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QCI-WSC: Estimation and prediction of QoS confidence interval for web service composition based on Bootstrap

  • Qinying Li EMAIL logo , Wei Lu , Fangli Li , Taotao Wang and Hao Wang
Published/Copyright: July 28, 2025
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Open Computer Science
From the journal Open Computer Science Volume 15 Issue 1

Abstract

In web service composition, the Quality of Service (QoS) prediction applications based on the statistical point estimation method in accuracy consist of many challenges. Aiming at allowing users to select the web service composition based on their requirements, this study proposed a method based on Bootstrap to estimate and predict the QoS confidence interval for web service composition (QCI-WSC). The QCI-WSC first indicates the structure of the web service composition and simplifies the structure model. Apart from that, the QoS estimation interval can be calculated by the historical QoS data, which are invoked by users. Meanwhile, the user similarity is calculated, and the QoS of web service invoked by the similar users is used to predict QCI-WSC. Finally, the results of user-invoked web service composition QoS are verified by the average interval coverage rate, compared to the actual QoS values and prediction values of the other methods, such as adaptive QoS prediction method based on collaborative filtering (QACF) and QoS-Aware web service recommendation (WSRec). Additionally, in this work, dataset1 in WSDream is adopted to estimate and predict the QCI-WSC. Experiments show that the QoS confidence interval estimation results conform to the exponential distribution, and the validity of the QCI-WSC is proved. Furthermore, the average interval probability of the prediction algorithm was more than 75%. The QCI-WSC can accurately cover the actual QoS values of the web service composition and most of the accurate QoS values predicted by QACF and WSRec. It effectively improves the selectivity of service, which provides web service composition featuring better quality for users.

Keywords: web service composition; confidence interval; QoS estimation; QoS prediction; Bootstrap

1 Introduction

Web service [1,2] improves interaction and computing efficiency by establishing a distributed platform that can be operated interactively as a way to achieve cross-platform communication between programs. Based on the development of web service technology, a single web service can no longer meet user needs well, and how to combine existing web services to connect and interact in a friendly and collaborative way has received widespread attention. As users are affected by external network congestion, server load, and geographical changes in the process of selecting service [3,4] for web service composition, Quality of Service (QoS) [5,6] is characterized by random dynamics and nonlinearity.

QoS is gradually playing an important role in the process of web service composition. In order to ensure that users can choose the web service composition that meets their needs, QoS prediction is a crucial basis for web service selection and service recommendation. Recently, QoS prediction is a research area that has received extensive attention in the field of web services. The main methods are workflow-based prediction methods [7,8,9], collaborative filtering (CF)-based prediction methods [10,11,12,13], and model-based prediction methods [14,15,16].

Although existing research has made significant progress in predicting the QoS of web service composition, achieving the use of statistical point estimation methods to accurately predict the QoS of web service composition, the QoS change mode of the web service composition has not been considered. Therefore, the prediction results lack credibility. Therefore, this study proposed an estimation and prediction method of the QoS confidence interval for web service composition (QCI-WSC) based on Bootstrap technology to quantify the uncertainty of QoS prediction values. The contributions of the proposed method are threefold:

  1. Use the list structure of list processor (LISP) language [17] to build a web service composition model to effectively express the complexity of the composition structure. Other than that, the QoS attribute value calculation formulas for non-nested combination structures and nested combination structures are put forward to improve QoS calculation efficiency.

  2. Adopt non-parametric statistical Bootstrap technology to estimate and predict the QCI-WSC with reference to the historical QoS data of a single web service invoked by the user, so that the results meet the dynamic characteristics of the QoS attribute value. Furthermore, user service recommendations and accuracy and credibility of selection are ensured.

  3. Based on the WSDream dataset from the study by Zheng et al. [18] implemented to conduct related experiments, the average interval probability is used to derive the reliability of the prediction results. Besides, it is compared with the classic methods adaptive QoS prediction method based on collaborative filtering (QACF) and QoS-Aware web service recommendation (WSRec) to verify the coverage of the confidence interval and prediction value to ensure the prediction range accuracy.

