Procedia Engineering 15 (2011) 3487 – 3494

1877-7058 © 2011 Published by Elsevier Ltd.doi:10.1016/j.proeng.2011.08.653

Available online at www.sciencedirect.com

Available online at www.sciencedirect.com

Procedia

Engineering Procedia Engineering 00 (2011) 000–000

www.elsevier.com/locate/procedia

Advanced in Control Engineering and Information Science

The reduction and deadlock detection of cross-organizational business process based on Pi-calculus

Xin Yea,Xinghua Binga*,Chao Zuoa aInstitute of Information and Decision Technology, Dalian University of Technology,Dalian,116023,China

Abstract

Deadlock detection of large-scale and complicated cross-organizational business process is an important part of business process analysis. Due to the strong ability of algebraic deduction of Pi-calculus, it is suitable for the modelling and analysis of cross-organizational business process. Therefore Pi-calculus is chosen as the modelling and analysis means for cross-organizational business process in this paper. Furthermore, on the basis of Pi-calculus，the deadlock verification method of process is proposed and the formal descriptions of several typical reduction rules are presented. Finally, a case study is presented, and the result shows that the proposed method can achieve the deadlock detection of large-scale and complicated cross-organizational business process. © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Keywords: cross-organizational business process; Pi-calculus; deadlock; reduction rule

1. introduction

With more detailed of the division of work and the rapid development of the information technology (IT), the collaboration of organizations has become increasingly various and more complicated. And then, the cross-organizational business process is becoming more dynamics, larger and more complex. How to detect deadlocks of large-scale and complicated business process to guarantee the correctness of the process has become the focus both in theoretical research and practical application.

* Corresponding author. Tel.: 15040535389. E-mail address: wisboy@163.com

3488 Xin Ye et al. / Procedia Engineering 15 (2011) 3487 – 34942 Xin Ye, Xinghua Bing, Chaos Zuo/ Procedia Engineering 00 (2011) 000–000

Currently, the methods of the deadlock detection of business process include reachability tree based method [1,2], Petri Net based method[2,3], Pi-calculus based method[4], the method by matching with the typical deadlock patterns manually [5,6] and so on. But when the business process model is larger and more complex, the state space explosion may occur. And some scholars have proposed process reduction methods to reduce the complexity of analyzing business process models and solve the potential problem of state space explosion. But these methods are based on directed acyclic graph, which can not satisfy the needs of modelling and other analysis of cross-organizational business process completely. And the deadlock detection after reduction is achieved mainly by observation [7,8] in these works, Thus, the accuracy and completeness of discrimination of the deadlock may not be guaranteed completely. Pi-calculus can formally describe the distributed, interactive and dynamic systems, and it can be used to make a variety of business processes analysis including deadlock detection based on its strong ability of algebraic deduction. Therefore Pi-calculus is considered as the core technology of the next generation of business process management[9,10]. For these reasons, Pi-calculus is chosen as the formal modeling method for cross-organizational business process. Furthermore, combining the process reduction with the analysis ability of Pi-calculus, the deadlock detection method based on Pi-calculus is proposed.

The remainder of this paper is organized as follows. In section 2, a deadlock detection method of cross-organizational business process is proposed and some typical reduction rules are described formally based on Pi-calculus. In section 3, the proposed method is verified by one case study. At last, the conclusions are presented.

2. The reduction and deadlock detection method of cross-organizational business process based on Pi-calculus

2.1. The syntax of Pi-calculus

In Pi-calculus, there are two basic concepts: name and process. The communications of processes are achieved by sending and receiving names. A brief introduction of syntax of Pi-calculus is summarized as follows[10].

1) prefix: the input prefix a(x) means that the channel a can be used to receive input x. The output prefix a <x> means that x is sent along the channel a. 0 represents an inactive process. The τ represents the silent event.

2) a.P represents performing prefix a and continue as P. In Pi-calculus, the “.” represents sequential execution.

3) ∑∈Ii

iP means that only one process Pi will be chosen to execute. “I” is the finite index set.

4) P|Q represents process P and process Q are executed in parallel. 5) [x=y]P is read as “if x=y then P”. 6) (νx)P is a restriction that hides the name x from the environment of P.

2.2. The deadlock detection method based on Pi-calculus

The steps of deadlock detection method of the cross-organizational business process are described as follows.

