generation on day off.Compensating factor can be obtained by following formula:

$p\left(t\right)=\frac{f_j\left(t\right)}{f_s\left(t\right)}$

$\mathrm{CF}\left(t\right)=\frac{1}{5}(p\left(1\right)+p\left(2\right)+...+p\left(n\right))$

Wherein, f _j(t) (j=1,2 ..., 5.t=1,2 ..., n) represent the sequence in jth sky in working day, f _s(t) (t=1,2 ..., n) represent the sequence that the week number of days that will predict produced at upper a week.P (t) is f _j(t) and f _sthe ratio of (t).

4. the compensating factor obtained is used for the compensation to flow yardstick on working day, thus obtains new flow sequence, given by following formula:

f _{new_j}(t)＝CF(t)·f _j(t)

Wherein, f _{new_j}t () represents the flow sequence on working day obtained after compensating factor reparation, therefore, the discontinuous temporal correlation combination on day off can be expressed as:

$y_{\mathrm{weekends}}\left(t\right)=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{w}_j{f}_{\mathrm{new}\_j}\left(t\right)$

Wherein, y _weekends(t) (t=1,2 ..., n) represent the flow correlations combination that relevant number of days produces.

5., in order to find best of breed, this invention proposes following optimal models:

$\max R_{\mathrm{weekdays}}=\frac{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_k\left(t\right)-f_A)\·(y_{\mathrm{weekdays}}\left(t\right)-y_A)}{\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_k\left(t\right)-f_A)}\·\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(y_{\mathrm{weekdays}}\left(t\right)-y_A)}}$

$s.t.\left\{\begin{array}{c}{e}^{T}w=1\\ w\≥0\end{array}\right.$

$\max R_{\mathrm{weekends}}=\frac{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_s\left(t\right)-f_B)\·(y_{\mathrm{weekends}}\left(t\right)-y_B)}{\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_s\left(t\right)-f_B)}\·\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(y_{\mathrm{weekends}}\left(t\right)-y_B)}}$

$s.t.\left\{\begin{array}{c}{e}^{T}w=1\\ w\≥0\end{array}\right.$

Wherein, f _kt () represents that the sequence pair needing prediction answers workaday flow value last week, f _st () represents the flow value needing the sequence pair of prediction to answer day off last week.F _a, f _brepresent f respectively _k(t) and f _sthe mean value of (t).Y _a, y _brepresent y respectively _weekdays(t) and y _weekendsthe mean value of (t).

6. solve after obtaining optimum combination vector, by following equations volume forecasting sequence:

$P_{\mathrm{weekdays}}\left(t\right)=\frac{1}{2}(y_{\mathrm{weekdays}}\left(t\right)+f_k\left(t\right))$

$P_{\mathrm{weekends}}\left(t\right)=\frac{1}{2}(y_{\mathrm{weekends}}\left(t\right)+f_s\left(t\right))$

Wherein, P _weekdays(t), P _weekendst () represents working day and volume forecasting on day off formula respectively.

Embodiment:

First the present invention draws the correlation between one week actual flow based on the existing network data on flows analysis of Chongqing commmunication company, as shown in Figure 7, correlation between number of days different in a week is different, and working day or day off, correlation was each other apparently higher than the correlation between working day and day off.For above feature, the present invention considers to predict the correlation between time series (as Monday) and other number of days, according to relevance order size, constructs six and prediction group can be selected to close:

Trial#1:{Tue.}；

Trial#2:{Tue.,Thur.}；

Trial#3:{Tue.,Wed.,Thur.}；

Trial#4:{Tue.,Wed.,Thur.,Fri.}；

Trial#5:{Tue.,Wed.,Thur.,Fri.,Sat.}；

Trial#6:{Tue.,Wed.,Thur.,Fri.,Sat.,Sun.}；

According to the flux prediction model on working day introduced before, six kinds of best initial weights parameters that prediction group can be selected to close as shown in Figure 8.

Consider that the number of days comprised day off is less, the present invention propose flow yardstick on working day is compensated, with increase day off and working day correlation each other, the correlation between one week flow after compensation is as shown in Figure 9.