The remainder of this study is organized as follows: Section 2 introduces the literature review of QoS prediction. Section 3 describes the web service composition structure model based on LISP language and the calculation method of QoS, and presents the estimation and prediction process of the QCI-WSC. Section 4 depicts the experimental design and evaluation of the method, and analyzes the experimental results. In Section 5, the conclusion and future recommendations of the research are given.

2 Related work

The related works of QoS prediction for web service composition have attracted widespread attention. Typically, the workflow-based QoS prediction method is proposed due to the similarity between the workflow and web service composition process. Wu and Yang [19] proposed a QoS prediction method of web service composition with the transaction mechanism, which considers normal and exception handling processes during the execution of web service composition. Liu et al. [20] presented a QoS dynamic prediction approach based on case-based reasoning to improve the reliability of web service composition by predicting the QoS value of candidate service and selecting the best web service node. Wu et al. [21] took a general context-sensitive matrix-factorization approach to enhancing the prediction accuracy of QoS by fusing implicit and explicit factors in QoS data. Although the workflow-based prediction approach is conducive to simplifying the process of web service composition, it mainly focuses on the contextual association of workflows. Therefore, it cannot be applied in a prediction environment as the time factor.

Furthermore, the CF [22] method is the current QoS prediction method with the highest prediction accuracy. CF uses the historical QoS data of similar users as the basis for predicting the QoS values of web service composition invoked by the current users. Zhang et al. [23] designed a QoS prediction framework, which utilizes the historical experiences generated by users invoking web services to construct feature models and provide personalized QoS predictions for users. Chen et al. [24] considered the bias between the user and web service, thus establishing the matrix decomposition model for selecting geographical neighbors with the hierarchical domain clustering algorithm and predicting QoS value by geographic neighbor information. Due to the fluctuation of QoS prediction results caused by environmental factors, Thakker et al. [25] constructed a QoS prediction method based on hybrid CF for movie recommendation, and considered the weight of movie recommendation factors to reduce the accuracy error of prediction results caused by label fluctuations. The CF algorithm solves the problem from a global perspective and can fully consider the relationship between users and services. However, the prediction results of this method are susceptible to the sparsity and cold start of historical QoS data, which leads to prediction results that do not better meet user needs.

To better predict QoS, the model-based QoS prediction method is proposed. The method designs a corresponding model to predict unknown QoS values by learning and training user historical QoS data. Luo et al. [26] introduced a fuzzy neural network QoS prediction method based on adaptive dynamic programming to learn the parameters of fuzzy rules. Anithadevi and Sundarambal [27] adopted neuro-fuzzy logic and combined it with users’ personalized needs to intelligently identify untrusted services and improve the accuracy of service classification. Xiong et al. [28], combined deep learning methods in the time-space-sensitive QoS prediction model to extract the hidden features of multi-dimensional factors for QoS value to enhance the accuracy of the prediction results. In the method based on the GCN proposed by Wang et al. [29], potential user preferences for services in user-item interaction information were considered, and abstract preferences were mapped to specific components, thus having the ability to mine potential preferences of users or services. Due to the nonlinear and dynamic nature of QoS, the model-based QoS prediction method has disadvantages such as slow extraction of features and difficulty in feature extraction.

In summary, the current research can effectively predict the QoS attribute value of web service composition, but the attribute values of QoS fluctuate when users invoke services in different environments, leading to a decrease in the accuracy of the prediction results. In Table 1, the related research work is summarized. Aiming at this problem, this study adopts the QoS confidence interval of web service composition estimation and prediction method QCI-WSC to enable the QoS values within the interval, so that users can make choices flexibly according to their own needs.

