The predicted load balancing algorithm based on the dynamic exponential smoothing

2.1 The calculation of server node load

The load reflects the current equipped performance of the server, and each server node is oftentimes heterogeneous in the computer cluster. This will make the allocation task of the dispatcher more balanced, show the largest utilization ratio of all the resources clearly, and guarantee that the current performance of the characterization server node will not encounter mistakes. In general, some indexes have an effect on the server load, which include the utilization of disk I/O and memory usage. Assuming I _C, I _D, I _M, and I _N to represent, respectively, the server node CPU, disk bandwidth utilization, memory utilization, and Internet bandwidth utilization, then the calculation formula of the load is

where φ i represents the coefficient with the weight of all the indexes; furthermore, ∑ q i = 1 .

For instance, when the streaming media server in the RTP contract is selected as the object and the FTP server is selected as the object, the weighted value of disk I/O utilization should be promoted to a level. In addition, the weighted value of bandwidth utilization should be promoted to a certain level. In the practical application, researchers have taken the particular emphasis of server node as the proof to adjust φ , which aims to get a better effect.

2.2 Single exponential smoothing model

The exponential smoothing model, a kind of short time series prediction method, is both concise and practicable. The model covers all the fields such as electricity and business. In addition, the secondary exponential smoothing and single exponential smoothing models are exponential smoothing methods since the higher level exponential smoothing algorithm brings larger pressure to the load dispatcher on the calculation, which is not good for the normal expression of computer cluster performance. Therefore, a single exponential smoothing model has been selected. Assuming {L _t } to represent the time series of the server node load, and the load predicted value at the moment of t + 1 needs to be obtained as for the t moment. For the single exponential smoothing prediction model [16,17,18,19,20,21,22], it is represented in the following formula:

where S _t represents the smoothing value at the moment of t, namely, the predicted value at the moment of t + 1, α represents the smoothing coefficient, and L _t and S _t−1, respectively, represent the load value at t moment and the smoothing value of t − 1 moment of the server node; unfolding it with the recursive method, and we may obtain the following formula:

In this formula, S ₀ refers to the initial smoothing value. It can be obtained from Eq. (4) that the predicted value S _t at t moment involves the use of all the historical data {L _t }, in addition, aiming at the specific load time series {L _t }, the smoothing initial value S ₀, and the smoothing coefficient α affect the predicted value at t moment to a great extent.

S ₀ and α represent themselves with the static model in the traditional exponential smoothing model. We have only discussed smoothing coefficient α while ignoring the influence of smoothing initial value S _0, and what is definite is that α affects the predicted result accuracy to a larger degree. The most important point of the exponential smoothing model is to find the reasonable smoothing coefficient α.

As for the static smoothing coefficient α, some means of improvement are given. In fact, it is not comprehensive if one attempts to find the optimal static smoothing coefficient, and certain conflicts will arise with the load time series {L _t }. On the server node, the length of time series {L _t } of load prediction is always becoming ever longer, and this changing trend is unpredictable, which leads to the attempting method to obtain the optimal smoothing coefficient α without any availability. Therefore, one kind of the prediction model of dynamic smoothing coefficient is put forward.

2.3 Dynamic exponential smoothing model

The exponential smoothing method [23,24] is easy to be operated and possesses rather stronger adaptability, and its compiling procedure is not complicated. However, it has increasingly imposed an effect on the practical application. α exponential smoothing method shows the historical data by means of historical information, which covers the entire model. What’s more, it follows the rule that the closer with the current moment means the larger information weighted. Such an idea of revising the historical data weight is relatively consistent with the actual situation. In general, the more recent information will have a higher value, and viewing from a certain extent, it reflects the practical rules. The exponential smoothing method [20,21,22] has a wider range of usage and leads to a gradually increasing utilization ratio. Therefore, the research of the exponential smoothing method becomes more significant. However, during the specific usage, there exists a rather prominent issue in the exponential smoothing method, namely, the selection of the smoothing coefficient α. In the practical application, it should be selected in relation to the experience. When the data have a smaller fluctuation, it has usually been selected between 0.1 and 0.3; if the data have a bigger fluctuation, then it has usually been selected between 0.6 and 0.8.