The present invention consider to predict time series (as Sunday) and other compensates correlation afterwards between number of days, according to relevance order size, construct six and prediction group can be selected to close:

Trial#1:{Tue.}；

Trial#2:{Tue.,Wed.}；

Trial#3:{Tue.,Wed.,Thur.}；

Trial#4:{Mon.,Tue.,Wed.,Thur.}；

Trial#5:{Mon.,Tue.,Wed.,Thur.,Fri.}；

Trial#6:{Mon.,Tue.,Wed.,Thur.,Fri.,Sat.}；

According to the flux prediction model on day off introduced before, six kinds of best initial weights parameters that prediction group can be selected to close as shown in Figure 10.

In order to verify mobile volume forecasting effect, the present invention adopts mean absolute percentage error (MAPE) as measurement index, and its expression formula is as follows:

$\mathrm{MAP}{E}_{\mathrm{weekdays}}=\frac{1}{n}\underset{t=1}{\overset{n}{\mathrm{\Σ}}}\left|\frac{f_k\left(t\right)-P_{\mathrm{weekdays}}\left(t\right)}{f_k\left(t\right)}\right|$

$\mathrm{MAP}{E}_{\mathrm{weekends}}=\frac{1}{n}\underset{t=1}{\overset{n}{\mathrm{\Σ}}}\left|\frac{f_k\left(t\right)-P_{\mathrm{weekends}}\left(t\right)}{f_s\left(t\right)}\right|$

By above-mentioned expression formula, the MAPE that Monday and Sunday six kinds prediction group can be selected to close can be calculated respectively, as is illustrated by figs. 11 and 12.For volume forecasting Monday, as shown in Figure 11, its optimum prediction sequential combination: the two day flow combined sequence the strongest with correlation Monday.For all forecast of daily discharges, as shown in Figure 12, its optimum prediction sequential combination: after one week flow is compensated, the five day flow combined sequence the strongest with correlation on Sunday.Consider that working day or day off have stronger correlation each other, draw thus, for the volume forecasting of any darg day, we can combine by two days flow sequences the strongest with this day correlation, and be averaging, as volume forecasting on working day final mask with the flow sequence that this day of last week produces.For the volume forecasting on any day off, we can to after carrying out the compensation of flow yardstick working day, get the flow sequence of five day the strongest with this day correlation to combine, and be averaging, as volume forecasting on day off final mask with the flow sequence that this day of last week produces.Therefore, volume forecasting in a week can be carried out.

Figure 13 shows this invention and contrasts figure with the one week flow prediction effect obtained based on neural net method, Figure 14 and Figure 15 is respectively in Monday and all forecast of daily discharges, this invention and the volume forecasting effect comparison figure obtained based on neural net method.Can find out, contrast the volume forecasting obtained based on neural net method, the present invention can obtain better prediction effect.

Figure 16 shows this invention and contrasts with the MAPE based on neural net method.As can be seen, for volume forecasting on working day, on neural net method fundamentals of forecasting, MAPE of the present invention reduces 35.7%; For volume forecasting on day off, on neural net method fundamentals of forecasting, MAPE of the present invention reduces 43.8%.

As can be seen here, the method for predicting that the present invention proposes can effective control system amount of calculation, reaches higher prediction effect simultaneously.

What finally illustrate is, above preferred embodiment is only in order to illustrate technical scheme of the present invention and unrestricted, although by above preferred embodiment to invention has been detailed description, but those skilled in the art are to be understood that, various change can be made to it in the form and details, and not depart from claims of the present invention limited range.

Claims (2)

1. a mobile network data flow analysis and Forecasting Methodology, it is characterized in that: the method is on the basis of conventional time series Forecasting Methodology, consider the relevance between discharge characteristic and social factor, angle volume forecasting being divided into working day different with day off two is carried out: for the volume forecasting of any darg day, the two day flow sequences the strongest with this day correlation are adopted to combine, and average, as volume forecasting on working day final mask with the flow sequence that upper one week this day produced; For the volume forecasting on any day off, adopt after carrying out the compensation of flow yardstick working day, get the flow sequence of five day the strongest with this day correlation to combine, and average, as volume forecasting on day off final mask with the flow sequence that upper one week this day produced.