Table 1

Related research work

Algorithm Principle of the algorithm Advantages Disadvantages
QoS prediction method based on workflow [7,8,9] The method builds a web service composition model through the workflow technique so that the QoS attributes can be constrained. Apart from that, it is able to estimate the predicted QoS attribute values during the processes of service creation and management The approach simplifies the structure of web service composition and describes the portfolio process rationally, avoiding complex processing tasks during the prediction phase The approach ignores the dynamic characteristics of QoS properties, and it focuses on the contextual association of workflows, which cannot be applied in a forecasting environment that considers the time factor
CF based QoS prediction method [10,11,12,13] The method collects user historical QoS data for setting user preferences and calculates the similarity degree by the user-item relationship. Based on the historical QoS data of similar users, the QoS attribute values are predicted, and items are recommended for the current users This method is the most widely used technique at present, and is mainly used for real-time recommendation and small data volume scenarios with high accuracy The method is not suitable for scenarios with sparse or large data volumes, and is susceptible to the sparsity and cold start of historical QoS data. Therefore, the prediction results cannot better meet user needs
Model-based QoS prediction method [14,15,16] The method divides the data into two parts. It designs the model by learning historical user QoS data from the training set, and then uses the test set to verify the accuracy of the model. When the accuracy reaches a specific threshold, unknown QoS values are predicted The method is mainly used for scenarios with large data volume as well as offline computation The training time of the method is too long to extract eigenvalues slowly. Other than that, QoS has the characteristics of nonlinearity and dynamics, which makes the method feature extraction difficult

3 Method

3.1 Structure model of web service composition

To calculate QCI-WSC more efficiently based on Bootstrap, a list structure similar to LISP Language is proposed to express web service composition. The structures of the non-nested list and the nested list are shown below.

Sequence list: The structure of sequence (sequence, s 1, s 2, …, s n ) is illustrated in Figure 1. In this model, sequence means the type of sequence structure, while s 1, s 2, …, s n represent the web service node executed in sequence.

Figure 1 Sequence structure of web service composition.
Figure 1

Sequence structure of web service composition.

Loop list: The structure of loop (loop, k, s 1, s 2, …, s n ) is shown in Figure 2, where loop is the type of loop structure; and k represents the cycle number of the web service nodes s 1, s 2, …, s n in the loop body.

Figure 2 Loop structure of web service composition.
Figure 2

Loop structure of web service composition.

Choose list: Structure of the choose is described in Figure 3. In the structure (choose, p 1, s 1, p 2, s 2, …, p n , s n ), choose represents the type of choose structure; p i (i = 1, 2, …, n) means executive probability of web service nodes, and the total probability of web service composition is 1.

Figure 3 Choose structure of web service composition.
Figure 3

Choose structure of web service composition.

Parallel list: The structure of parallel (parallel, s 1, s 2, …, s n ) is presented in Figure 4. In this model, web service nodes s 1, s 2, …, s n in parallel structure execute tasks concurrently.

Figure 4 Parallel structure of web service composition.
Figure 4

Parallel structure of web service composition.

Nested list: The workflow-based web service composition structure is shown in Figure 5, and this structure is the nested list structure web service composition for the participating experimental design. As it is shown in Figure 5, web service composition is composed by multiple web service nodes on the basis of designated correlation. It can be presented as (sequence, s 1, (loop, k, s 2), (parallel, s 3, …, (choose, p 1, s i , p 2, s i + 1, …, p n , s n − 1)), s n ). In this structure, (parallel, s 3, …, (choose, p 1, s i , p 2, s i + 1, …, p n , s n − 1)) and (loop, k, s 2) indicate the nested child nodes of web service composition, while (choose, p 1, s i , p 2, s i + 1, …, p n , s n − 1) is the nested child nodes of parallel structure.

Figure 5 Web service composition based on workflow.
Figure 5

Web service composition based on workflow.

3.2 QoS calculation of web service composition

The calculation of QoS values for web service composition can be classified into non-nested list structure and nested list structure. Considering that web service composition contains multiple measurements, the value of web service composition QoS is defined as QoS = (Q ava, Q rel, Q time, Q cost, Q rep), where Q ava, Q rel, Q time, Q cost, and Q rep represent the availability, reliability, response time, service costs, and reputation attributes of QoS.

3.2.1 QoS calculation for non-nested list web service composition

Before QoS of non-nested list web service composition is calculated, the model structure type of web service composition should be determined. Then, the QoS by quality criteria can be calculated.

The sequence structure web service composition contains n web service nodes. The QoS for sequence structure under different attributes Q seq can be computed as follows:

(1) Q seq = ∏ i = 1 n qos s i ( qos s i = { Q ava s i , Q rel s i , Q rep s i } ) ,

(2) Q seq = ∑ i = 1 n qos s i ( qos s i = { Q time s i , Q cos t s i } ) .

Assuming that the web service node number of loop structure is n and the cycle-index of service nodes is k, the QoS of loop structure web service composition Q loo can be computed using (3) and (4).

