# A Distributed Business Process Collaboration Architecture Based on Entropy in Cloud Computing

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## Abstract

Business process collaboration enable organizations to communication, interact and cooperate with each other to achieve specific business goals. Currently, the research work on business process mainly focus on the modelling and analysis for their organization structure or interactive relationship. This paper study business process collaboration from the view of software architecture, a distributed architecture called “agent end + stockholder end” is proposed, by analyzing the collaboration architecture finds, in the case of the participation organizations are given, determining the agents in collaboration and the participation organizations in every management region becomes the key for effective collaborating. For this reason, with the help of fuzzy cluster to determine the membership matrix and clustering centers firstly in this paper, then the best number of agent is determined through agent entropy, and thus the set of participation organizations in every management region are determined. Experiment results show that the method proposed in this paper is feasible and effective.

## Keywords

Cloud computing Software architecture Business process collaboration “agent end + stockholder end” Entropy## 1 Introduction

With the development of economic globalization and the advancement of enterprises’ information, the manage models of enterprises has taken place a great change, the business of enterprises have changed form a signal goal oriented represents an independent model to the model that represents multi-goals cooperation crossing organizational boundaries [1]. In the context of modern business, especially with the development of cloud computing and Big Data [19, 20, 21], there is not an enterprise is isolated. An enterprise as a participant participates the business collaboration, and they interact with others to complete the particular business function in the process of collaboration. Business process is an important research field in industry information system [2, 3], a business process is used to describe the activities in an organization and the relationships among organizations in order to achieve the given business goal [4]. With regard to the cross-organizational business process, because of involving many organizational process units, crossing the boundaries of organizations, in the cross-organizational enterprise information system [5, 6, 7, 8] and the context of e-commerce [9], it focuses on the flow relationship between business function and manufacturer activities. Its main task is to via the information systems respectively, different enterprises can cooperate and collaborate conveniently in business [10] used to complete specific business goal, it plays a more and more important role in the context of business.

Currently, researches on business process collaboration mainly focus on modeling. Namely through some formal methods, i.e., Petri Net, CCS(A Calculus of Communicating Systems), Pi Calculus and so on, to model the structure and interactive behaviors of cross-organizational business process collaboration, then verifying some properties of established model, such as Sound, Consistent and so on. [12] proposes IOWF(International Organization Workflow) used to model the Inter-organizational Workflows based on WF-net(Workflow Net) and Colored Petri Nets; [13] proposes a method to model the business process of Web Service form internal and external view; [14] proposes to use WF-net to describe the private process inside an organization and providing interactive interfaces for external environment, then using Interaction-Oriented Petri Nets model to define the interactive relationship between organizational business processes based on WF-net, [15] proposes the Open Workflow Nets to model cross-organizational business process, and then supporting a design by contract; [16] proposes a method that combines Petri Net and Pi Calculus, proposing to model local flow of business process based Petri Net and model interactive behaviors of business process based on Pi Calculus; [17] proposes a model called OTRM-Net and used to describe the task coordination patterns and disposal process in the emergency response systems formally.

- (1)
This paper propose a new distributed business process collaboration architecture called “agent end + stockholder end” and define it formally, which can discuss business process collaboration form macroscopic view.

- (2)
For this distributed collaboration architecture, in the case of the participation organizations are given, how to determine the agents in collaboration and the participation organizations in every management region becomes the key for efficient collaborating. For this reason, this paper uses fuzzy cluster to determine the membership matrix and clustering centers firstly, then the best number of agent determined through agent entropy, and then the set of participation organizations in every management region are determined, which can conduct the structure for collaboration applications.

The rest of this paper is organized as follows. Section 2 discusses the system architecture for business process collaboration; Sect. 3 discusses the method for determining agents in this architecture and the method for organizations partition based on entropy and Fuzzy Cluster; Sect. 4 is the experiment and results discussion; Sect. 5 concludes and presents our future work.