2. a kind of mobile network data flow analysis according to claim 1 and Forecasting Methodology, is characterized in that: this Forecasting Methodology specifically comprises the following steps:

Step one: gather upper one week original data on flows, forms raw data set;

Step 2: raw data set is divided into working day data set and day off data set;

Step 3: analytical work day data set and day off data set between correlation;

Step 4: for workaday volume forecasting, first, consider the correlation between working day and day off data set, according to correlation size sequence, the flow correlations combination of using one week characterizes the flow of the time period needing prediction, and its discontinuous temporal correlation combination can be expressed as:

$y_{\mathrm{weeddays}}\left(t\right)=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{w}_i{f}_i\left(t\right)$

Wherein, f _i(t) (t=1,2 ..., n.i=1,2 ..., m) represent the composite sequence i on time t, y _weekdays(t) (t=1,2 ..., n) represent f _ithe combined sequence of (t); The mix vector of m sequence is expressed as w=(w ₁, w ₂..., w _m), and meet condition below:

e ^Tw＝1；w≥0；e ^T＝(1,1,...,1)；

Step 5: for the volume forecasting on day off, adopt compensating factor to reduce the difference of the yardstick of the flow of working day and generation on day off, compensating factor can be obtained by following formula:

$p\left(t\right)=\frac{f_j\left(t\right)}{f_s\left(t\right)}$

$\mathrm{CF}\left(t\right)=\frac{1}{5}(p\left(1\right)+p\left(2\right)+...+p\left(n\right))$

Wherein, f _j(t) (j=1,2 ..., 5.t=1,2 ..., n), represent the sequence in jth sky in working day, f _s(t) (t=1,2 ..., n) represent the flow sequence that the week number of days that will predict produced at upper a week, p (t) is f _j(t) and f _sthe ratio of (t);

Step 6: the compensating factor obtained is used for the compensation to flow yardstick on working day, thus obtain new flow sequence, given by following formula:

f _{new_j}(t)＝CF(t)·f _j(t)

Wherein, f _{new_j}t () represents the flow sequence on working day obtained after compensating factor reparation, therefore, the discontinuous temporal correlation combination on day off is expressed as:

$y_{\mathrm{weekends}}\left(t\right)=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{w}_j{f}_{\mathrm{new}\_j}\left(t\right)$

Wherein, y _weekends(t) (t=1,2 ..., n) represent the flow correlations combination that relevant number of days produces;

Step 7: by following optimal models, obtain best of breed:

$\max R_{\mathrm{weekdays}}=\frac{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_k\left(t\right)-f_A)\·(y_{\mathrm{weekdays}}\left(t\right)-y_A)}{\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_k\left(t\right)-f_A)}\·\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(y_{\mathrm{weekdays}}\left(t\right)-y_A)}}$

$s.t.\left\{\begin{array}{c}{e}^{T}w=1\\ w\≥0\end{array}\right.$

$\max R_{\mathrm{weekends}}=\frac{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_s\left(t\right)-f_B)\·(y_{\mathrm{weekends}}\left(t\right)-y_B)}{\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(f_s\left(t\right)-f_B)}\·\sqrt{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}(y_{\mathrm{weekends}}\left(t\right)-y_B)}}$

$s.t.\left\{\begin{array}{c}{e}^{T}w=1\\ w\≥0\end{array}\right.$

Wherein, f _kt () represents that the sequence pair needing prediction answers workaday flow value last week, f _st () represents the flow value needing the sequence pair of prediction to answer day off last week, f _a, f _brepresent f respectively _k(t) and f _sthe mean value of (t), y _a, y _brepresent y respectively _weekdays(t) and y _weekendsthe mean value of (t);

Step 8: solve after obtaining optimum combination vector, by following equations volume forecasting sequence:

$P_{\mathrm{weekdays}}\left(t\right)=\frac{1}{2}(y_{\mathrm{weekdays}}\left(t\right)+f_k\left(t\right))$

$P_{\mathrm{weekends}}\left(t\right)=\frac{1}{2}(y_{\mathrm{weekends}}\left(t\right)+f_s\left(t\right))$

Wherein, P _weekdays(t), P _weekendst () represents working day and volume forecasting on day off formula respectively.