(3) Q loo = ∏ i = 1 n qos s i ( qos s i = { Q ava s i k , Q rel s i k , Q rep s i k } ) ,

(4) Q loo = k ∑ i = 1 n qos s i ( qos s i = { Q time s i , Q cos t s i } ) .

In the choose structure of web service composition, n web service nodes correspond to executive probability p i , and ∑ i = 1 n p i =1 . The QoS of choose structure Q cho can be expressed as

(5) Q cho = ∑ i = 1 n p i × qos s i ( qos s i = { Q ava s i , Q rel s i , Q time s i , Q cos t s i , Q rep s i } ) .

There are n web service nodes in parallel structure. According to the execution sequence of the parallel structure, the QoS of the web service composition Q par can be represented as follows:

(6) Q par = ∏ i = 1 n qos s i ( qos s i = { Q ava s i , Q rel s i , Q rep s i } ) ,

(7) Q par = max { Q time s 1 , Q time s 2 … Q time s n } ,

(8) Q par = ∑ i = 1 n Q cos t s i .

3.2.2 QoS calculation for nested list web service composition

To calculate nested list-structural web service composition QoS, the nested child nodes can be converted to non-nested child nodes by the recursive method. In the process, the first step is to determine the type and nested substructure for calculating the composition of web services. Then, all service nodes for web service composition can be simplified as non-nested child nodes, and the QoS value of web service composition can be computed by the QoS calculation formula.

Figure 6 illustrates the calculating processes of web service composition QoS based on the workflow. The processes are shown below:

  1. Separate the structure of web service composition. In the nested list structure (parallel, s 3, …, (choose, p 1, s i , p 2, s i+1, …, p n , s n−1)), the QoS of nested child nodes (choose, p 1, s i , p 2, s i+1, …, p n , s n−1) is calculated preferentially and represented as T 1.

  2. Substitute nested child nodes by QoS value, and the QoS of the nested list structure in the previous step is expressed as T 2 = (parallel, s 3, …, T 1).

  3. For each nested structure, simplify them to sequence structure of web service composition, and calculate loop structural QoS value T 3 = (loop, k, s 2).

  4. Calculate the QoS for simplified web service composition QoS = (sequence, s 1, T 3, T 2, s n ).

Figure 6 Flow chart of web service composition calculation.
Figure 6

Flow chart of web service composition calculation.

3.3 Estimation of QCI-WSC based on Bootstrap

In this section, the non-parametric statistical Bootstrap technology is adopted to estimate the QCI-WSC, and the key components are elaborated as follows:

  1. The QoS value (e.g., response time) Q s = { Q s 1 , Q s 2 , … , Q s n } of n web service nodes and web service composition WS = {s i |∀s i ∈ s, i = 1, 2, …, n} are original sample data invoked by User l (l = 1, …, m).

  • QoS contains two types: one is independent of the user and its value is uniformly provided by the service provider, such as service cost; the other type is related to the user and the service environment, and the QoS values are susceptible to the network environment and the level of equipment, such as response time. However, it is unrealistic to require each user to invoke all services to obtain QoS values. Therefore, in the study, a common attribute response time in QoS was used.

  • The QoS value of web service node s k invoked by User l (l = 1, …, m) is Q User l s k = { Q User 1 s k , Q User 2 s k , … , Q User m s k } .

  • When current user User x invoked web service node s k , the QoS value is Q User x s k = { qos 1 , qos 2 , … , qos a } .

  1. Replace n web service nodes in a nested list structure web service composition and sample historical QoS values, and obtain Bootstrap sample data of web service composition as Q s ⁎ = { Q s 1 ⁎ , Q s 2 ⁎ , … , Q s n ⁎ } , Q s ⁎ ∈ Q s .

  2. About the Bootstrap sample data, QoS of web service composition named Qws was calculated by the current user as “Bootstrap estimated value.” The formulation is shown as (9).

    (9) Q w s = Q s 1 ⁎ + T 3 + T 2 + Q s n ⁎ ,

    where Q s 1 ⁎ and Q s n ⁎ indicate the response time of web service child nodes s 1 and s n , respectively. T 2 and T 3 are QoS value of web service nested child nodes, which can be calculated using (10) and (11).