## 2 System Architecture for Business Process Collaboration

From the Fig. 1, we can see that the business process collaboration architecture, namely “agent end + stockholder end” is a model with three levels. The lowest level is organization level, some diversities exist among participation organizations, the whole collaboration process is composed by organizations and the communications among organizations; the middle level is agent level, for a category of similar organizations, there is an agent in charge of monitoring the operation situations of this category of organizations and a management region is produced, and when an organization can’t provide services sequentially, the agent reports to stockholders timely; the top level is stockholder level, though the communications between the agents, the stockholder can learn the changes of organizations and react, also can monitor the operation situations of agents.

### 2.1 The Formal Definition for Business Process Collaboration Architecture

### **Definition 1**

**(Organization).**Let \( org_{1} , \ldots ,org_{n} \) are the all organizations in business collaboration, the set \( Org = \{ org_{1} , \ldots ,org_{n} \} \) is called organization region in business process collaboration, for \( \forall \,org_{i} \in \,Org \) can be defined formally as a two-tuples \( Org_{i} \, = (id,\,I) \), where,

- (1)
*id*is used to identity an organization uniquely in collaboration process; - (2)
the set \( I = \{ I_{1} , \ldots ,I_{m} \} \) is

*m*-dimension measurement index, its measurement value are \( v_{1} , \ldots ,v_{m} \), and every element \( I_{i} \) is called decision factor, which is used to determine this organization belongs to.

### **Definition 2**

**(Agent).**Let \( agent_{1} , \ldots ,agent_{n} \) are the all agents in business collaboration, the set \( Agent = \{ agent_{1} , \ldots ,agent_{n} \} \) is called agent region in business process collaboration, for \( \forall \,agent_{i} \, \in \,Agent \) can be defined formally as a three -tuples \( agent_{i} = \left( {id,Org,R} \right), \) where,

- (1)
*id*is used to identity an agent uniquely in collaboration process; - (2)
the set \( Org = \{ org_{1} , \ldots ,org_{m} \} \) is the set of similar organizations which the number is m, called a management region;

- (3)
\( R \subseteq agent_{i} \times Org \cup Org \times agent_{i} \) is “agent-organization” flow relationship.

### **Definition 3**

**(Business Process Collaboration Architecture).**Let the set \( Org = \{ org_{1} , \ldots ,org_{n} \} \) and the set \( Agent = \{ agent_{1} , \ldots ,agent_{n} \} \) are organization region and agent region respectively in business process collaboration, then the whole of business process collaboration architecture can be defined formally as a three-tuples \( BPA = \left( {stockholder,Org,Agent,R} \right) \), where,

- (1)
\( stockholder \) is stockholder;

- (2)
\( R \subseteq Agent \times stockholder \cup stockholder \times Agent \) is “stockholder–agent” flow relationship.

## 3 Agent Determination and Organization Partition Based on Entropy and Fuzzy Cluster

From the Sect. 2 above, we can know that for the specific business goals, different organizations combine to achieve the solution for problems in the way of collaboration in the business process collaboration architecture. Because of the autonomous character of participation organizations, which needs corresponding man or organization, namely stockholders, to select members dynamically and some constraints and control strategies are settled to complete some specific business goals successfully. In one process of collaboration, there are a large number of organizations, for alleviating the load of communication and monitoring of stockholder, it is reasonable to set several agents using for cooperating work of stockholder in collaboration architecture. In the specific architecture, to processed with the collaboration work effectively, agent determination and organization partition become a key issue in the design of business process collaboration architecture, namely in the case of the participation organizations are given, how to determine the agents and the participation organizations included in every management region.

### 3.1 Fuzzy Cluster for Participation Organizations

In this paper, fuzzy cluster is used to get the membership matrix and clustering centers in the case of the number of agents *C* (2 \(\le\) *C* \( \le \) *N*, *N* denotes the number of participation organizations) is given, and the membership matrix and clustering centers are the basis for agent determination and organization partition based on entropy in next section. So algorithm 1 is proposed to get the membership matrix and clustering centers.