Since the selection standard of α is not very clear, some problems may appear in the practical application. Due to the arising problems, the accuracy of the model prediction will undoubtedly be affected, which is not good for the people lacking experience. Given the existed error, we may then construct the dynamic exponential smoothing model, and we may select the predicted value and practical value for the aiming function. We can construct a two-dimension planning model and use this model to obtain the dynamic answer of the exponential smoothing method, though this kind of parameter is subject to changes as time goes by. Through comparison by means of practical examples, we may conclude that this method has a higher accuracy, which is contributory to ensure the smoothing coefficient α. If L _t+1 is the predicted value at t + 1 moment, then the predicted model of dynamic smoothing coefficient is

where α t represents the optimal dynamic smoothing coefficient at t moment on the basis of the load time series {L _t }, and at the same time of the continuing longer of {L _t }, α t makes the change in order to correspond with the load time series {L _t } and represents the dynamic characteristic. When making an assessment with the optimal dynamic smoothing coefficient on the basis of the load time series {L _t }, the raised assessing model can predict the error square and regards the minimal SSE as the target, namely,

then put the formula (4) into it to obtain:

Then, the optimal smoothing coefficient α _t can be obtained through the formula (7), and while solving the similar nonlinear optimizing model, we should adapt the steepest descent method with the quicker disappearing rate to the model. At first, we should set the smoothing coefficient initial value α t 0 , ε > 0 , and take it as the control condition:

Step 1, aim at the given smoothing coefficient α t i (the value of i is 0, 1, 2, etc.), and then calculate SS E ′ ( α t i ) . If | SS E ′ ( a t i ) | ≤ ε , then α t i is the similar optimal answer. Step 2, assume | SS E ′ ( α t i ) | > ε , and then calculate with the optimal step λ _i (the value of i is 0, 1, 2, etc.) with the golden section method in the one-dimension exploration, in the meanwhile, assume α t i = a t i − λ × SS E ′ ( α t i ) , then go back to the first step. And SS E ′ ( a t i ) = dSSE dat | α t − α t i . Acquire the optimal dynamic smoothing coefficient based on the formula (7) and construct the dynamic smoothing prediction model of formula (5) on this basis, into which we can’t directly apply the load balancing algorithm.

At first, the load time series {L _t } is becoming ever longer, so both of the times of formula (5, 7) are increasing, and the complexity of this algorithm is increasingly higher. In addition, the load dispatcher needs to retain lots of time series {L _t }, which makes it more time-consuming on obtaining the optimal smoothing coefficient. Thus, the computer cluster is not corresponding with the given purpose. Next, α in the dynamic smoothing coefficient is not the same with the one in the traditional static smoothing coefficient, due to the existence of the limit of 0 < α < 1.

The existing load time series {L _t } is sharply declining or increasing with the condition of α > 1; in fact, in the {L _t } with concave or convex type, the condition of the smoothing coefficient α < 0 might appear. Under the above circumstances, the application of the exponential smoothing method cannot manifest the thinking of “laying more emphasis on the closer than the farther,” and it is not necessary to consider the smoothing initial value S ₀ according to formula (5). In addition, to connect with the definition of load in formula (1), there surely exists 0 < Li < 100. Therefore, while the load time series {L _t } is continuously increasing, there always exists the trend of sharply declining or increasing, or viewing from the entirety, the probability of concave or convex type is gradually becoming smaller. It can be assumed that the load time series {L _t } achieved the certain length, and the smoothing coefficient α is up to 0 < α < 1. In this way, the time series {L _t−t0} with the sufficient distance from the current t moment cannot manifest its importance. Given the above condition, the dynamic smoothing prediction model through the improvement is put forward:

In this formula, t ₀ expresses the length of retained load time series {L _t }. Furthermore, we can revise the assessment model of solving the optimal smoothing coefficient αt as

Due to the improved model and the loss of the load time series prior to the moment of t − t0, both of the times of formula (8) and (9) are increasing while load time series {L _t } are continuously changing, which helps keep at the constant time square relevant with t0 and make the complexity of algorithm declining further. In addition, when load time series {L _t } reaches a certain length, the accepted effect of smoothing initial value S ₀ is gradually smaller, ending with the loss. Thus, the static value can be regarded as the smoothing initial value, and its definition based on this perception is

The most critical point of the dynamic smoothing prediction model obtained through the improvement is to select the appropriate retained series length t ₀ and to ensure that the application of algorithm reaches the prediction accuracy and that complexity strikes a rational balance.