    (10) T 3 = k × Q s 2 ⁎ ,

    (11) T 2 = max { Q s 3 ⁎ , … , T 1 } ,

    where k represents the cycle index of web service nodes; Q s 2 ⁎ and Q s 3 ⁎ are response times of web service child nodes s 2 and s 3, and T 1 denotes QoS value of web service nested child nodes that can be represented as (12).

    (12) T 1 = ∑ x = i n − 1 p x × Q s x ⁎ ,

    where p x represents executive probability of web service nodes; and Q s x ⁎ refers to the response time of web service child node s x .

  3. Calculate B-time (B = 10,000) web service composition estimated values based on Bootstrap, and it is represented as Q w s = { Q w s 1 , Q w s 2 , … , Q w s B } .

  4. The B Bootstrap estimated values are sorted as Q ws [1] ≤ Q ws [2] ≤ … ≤ Q ws [B], calculated in ascending order by percentile Bootstrap. Hence, the QCI-WSC based on workflow is [low(Q ws ), up(Q ws )] when the confidence level is 1 – α (α = 0.05). The lower bound of the confidence interval is low ( Q w s ) = Q w s ( ∣ B × α / 2 ∣ ) , and the upper bound is up ( Q w s ) = Q w s ( ∣ ( B × ( 1 − α / 2 ) ) ∣ ) .

The procedure of estimating the QCI-WSC based on the study by Zheng et al. [18] is described in Algorithm 1.

Algorithm 1: Estimation of confidence interval for Web service composition QoS based on Bootstrap
Input: WS: Web service composition; Q s : historical QoS data of Web service node s
Output: Estimation of QCI-WSC
1: Q ws ←[]
2: for i = 1 to B do //Calculate B-time Web service composition estimated values
3:  for j = 1 to length(WS) do //Read Web service nodes of composition
4:   if WS[[j]] in nested list structure
5:    Add WS[[j]] to WS_new //Add nested nodes to newly Web service composition
6:    Q s* = random(Q s ) //Randomly extract QoS value of WS_new
7:    Add Q s* to Q ws //Calculate QoS attribute value of WS_new by formula (9)
8:   else
9:    Add Q s* to Q ws //Calculate QoS attribute value of WS_new by formulas (1) to (8)
10: end for
11: end for
12: Sort(Q ws )
13: Return [low(Q ws ), up(Q ws )] //Estimate QCI-WSC when confidence level is 1 – α

3.4 Prediction of QCI-WSC based on Bootstrap

The prediction method utilizes QoS sample data to calculate user similarity, predicts QoS value of current user invoking web service according to similar users, and then calculates the QCI-WSC invoked by the current user based on the method of percentile interval estimation.

3.4.1 Similarity calculation

Due to the diversity of QoS influencing factors, different users have different QoS values for invoking service. Therefore, original sample data and adjusted cosine are shown in (13) to calculate the similarity between users.

(13) sim ( test i , train i ) = ∑ w ∈ W test i , train i ( Q w test i − Q test i ¯ ) ( Q w train i − Q train i ¯ ) ∑ w ∈ W test i ( Q w test i − Q test i ¯ ) 2 ∑ w ∈ W train i ( Q w train i − Q train i ¯ ) 2 ,

where W test i , train i represents the web service set that both user test i and user train i have invoked. W test i and W train i refer to the web service sets invoked by user test i and user train i , respectively. Q w test i and Q w train i are historical QoS data for web service w invoked by user test i and user train i , respectively. Q test i ¯ and Q train i ¯ are average web service QoS data used by users described as follows:

(14) Q test i ¯ = 1 W ∑ w ∈ W test i Q w test i ,

(15) Q train i ¯ = 1 W ∑ w ∈ W train i Q w train i ,

where W represents the number of all web services that current users invoke.

3.4.2 Prediction of web service composition QoS

Define Top ( test ) = { top 1 , top 2 , … , top k } to represent the similar users of top k with current user test i . The original sample data are sampled from historical data of web service composition, and it is Q top s = { Q top s 1 , Q top s 2 , … , Q top s n } , Q top s ∈ Q s , invoked by similar users.

Hence, the QoS in original sample data that current web service node Sk invoked by similar users Top(test) is Q top s k is Q top s k = { Q top 1 s k , Q top 2 s k , … , Q top k s k } , and Q top x s k = { qos 1 , qos 2 , … , qos a } .

