CIMS Vol.8No.72002pp.527-532 ( 100084) Petri Petri F270.7 A Schedulability Analysis Algorithm for Timing Constraint Workflow Models Li Huifang and Fan Yushun (Department of Automation, Tsinghua University, Beijing, 100084, PRC) Abstract The ultimate goal of workflow management is to make sure that the proper activities are executed by the right person at the right time, a business activity which satisfies workflow control logic but violates specified time constraints is actually insignificant. So a workflow model requires time specification and verification before it is instanced and executed to guarantee the correctness of time behavior in WorkFlow Management Systems (WFMS). For the important limitation of actual WFMS, a Petri nets-based workflow modeling method for time constraints is put forward in this paper. Firstly, we extend Workflow nets with time constraints and call the new nets Timing Constraint WorkFlow nets (TCWF-nets), then after analyzing the timing property of WorkFlow nets (WF-nets), the schedulability analysis algorithm of TCWF-nets is proposed. Research results show that our method can roundly describe time information and has important reference value in enriching the time constraint modeling in WFMS. Keywords Workflow; Modeling; Time Constraints; Petri Nets; Schedulability Analysis 1 [1] 1
CIMS Vol.8No.72002pp.527-532 (Timing Constraint WorkFlow net TCWF-net) Petri [2-3] (Timing Constraint Petri Nets TCPN s) (WorkFlow net WF-net) [4] TCWF-net WF-net TCWF-net 2 2.1 Petri PN=(P, T, F) (WorkFlow net WF-net) (i P i = ) (o P o =) N =(P, T {t}, F {(o, t), (t, i)}) t N \T i o WF-net WF-net D TC TCWF-net 6 TCWF-net=(P, T, F, TC, D, M 0 ) WF-net(PTFM 0 ) TCTZZZ TC TC=([TC min (pt) TC max (pt)] ZZTCmin(pt)TC max (pt) p P t T}pt (TC min (pt) TC max (pt)) DTZD D={FIRE Dur (t)fire Dur (t) Z t T}FIRE Dur (t) WF-netTCWF-net (TC min (p j ), TC max (p j )) p j (TC min (t), TC max (t)) t t T 0 T 0 +TC min (t)τ T 0 +TC max (t)) p j t t TOKEN arr (p j ) TC min (p j )/TC max (p j ) TC min (t)/tc max (t) TCWF-net 2
CIMS Vol.8No.72002pp.527-532 ( ) t TK s t t t TK s t FIRE enabled (t)t EEBT(t)/LEET(t)t / EFBT(t)/LFET(t) t / FIRE begin (t)/fire end (t)t / I p (t)/o p (t) t / I t (p j )/O t (p j ) p j / 2.2 TCWF-net WF-net WF-net (1) TCWF-net i oi I t (i)= o O t (o)= (2) TCWF-net t * i o I p (t * )={o}o p (t * )={i} Petri oi t * (3) o (4) TCWF-net [4] TCWF-net WF-net 3 TCWF-net 3.1 WF-net WF-net T c p 2 1 Petri Fig. 1 Petri-net models of the four routing constructs [5] 1 3.2 / p 1 A 3
CIMS Vol.8No.72002pp.527-532 TOKEN arr (p) i TOKEN arr (i) ptoken arr (p) (TC min (p j ), TC max (p j )) p j TC min (p j )/TC max (p j ) TC min (p j )0 t TC min (t)0 TC min (t)0 TC max (t) TC min (t) 8:00~12:00 (TC min (p j ), TC max (p j ))(8, 12) 8:00~18:00 (TC min (t), TC max (t)) (8, 18)( ) FIRE Dur (t) FIRE Dur (t) FIRE Dur (t) (TC min (t), TC max (t)) (TC min (t), TC max (t))(0, ) FIRE Dur (t)=0 4 (specification) [2,6] Petri TCWF-net ( ) Petri 4