### **Algorithm 1.**

Obtaining the membership matrix and clustering centers

**Input:** the set of participation organizations \( Org = \{ org_{1} , \ldots ,org_{n} \} \), the number of agents \( C\,( 2\le C \le N) \), fuzzy-weighted coefficient *m*, Matrix A and iteration stop threshold value \( \varepsilon \);

**Output:** the set of membership matrix *M* and the set of clustering centers *C*.

**Step 1.** Structuring the measure index matrix *K* for the set of participation organizations \( Org = \{ org_{1} , \ldots ,org_{n} \} \), for \( \forall \,\,\,v_{ij} \) in *K*, taking a normalization, namely, when \( v\,_{ij} \) is positive increment dimension value, such as validity, reliability and so on, processing it by formula \( v_{ij} ' = \frac{{v_{ij} - r_{\hbox{min} }^{j} }}{{r_{\hbox{max} }^{j} - r_{\hbox{min} }^{j} }} \), while the \( v\,_{ij} \) is positive decrease dimension value, such as response time, cost and so on, processing it by formula \( v_{ij} ' = \frac{{v_{ij} - r_{\hbox{min} }^{j} }}{{r_{\hbox{max} }^{j} - r_{\hbox{min} }^{j} }} \), while the \( v\,_{ij} \) is positive decrease dimension value, such as response time, cost and so on, processing it by formula \( v_{ij} ' = \frac{{r_{\hbox{max} }^{j} - v_{ij} }}{{r_{\hbox{max} }^{j} - r_{\hbox{min} }^{j} }} \), obtaining the normalization matrix *K’* lastly.

**Step 2.** For the number of agents \( C\;( 2\le C \le N) \), clustering it by applying the fuzzy *C*-mean cluster algorithm [17], when \( \varepsilon \) satisfies, the algorithm stops and records the membership matrix and clustering centers to *C*.

**Step 3.** For every *C*, outputting the membership matrix and clustering centers.

### 3.2 Agent Determination and Organization Partition Based on Entropy

In the information theory, information entropy is used to measure the uncertainty of event, we can obtain information content after the event occurs. Information content denotes the information entropy before the event occurs minus the information entropy after the event occurs.

For the discrete and immemorial information source, if the space of probability is \( \left[ {X,P} \right] = [x_{k} ,p_{k} |k = 1, 2,..,N] \), then the uncertainty of information source denotes *H*(*X*), namely the entropy of information source *X*, its calculation formulate is \( H\left( X \right) = \sum\limits_{k} {p_{k} \log \frac{1}{{p_{k} }}} \).

*C*is the number of agents and

*U*is the membership matrix obtained by algorithm 1, then agent entropy

*H*(

*C*) is defined as follows,

- (1)
when \( \mu_{ij} \ne 0, \) then \( H\left( C \right) = - \frac{1}{N}\sum\limits_{i = 1}^{C} {\sum\limits_{j = 1}^{N} {\mu_{ij} \ln (\mu_{ij} )} } \);

- (2)
when \( \mu_{ij} = 0, \) then

*H*(*C*) = 0.

### **Theorem 1.**

- (1)
\( 0 \le H\left( C \right) \le { \ln }\left( C \right); \)

- (2)
when

*U*is hard partition,*H*(*C*) = 0; - (3)
when \( \mu_{ij} = 1/C,\,H\left( C \right) = { \ln }\left( C \right). \)

Proving this theorem is very simply, it is limited to the length of this article, so the process omits.

For the different *C*, there is different agent entropy *H*(*C*), if there is a \( C^{ * } \) can lead to minimum *H*(*C*), then \( C^{ * } \) is the best number of cluster, combining with the membership matrix and clustering centers obtained by algorithm 1, thus the agents and the participation organizations included in every management region can be determined in the collaboration architecture. So algorithm 2 is proposed for this purposes.

### **Algorithm 2.**

Determining the agents and the organizations partition

**Input:** the number of agents \( C\;( 2\le C \le N), \) the set of membership matrix \( M = \{ A_{1} , \ldots ,A_{C} \} \) and the set of clustering centers \( C = \{ B_{1} , \ldots ,B_{C} \} \);

**Output:** the set of agents \( Agent = \{ agent_{1} , \ldots ,agent_{k} \} \) and the set of organizations in every management region \( Org = \{ Org_{1} , \ldots ,Org_{k} \} \).