Based on Q top s k , the data is sampled with replacement to obtain the “Bootstrap sample value” Q top s ⁎ = { Q top s 1 ⁎ , Q top s 2 ⁎ , … , Q top s n ⁎ } .

The sample data Q top s ⁎ is presented to predict QoS value Q test i ^ , and Bootstrap predicted sample data are computed by user test i invoking current web service node s j . The calculation is carried out using the below expressions:

(16) Q test i ^ = Q test i ¯ + ∑ i = 1 k sim ( test i , train i ) ( Q top s j ⁎ − Q User i s j ¯ ) ∑ i = 1 k sim ( test i , train i ) ,

(17) Q User i s j ¯ = 1 n ∑ k = 1 n Q User i k s j ,

where n represents the total number of User i who invokes current web service s j , and Q User i k s j is the historical QoS value that User i invokes current web service at kth time.

Given the above process, the QoS value of web service composition predicted for user test i can be represented as Q test i ^ = { Q test 1 ^ , Q test 2 ^ , … , Q test n ^ } , and the QoS value based on workflow for web service composition calculated by (9) is Q w s ^ .

3.4.3 Prediction of confidence interval for web service composition QoS

The percentile interval estimation method is utilized, and B (B = 10,000) times are calculated repeatedly following the steps in this section, so that B Bootstrap prediction QoS values of web service composition obtained by user test i are presented as Q w s 1 ^ , Q w s 2 ^ , … , Q w s B ^ . Then, the B predicted Bootstrap values are sorted in ascending order and denoted as Q w s ^ [ 1 ] ≤ Q w s ^ [ 2 ] ≤ … ≤ Q w s ^ [ B ] ; the QCI-WSC invoked by current users is calculated as [ low ( Q w s ^ ) , up ( Q w s ^ ) ] at confidence level of 1 – α (α = 0.05). Wherein, the lower bound of the confidence interval is low ( Q w s ^ ) = Q w s ^ ( ∣ B × α / 2 ∣ ) , and the upper bound of the confidence interval is up ( Q w s ^ ) = Q w s ^ ( ∣ ( B × ( 1 − α / 2 ) ) ∣ ) .

3.4.4 Confidence interval evaluation

To verify the authenticity of the prediction method for the QCI-WSC, the interval coverage rate (ICR) and average interval coverage rate (AICR) methods were proposed for the main purpose of determining whether the calculated actual QoS value QoSws is within the predicted range of the QCI-WSC. The formula of AICR is shown as follows:

(18) AICR = 1 n ∑ i = 1 n ICR test i ,

(19) ICR test i = 1 , low ( Q w s ^ ) ≤ Q w s ≤ up ( Q w s ^ ) 0 , else .

where low ( Q w s ^ ) represents the lower bound of the QoS prediction confidence interval, and up ( Q w s ^ ) refers to the upper bound. Besides, ICR denotes the interval probability. When the QoS real values of the web service composition invoked by the current user are within the QoS confidence interval, the interval probability is taken as 1. Otherwise, interval probability is taken as 0. Therefore, AICR is a measure of the probability that is the real value in the confidence interval.

In brief, the description of QoS confidence interval prediction for web service composition is shown in Algorithm 2.

Algorithm 2: Confidence interval prediction based on Bootstrap of web service composition
Input: WS: Web service composition, test: testing users set, train: training users set
Output: Predicted value of QCI-WSC
1: Q w s ^ ←[]
2: for e = 1 to length(test) do
3:  for a = 1 to length(train) do
4:   Sim(e,a) //Calculate similarity between test user and train user by formula (13)
5:   Add top k users to Top(test) //Choose the top users based on similarity
6:  end for
7: end for
8: for i = 1 to B do //Calculate B-time Web service composition prediction
9:  for j = 1 to length(WS) do
10:    Q top s ⁎ = random( Q top s ) //Randomly extract the QoS values of similar user invoked service nodes
11:   Add Q top s ⁎ to Q test i ^ //Calculate the prediction value of current service node by formula (16)
12:   Add Q test i ^ to Q w s ^ //Calculate QoS attribute value of WS_new by formula (9)
13:  end for
14: end for
15: Sort( Q w s ^ )
16: Return [ low ( Q w s ^ ) , up ( Q w s ^ ) ] //Predict QCI-WSC when confidence level is 1 – α

4 Experiment

In this section, workflow-based QCI-WSC estimation and prediction experiments were conducted using Bootstrap. In addition, the WSDream dataset 1 published in the study by Wang et al. [30] was used. This dataset contains historical response time data of 107 users calling 99 web services at different times. In addition, the experimental environment was Rstudio Version 1.2; the experimental machine was configured with 16G memory, and the CPU was an i7-7700 3.6GHZ processor.