(1) The modeling of cross-organizational business processes is conducted based on Pi-calculus at first. The organizations involved in cross-organizational business processes and their activities can be represented by Pi-calculus. Channels denote the cross-organizational collaborations. To accomplish the business collaboration of organizations, the information is transmitted on channels, and then the

3489Xin Ye et al. / Procedia Engineering 15 (2011) 3487 – 3494 Xin Ye, Xinghua Bing, Chao Zuo/ Procedia Engineering 00 (2011) 000–000 3

corresponding activities are executed. Both the channel and the information can be represented by names of Pi-calculus. In particular, the information may be omitted depending on the detail context. If the process model is large-scale and more complicated, then go to step (2), otherwise go to step (3) directly.

(2) The business process formal reduction based on Pi-calculus. If the reduction result is nil-process, it indicates that there is no existing deadlock, otherwise go to step (3).

(3) The deadlock detection based on Pi-calculus. Like other powerful and sophisticated formal model, there are many tools which support the automatic

model checking and verification, such as JACK toolkit and Mobility Workbench (MWB).

2.3. The formal description of typical reduction rules based on Pi-calculus

For space limited, there are only iteration omitting rule, terminal reduction rule, sequential reduction rule, adjacent reduction rule and closed reduction rule to be described formally based on Pi-calculus for the structural deadlock detection of the process. These rules can be applied in not only cross-organizational but also intra-organizational business process reduction.

(1) Iteration Omitting Rule If an activity can be executed by an organization has one output channel and the channel connects to

the activity itself, there exists a self-cycle for the activity. In this context, the channel can be removed as shown in Fig.1 if it is exclusive with other output channels of this activity. The oval denotes organization, and it is represented by capital letters. The rectangle denotes the activity. The solid arrow denotes channel, and it is represented by lowercase.

abaa

A Bab

A B

Fig. 1. Example of applying iteration omitting rule

The formal description of the process before applying iteration omitting rule based on Pi-calculus is shown as follows.

( ) ( )( ) ( ) ( )( )0..|0.0...)()(|)()( ba ababaaaaaaababBaa,ab,acAaaabdefITERATION ττνννν +=

The formal description of the business process after applying iteration omitting rule is shown as follows.

( ) ( )( ) ( )0..|0.)(|)(' bababababBab,acAabdefITERATION τνν =

(2) Terminal Reduction Rule If the total amount of the input channel and the output channel of an activity less than or equals 1, i.e.

this activity only has one input channel or one output channel or not any channel, the channel can be removed. The Fig.2 shows the example when an activity only has one output channel.

ab bc cx

cy

bc cx

cy

A B C A B C

Fig. 2. Example of applying terminal reduction rule

The formal description of the business process before applying terminal reduction rule based on Pi-calculus is shown as follows.

3490 Xin Ye et al. / Procedia Engineering 15 (2011) 3487 – 34944 Xin Ye, Xinghua Bing, Chaos Zuo/ Procedia Engineering 00 (2011) 000–000

( )( ) ( ) ( )( )( )0.|)0...),(|0...|0.),(

),,(),(|),(|)(),(

cycxbccycxbcababbcab

cycxbcCcycxbcabBabAbcabdefTERMINAL

cb τντν

νν

=

The formal description of the business process after applying terminal reduction rule is shown as follows.

( ) ( ) ( )( )( )0.|0...),(|0.)(),,(),(|)()(' cycxbccycxbcbccycxbcCcycxbcBbcdefTERMINAL cτνννν =

(3) Sequential Reduction RuleIf an activity has exactly one input channel and one output channel and its preceding and succeeding

activity are not the same activity, the input channel and output channel can be removed and a new channel is created between its preceding and succeeding activity as shown in Fig. 3.

ab bccx

cy ac

cx

cy

A B C CA

B

zaza

Fig. 3. Example of applying sequential reduction rule

The formal description of the business process before applying sequential reduction rule based on Pi-calculus is shown as follows.