CIMS Vol.8No.72002pp.527-532 4.1 EFBT(t)/LFET(t) WF-net TCWF-net WF-net TCWF-net 1. TCWF-net M t LFET(t)EFBT(t)0 t LFET(t)EFBT(t)FIRE Dur (t) 2. TCWF-net M t t TOKEN arr (p j ) t TOKEN arr (p j ) t TOKEN arr (p j )0 [3]EEBT(t)/LEET(t)EFBT(t)/LFET(t) p j I p (t) EEBT(t) MAX [TOKENarr(p j )+TC min (p j )] (1) j LEET(t) MIN [TOKENarr(p j )+TC max (p j )] (2) j EFBT(t)EEBT(t)+TC min (t) (3) LFET(t)LEET(t) (4) 4.2 TCWF-net TCWF-net M n M 0 (M 0 t 1 M 1 t 2 M 2 t i M i t n M n )(t 1 t 2 t i t n ) M 0 M n TC max (t i )TC min (t i ) TC max (t i )TC min (t i )FIRE Dur (t i ) t 1 t n M 0 M 0 M n M n M n t 1 t 2 t n (1)~(4)M n t 1 t 2 t n EFBT(t i )/LFET(t i )(i=1, 2,, n) 2 t i ()t i t i t i t i t n LFET(t n ) 5 TCWF-nets 3. TCWF-net M t D(t) t 5 M n
CIMS Vol.8No.72002pp.527-532 UD(t)D(t) 0D(t)UD(t)LFET(t)EFBT(t)FIRE Dur (t) (5) t FIRE begin (t)d(t)efbt(t) t p j O p (t) TOKEN arr (p j )FIRE end (t)d(t)efbt(t)fire Dur (t) t t FIRE end (t)lfet(t)d(t)ud(t) FIRE end (t)fire begin (t)fire Dur (t)lfet(t) t t p i TOKEN arr (p i )LFET(t)1p i I p (t) TCWF-net M n M 0 M n M 0 M 0 LFET(t i )EFBT(t i ) FIRE Dur (t i )i=1, 2,, n t i (i=1, 2,, n)d(t i ) UD(t i ) (3)~(5) t i D(t i ) 5.1 t i (i=1, 2,, n) D(t i ) Step 1 ( ) Step 2 M 0 TOKEN arr (M 0 )M 0 M End k0 Step 3 M k k0 M k M 0 J(k) t j j1, 2,, J(k) j=1 Step 4 (1)~(4) t j EFBT(t j )/LFET(t j ) t j UD(t j ) D(t j ) 0D(t j )UD(t j )LFET(t j )EFBT(t j ) t j M k ( ) Step 5 jj+1 j<j(k) Step 4 jj(k) Step 6 + 1 j Step 6 M k+1 M k + ( J ( )) Mk+1 k=k+1 Step 3 Stop Step 7 Stop 1 k M End 0D(t) UD(t) i ) f k (CC, DT)0k1, 2,, n (6) CC TC min (p j )/TC max (p j )TC min (t i )/TC max (t i )FIRE dur (t i ) DT (D(t 1 ), D(t 2 ),, D(t n )) D{DTf(j, DT)0j0, 1,, n-1} J(DT)FIRE end (t n )(M n ) 6
CIMS Vol.8No.72002pp.527-532 Min J( DT ) DT s. t. f (j, DT ) 0, j = 0,1, L, n 1 (7) (6) (7) DT 5.2 TCWF-nets 2 TCWF-net t 22 t 21 ( ) M(p 22 ) p 0 p 1 (21, 31)[d 22 ] WF-net M(p 0 )M(p 22 ) p t t 3 1 t 21 3 (t 1 t 22 )TCWF-net p (0, 20)[d 21 21 ] t 22 t 21 2 TCWF-net 1 Fig.2 A fragment of a TCWF-net with OR-split structure (t 1 t 21f t 22 )t 21f t 21 t 21 p 1 Token =FIRE end (t 21f )+1 (D(t 1 )) Token t 22 1 (6)~(7) 6 ( ) t 22 p 22 7
CIMS Vol.8No.72002pp.527-532 TC min (pt)/ TC max (pt) FIRE Dur (t) t EFBT(t)/LFET(t) t t TCWF-net DT DT D(t i )t i D(t i ) TCWF-net D(t i ) (FIRE Dur (t i ) ) D(t i ) t i Petri Petri TCWF-net [1] Eder J, Panagos E, Pozewaunig H and Rabinovich M. Time Management in Workflow Systems[A]BIS 99 3 rd International Conference on Business Information Systems[C]BerlinSpringer Verlag1999266-280 [2] Tasi J J P, Yang S J. Timing Constraint Petri Nets and Their Application to Schedulability Analysis of Real-Time System Specifications[J]IEEE Trans Software Engineering, 199521(1)32-49 [3] Petri [J] 2000 15(5) 609-612 [4] Van der W MPThe Application of Petri nets in Workflow Management[J]The Journal of Circuits, Systems and Computers19988(1)21-66 [5] [M] 2001150-156 [6] Joel T, Francoise S, Jean-Pierre T. Time Constraints Verification Methods Based on Time Petri Nets[A]Proceedings of the IEEE Computer Society Workshop on Future Trends of Distributed Computing Systems[C]Central AmericanLos Alamitos1997262-267 (1965.11-) ( ) Petri 8