4.1 Analysis of QoS confidence interval estimation results

According to Algorithm 1, the estimated results of 107 users invoking nested list web service composition with the 95% confidence level were calculated. From Figure 7, it was discovered that the upper bound of the QoS confidence was mostly between 0 and 4,000 ms; a small portion of users were between 10,000 and 20,000 ms, and the rest users were between 10,000 and 20,000 ms. However, the lower bound of the QoS confidence was almost distributed between 0 and 20,000 ms, partially between 20,000 and 40,000 ms, and rarely between 40,000 and 50,000 ms. Figure 8 illustrated exponential distribution of the confidence interval, and the distribution of the upper and lower bound for the confidence interval was mainly adjacent straight lines. Therefore, the QoS confidence interval estimation result of the web service composition fitted the exponential distribution, which proved the effectiveness of the computation of the QCI-WSC.

Figure 7 Confidence interval estimation of QoS.
Figure 7

Confidence interval estimation of QoS.

Figure 8 QoS confidence interval exponential distribution.
Figure 8

QoS confidence interval exponential distribution.

4.2 Analysis of QoS confidence interval prediction results

4.2.1 Prediction result evaluation

In this experiment, the users of the dataset were randomly classified into 10, 15, 20, 25, 30, 35, and 40% as the test user dataset, and other users as the training user dataset. Then, the top 10, 20, and 30 similar training users were selected to predict the QCI-WSC invoked by the testing users. Finally, the reliability and authenticity of QoS confidence interval prediction results are verified through AICR.

Figure 9 shows the QCI-WSC prediction results for 25 and 30% of test users when selecting the top 10, 20, and 30 similar users. It can be seen that the proportion of test users and the number of similar users have little impact on the results of QoS confidence interval prediction. Furthermore, the actual QoS coverage of users tested by calling the web service combination is relatively high within the predicted range.

Figure 9 Distribution of QCI-WSC invoked by testing users. (a) The proportion of testing users is 25%. (b) The proportion of testing users is 30%.
Figure 9

Distribution of QCI-WSC invoked by testing users. (a) The proportion of testing users is 25%. (b) The proportion of testing users is 30%.

To demonstrate the practicality and reliability of the prediction method, the predicted QCI-WSC was validated using AICR, and the results are shown in Figure 10. It can be observed that when the average interval probability is 75%, there are many actual values in the confidence interval. In addition, the average interval probability increases with the increase in the proportion of test users. When the proportion of test users is 30% of the total users, the average interval probability is the highest.

Figure 10 Average interval probability results of testing users with different division ratios.
Figure 10

Average interval probability results of testing users with different division ratios.

4.2.2 Comparison results with other methods

To verify the scalability of the prediction results of the proposed method, the prediction interval results were compared with the QACF [31] and WSRec [12], when the proportion of test users was 25 and 30%, respectively. The results are shown in Figure 11.

Figure 11 Prediction value of QACF, WSRec, and QCI-WSC. (a) The proportion of testing users is 25%. (b) The proportion of testing users is 30%.
Figure 11

Prediction value of QACF, WSRec, and QCI-WSC. (a) The proportion of testing users is 25%. (b) The proportion of testing users is 30%.

When the proportion of test users is 25%, QACF and WSRec have higher prediction accuracy. In addition to that, the error between the predicted and accurate values of the two methods is relatively small, which can help users choose suitable services. However, when the proportion of test users rose to 30%, the deviation between the predicted and accurate values of the above two methods increased. Therefore, the QCI-WSC can accurately cover the actual QoS values composed of web services and most of the accurate QoS values predicted by QACF and WSRec. The QCI-WSC can provide users with more services or service combination choices, which helps them choose services that meet their needs.