( )( ) ( ) ( )( )( )0.|0...),(|0...|0...),(

),,(),(|),(|)(),(

cycxbccycxbcababzabcab

cycxbcCcycxbcabBabAbcabdefSEQUENCE

cba τνττν

νν

=

The formal description of the business process after applying sequential reduction rule is shown as follows. ( ) ( ) ( )( )( )0.|0...),(|0...)(),,(),(|)()(' cycxaccycxaczaaccycxacCcycxacAacdefSEQUENCE ca τντννν =

(4) Adjacent Reduction Rule If an activity has one input (or output) channel and more than one output (or input) channels and the

type of the activity is the same with its preceding (or succeeding) activity (e.g. they are both and-split type), the channels of this activity connecting to its preceding and succeeding can be removed and the new channels are established between its preceding and succeeding. The Fig. 4 shows an example that type of the activity and its succeeding are both are xor-join, and the corresponding description based on Pi-calculus is shown as below.

ad

de

cebd

ae

cebe

AA BB CC

D

D

EE

Fig. 4. Example of applying adjacent reduction rule

The formal description of the process before applying adjacent reduction rule based on Pi-calculus is shown as follows.

))0..0..(|)0.)0...0...(|)0.0.)(((,,,(

)),(|))(),,((|))()()(((,,,(

eedd dececedebddeadbdaddecebdad

deceEceCdebdadDbdBadAdecebdaddefADJACENT

ττττν

ν

++++=

++

3491Xin Ye et al. / Procedia Engineering 15 (2011) 3487 – 3494 Xin Ye, Xinghua Bing, Chao Zuo/ Procedia Engineering 00 (2011) 000–000 5

The formal description of the process after applying sequential reduction rule is shown as follows.

))0..0..0..( |)0.0.0.)((,,(

)),,(|))()()()((,,('

eee cebeaecebeaecebeae

cebeaeEceCbeBaeAcebeaedefADJACENT

τττν

ν

++++=

++

(5) Closed Reduction Rule If more than one output channels with and-relationship (or xor-relationship) of an activity are all the

input channels with and-relationship (or xor-relationship) of another activity, other channel can be deleted and only one channel is reserved. An example of Closed Reduction Rule is shown as Fig. 5.

ab

ab’

abAA BB

Fig. 5. Example of applying closed reduction rule

The formal description of the process before applying closed reduction rule based on Pi-calculus is shown as follows. ( ) ( )( )0.'.|0..|0.'|0.)',())',(|)',()(',a( 'bb ababababababababBababAabbdefCLOSED ττνν =

The formal description of the process after closed sequential reduction rule is shown as follows. ( )0..|0.)())(|)()((' bababababBabAabdefCLOSED τνν =

3. Case study

The book order processing on the Amazon online bookstore[11] is taken as an example to illustrate the proposed method in this paper.

(1)The modeling and description of the case For simplicity, credit card is used as the only means of payment and the inner business processes in

Bank, Delivery Company and Publish house aren't considered. The customized process is shown as Fig. 6.

ac

Place order

Reject order

Inform status of credit card

Check credit card

Receive order

Order request

Making shipping request

Receive order request and shipping Request

Receive shipping request &

Delivery books

Email shipping specification

Receive order rejecting

+

+

+

Bank

Publish house

Delivery company

ac1

ac2

aro2ccd

accd2ro

acs2or

ab

ab1

ap

ad pd

ad1

acs2msr

Check storage

accd2cs

Receive shipping

specification

End +

ce1

ce2

Receive information of the credit card

N2t2

t1N1

END

Customer

Amazon

invalid valid

sufficiencystockout

3492 Xin Ye et al. / Procedia Engineering 15 (2011) 3487 – 34946 Xin Ye, Xinghua Bing, Chaos Zuo/ Procedia Engineering 00 (2011) 000–000

Fig. 6. The book order processing

In this example, the activity “place order” is the initial activity and a virtual end activity is added. The end activity will be executed after either activity “receive order rejecting” or “receive shipping specification” executed by customer. Thus, there will be only one initial activity and one end activity in the model. In addition, in order to reflect the relationships of the organizations clearly, two virtual organizations N1 and N2 are introduced, which don’t perform any business action but transmit the received information only.

The model before reduction based on Pi-calculus is shown as follows. Customer is represented by C, Amazon is represented by A, bank is represented by B, delivery company is represented by D, publish house is represented by P, the virtual process that identifies the end of process is represented by End, and the whole process is represented by Sys. The letters near the arrows denote channels in Fig. 6.