**Step 1.** Computing the agent entropy according to the corresponding membership matrix to *C* obtains the set of agent entropy \( AE = \{ ae_{1} , \ldots ,ae_{k} \} \);

**Step 2.** Taking a normalization to *AE*, namely \( AE^{'} = \{ ae_{1} /{ \ln }(C_{1} ), \ldots ,ae_{k} /{ \ln }(C_{k} )\} \);

**Step 3.** Outputting \( C_{i} = \mathop {\arg \hbox{min} }\limits_{i} AE^{'} \), and the corresponding clustering centers and the set of cluster to \( C_{i} \).

## 4 Experiment and Analysis

For illustrating the effectiveness of the method proposed in this paper, supposing there are sixty eight organizations \( Org = \{ org_{1} , \ldots ,org_{68} \} \) in a supply chain. Generally, the measure indexes of organizations can be obtained by two way: (1) the data collected in practice. (2) the data is generated randomly by computer simulation. In this paper, we adopt the second way, and for the simpleness, supposing every organization has only two measure indexes. Algorithm 1 and algorithm 2 are realized by Matlab, and the fuzzy-weighted coefficient is 2, matrix A is unit matrix and iteration stop threshold value is \( \varepsilon = e^{ - 5} \).

### 4.1 Results Analysis

*C*, the agent entropy

*H*(

*C*), normalization agent entropy

*H*(

*C*)/ln

*C*obtained by algorithms 1 and 2 is shown in Table 1. It is limit to the length of this paper, only the front of 10 items is listed, because of the rest of items’

*H*(

*C*)/ln

*C*all less than

*H*(8)/ln8, which is not affect the discussion below so omits. The partition index(PI) [18], which is a valid index in fuzzy cluster also is listed in Table 1, only the front of 10 items is listed, because of the rest of items’

*PI*all greater than

*PI*(

*C*= 8), so omits.

The relationship among C, H(C), H(C)/lnC and PI

C | H(C) | H(C)/ln(C) | PI |
---|---|---|---|

2 | 0.2878 | 0.4152 | 0.8319 |

3 | 0.2878 | 0.4152 | 0.7919 |

4 | 0.2878 | 0.4152 | 0.7257 |

5 | 0.2878 | 0.4152 | 0.7039 |

6 | 0.2878 | 0.4152 | 0.7523 |

7 | 0.2878 | 0.4152 | 0.8066 |

8 | 0.2878 | 0.4152 | 0.8596 |

9 | 0.2878 | 0.4152 | 0.8336 |

10 | 0.2878 | 0.4152 | 0.8007 |

Form the Table 1, we can know that when *C* = 8, the *H*(*C*)/ln*C* gets the minimum value, so we can get the conclusion that *C* = 8 is the best number of agents. Comparing with the *PI*, we can see that when *C* = 8, the partition index get the maximum value, so a conclusion can be drawn that the method proposed in this paper is valid.

*C*= 8 is the best number of agents which got by analysis in Table 1, so according to algorithm 2, the participation organizations included in every management region can be obtained and is shown in Table 2, thus the collaboration architecture of this supply chain is determined.

The relationship between organizations and region

Management region | Participation organizations |
---|---|

1 | |

2 | |

3 | |

4 | |

5 | |

6 | |

7 | |

8 | |

## 5 Conclusions and Future Work

Currently, the researches on business process mainly focus on the modelling and analysis for their organization structure or interactive relationship, there are rare literatures pay attention to the business process collaboration from the view of architecture. Therefore, an architecture called “agent end + stockholder end” is proposed, and then the agents in collaboration architecture and organizations partition is determined though information entropy and fuzzy cluster, which can discuss business process collaboration form macroscopic view and conduct the structure for collaboration applications

Future work involves two aspects as follows: (1) the formal description and verification for this collaboration architecture; (2) discussing the schedule issues specifically based on collaboration architecture.

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