5 Conclusion

To solve the problem that the existing web service composition QoS prediction methods cannot better reflect the characteristics of stochastic dynamics of QoS, this study adopts a method for estimating and predicting the QCI-WSC based on Bootstrap technology. In this method, the composition structure model of web services is simplified, and the historical QoS data of web services are employed to estimate the QCI-WSC invoked by users; besides, the QCI-WSC invoked by current users is predicted based on the historical QoS data of similar users. The experimental results show that the QoS confidence intervals estimated and predicted in this study can cover the actual QoS attribute values more accurately, and the AICR used to measure the predicted confidence interval is above 75%. The method results can be replicated in the future to design QoS-aware web service composition optimization, service recommendation, and selection, and analyze the impact of changes in the confidence intervals on web service composition and service performance, thereby optimizing the combination method and making service selection and recommendation more stable. It can also make reasonable service selections and recommendations for service combinations under the Restful architecture, simplifying the development and design of future web systems and mobile applications.

In this work, five general QoS attributes were described in detail. However, in the actual network environment, the quality requirements of web services by different users and service providers are affected by the actual application scenarios, and the values of QoS attributes possess individual characteristics. Future research should further introduce more QoS attribute values, consider QoS confidence interval estimation and prediction based on QoS influencing factor weights in dynamic web service composition, and provide stronger basis for users to choose web service composition.

Acknowledgments

This work was supported by the Teaching Reform Project of Jiangxi Provincial Education Department (Nos. JXJG-21-24-6 and JXJG-24-24-2), Jiangxi University of Technology Collaborative Innovation Center Platform Open Project (XTCX2105), the National Natural Science Foundation of China (No. 61262014), the Science and Technology Project of Jiangxi Provincial Department of Education (Nos. GJJ202017, GJJ2402521 and GJJ212023), and Jiangxi University of Technology Teaching Reform Project (Nos. JY2104 and JY2004).

  1. Funding information: This work was supported by the Teaching Reform Project of Jiangxi Provincial Education Department (Nos. JXJG-21-24-6 and JXJG-24-24-2), Jiangxi University of Technology Collaborative Innovation Center Platform Open Project (XTCX2105), the National Natural Science Foundation of China (No. 61262014), the Science and Technology Project of Jiangxi Provincial Department of Education (Nos. GJJ202017, GJJ2402521 and GJJ212023), and Jiangxi University of Technology Teaching Reform Project (Nos. JY2104 and JY2004).

  2. Author contributions: Qinying Li conceptualized and designed the study, developed QCI – WSC, drafted and revised the paper, and handled communication; Wei Lu collected data from WSDream, analyzed structure simplification, and verified results; Fangli Li performed user similarity and QoS prediction experiments, and organized data; Taotao Wang analyzed Bootstrap – based QoS interval estimation and compared methods; Hao Wang validated result distribution, and polished language and logic.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: The data presented in this study are available on request from the corresponding author.

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Received: 2023-03-27
Revised: 2025-01-07
Accepted: 2025-02-21
Published Online: 2025-07-28

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/comp-2025-0028
Keywords for this article
web service composition; confidence interval; QoS estimation; QoS prediction; Bootstrap
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Intelligent data collection algorithm research for WSNs
  3. A novel behavioral health care dataset creation from multiple drug review datasets and drugs prescription using EDA
  4. Speech emotion recognition using long-term average spectrum
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  7. Evaluating impact of different factors on electric vehicle charging demand
  8. An in-depth exploration of supervised and semi-supervised learning on face recognition
  9. The reform of the teaching mode of aesthetic education for university students based on digital media technology
  10. QCI-WSC: Estimation and prediction of QoS confidence interval for web service composition based on Bootstrap
  11. Line segment using displacement prior
  12. 3D reconstruction study of motion blur non-coded targets based on the iterative relaxation method
  13. Overcoming the cold-start challenge in recommender systems: A novel two-stage framework
  14. Special Issue on AI based Techniques in Wireless Sensor Networks
  15. Blended teaching design of UMU interactive learning platform for cultivating students’ cultural literacy
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  18. Using artificial intelligence tools for level of service classifications within the smart city concept
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