)0.2.20.1.2(|0 )2,1,2,2,( ceaccet.acdefceceactacC +

))2.1|))..|0..2.|0...(.(

|..0.1..2|0..(.1|..|..(

)( )1,,1,2,1(

.0ac.τad0adacs2msr. τmsracs.0apacs2or. τacs2oraccd2cs

0accd2csacroaccdaccd2roab0ab.aro2ccd0aro2ccdac.τ

aess2osr,acs2msr,d2cs,acs2occd2ro,acc aro2ccd,adefadap,adab,abacac,acA

τττττττ

ν

+

+

.0ababdefababB 1.. )1,( τ

.0adpd.0adtdefpdad1,t1,D 1..1..1 )( ττ +

.0pdap.defap,pdP . )( τ

SysceSyscedef,ceceEnd .2.1 )21( +

.01. )(1 taddeft1ad,N

.02.1 )21(2 tacdeft,acN

)2,1(|)))1(|))()11(((2)1,2((|)1,(|)1,,1,2(

|)2,1,2,2,()(2,,1,1,2,1,,1,2,1(

ceceEnd,pdadt1,Dap,pdPad,tNtacNababBadap,adab,abacac1,ac,A

ceceactacCtpdtad,adacacap,acab,abcecedefSys

++

ν

(2)The reduction of business process and deadlock detection

From the established model, the activity “Receive order rejecting”, “Receive shipping specification”of Customer, “Receive order”, “Check credit card” and so on of Amazon, “Inform status of credit card” of bank, “Receive order request and shipping Request” of publish house and the virtual activities of N1 and N2 each has exactly one input channel and one output channel. It can be reduced by using the sequential reduction rule. In addition, the activity “Place order” of Customer has only one output channel and therefore it can be reduced according to the terminal reduction rule. Then one channel between “Check storage” of Amazon and “Receive shipping request & delivery books” of delivery company can be reduced by using Closed Reduced Rule. The model is reduced by the related reduction rules iteratively. At the end, the result is nil-process and it shows that there is no existing deadlock in the model. In order to verify the deadlock detection method, the activity “Receive shipping request & delivery books” of delivery company is changed to receiving request from Amazon and publish house synchronously instead of receiving request from Amazon and publish house alternatively. The modified model is reduced by applying related reduction rules iteratively and the reduced model is shown as Fig. 7,

3493Xin Ye et al. / Procedia Engineering 15 (2011) 3487 – 3494 Xin Ye, Xinghua Bing, Chao Zuo/ Procedia Engineering 00 (2011) 000–000 7

in which the “ad2”, “de”, “ae” are the new created channels during the reduction process.

Receive information of the credit card Receive shipping

request & Delivery books

+

Delivery company

ad2

Amazon

ae

adde

End

+

Fig. 7. The reduced business process model

The reduced model is shown as below.

)0.2( ),2,( ae.0ad.0addefaeadadA ++

0..2. ),2,( de.adaddefdeadadD τ

1.d1. )d( SyseSysaedefeae,End +

)).(|)(|),2,(|)0.2)((,,2 ( 1 deaeEnd.0aedeae,EnddeadadDad.0addeaead,addefSys ++ν

In this paper, MWB is taken as the detection tool to check whether there is any deadlock of the model

mentioned above. Few syntactic transformations on the reduced model are made to satisfy the syntax requirement of MWB[12], and then the “deadlocks” command is used to verify the reduced model. The result shown in Fig.8 indicates that there exists a deadlock that occurs during the collaborative process between Amazon and delivery company. Therefore the method is proved successfully. In addition, the “step” command of MWB can be used to simulate model step by step to find or verification the reason of deadlock occurs.

Fig. 8. The deadlock detection of the reduced model

4. Conclusion

Due to the characteristic of strong interactivity of cross-organizational business process, Pi-calculus is adopted to model the business process. And then, the method of deadlock detection of the cross-organizational business processes and the formal description of several typical reduction rules are proposed. The proposed method may weaken the problem of state space explosion which occur during the deadlock detection of large-scale and complicated cross-organizational business process. Additionally it meets the characteristics of cross-organizational business processes better and can guarantee the accuracy

3494 Xin Ye et al. / Procedia Engineering 15 (2011) 3487 – 34948 Xin Ye, Xinghua Bing, Chaos Zuo/ Procedia Engineering 00 (2011) 000–000

and completeness of detection. Finally, a case study is given to validate the proposed method in this paper. In the future, the method will be applied to more cross-organizational business process to be validated and improved further.

Acknowledge

This research is supported by the National Natural Science Foundation of China (Grant No. 91024029), Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.200801411060) and the Fundamental Research Funds for the Central Universities of China (Grant No. DUT09RC(3)060).

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