Figure 1 shows the result of the dynamic exponential smoothing prediction model obtained through the improvement on the load prediction. The actual load value refers to the actual result obtained from the specific one server through the collection with an interval of one minute. Viewing t ₀ = 5 and t ₀ = 10 as the selected points, and when t ₀ = 5, the prediction starts with the sixth load value; according to the similar analogy, when t ₀ = 10, the prediction starts with the eleventh load value. Through the analysis of Figure 1, it is not hard to find that both of the predicted results of t ₀ = 5 and t ₀ = 10 meet with the actual load curve. Furthermore, when t ₀ = 10, the improving predicted accuracy is not prominent, and comparing with t ₀ = 5, this algorithm has a higher degree of complexity. Therefore, with respect to the dynamic load prediction model, it is more reasonable to select the load time series retained length t ₀ = 5.

Figure 1

The predicted result of the dynamic exponential smoothing method on the load.

It can be seen from Figure 2 that the prediction model of the static smoothing coefficient led to the load predicted result. Due to the varieties of the changing of load time series, it is extremely complicated for the single smoothing coefficient to adapt the entire time series, and thus, it cannot lead to a higher accuracy of prediction. Obviously, judging from the comparison with the above two figures, the predicted result of the dynamic exponential smoothing method is superior to the result of the static exponential smoothing method.

Figure 2

The predicted result of the static exponential smoothing method on the load.

3.1 The description of load predicted function

Assume the serve node as { S v i } and the server number of computer cluster is expressed with n. If the specific server starts, then it will collect the self-load information every one-minute interval, and we may generate the initial time series with the load prediction { L t 0 = 5 } S v i before allocating this kind of series to the dispatcher. The dispatcher stores such a time series and helps obtain the smoothing initial value S S v i of S v i through formula (10). Assume the obtaining function of predicted value as S s v i = Exp prediction( L s v i ) , then the specific working process of this function is as follows:

(1) As for the server node S v i , the dispatcher finds its load time series { L t 0 = 5 } S v i and discards the earliest load value linearly in this time series while adding the latest load value L S v i at the end of time series { L t 0 = 5 } S v i . (2) Based on the smoothing value S s v i of the former moment and the new load time series { L t 0 = 5 } S v i as well as the dynamic smoothing coefficient assessment model of formula (9), we can obtain the optimal smoothing coefficient αt through the steepest descent method, which is corresponding with the load series. (3) In the dynamic smoothing prediction model of formula (8), we can put S s v i , the load time series { L t 0 − 5 } S v i and dynamic smoothing coefficient αt into the formula, and obtain the new smoothing value S s v i . We should no longer use the former smoothing value S s v i , but S s v i is regarded as the predicted value at the next moment of the server node S v i .

3.2 The description of load balancing algorithm

The user sends service request and the dispatcher accepts the request, and according to the load balancing algorithm, the request is sent to the optimal server node Sv _i of the load to complete the process. The algorithm procedure is set out as follows:

(1) The user sends the service request and the dispatcher accepts the request. Then, select the minimal server node Sv _i for the minimal Sv _i to express the minimal lad of the next moment node S v i . (2) The dispatcher sends the request to the server node Sv _i and makes the settlement. (3) After the server node Sv _i settled the request, it will bring the load data of itself current moment to the response, and in the meantime, it sends the response to the dispatcher. (4) The dispatcher receives the response from Sv _i and obtains the load S v i at the new moment, scheduling the load prediction function to dispatch the load function Exprediction( L s v i ) and acquire the load predicted value S v i of next moment to instruct the next scheduling of dispatcher.