Debit. Credit. trigger start. start. abort. commit. commit

Transcription

1 Suerviory Control of Workow Sheuling C. Wlle y P. Jenen z N. Sorkr Eletril Engineering & Comuter Siene The Univerity of Mihign Ann Arbor, MI USA fwlle,jenen,orkrg@ee.umih.eu Abtrt Workow h beome n imortnt rigm for itribute t n omuting ytem in wie rnge of lition re. In workow, tk exeuting on utonomou, heterogeneou ytem re oorinte through t n ontrol ow ontrint. An imortnt hllenge in workow mngement i the heuling of tion n oertion erforme by the onurrently exeuting tk. The legl interleving mong the tk mut be eie, n heuling ontrol mehnim mut be generte o tht the exeution rogreorretly n eiently. The heuling iue i rtiulrly iult beue the exeution ontrint my be lition-ei, n ertin utonomou tk exeution my be outie the oe of workow ontrol. We ue tehnique te from uerviory ontrol theory of irete event ytem for eifying n generting heuling ontroller in workow environment. We ue our moeling roh to eify the tk n the eenenie nite tte utomt. To ount for utonomou exeution hrteriti, ome of the event trnition in the tk utomt my be ientie being outie the ontrol of the workow mnger. Uing the tehnique in uerviory ontrol theory, we how how the exitene of heuler my be etermine n how heuler my be obtine lgorithmilly. Furthermore, where the reie l of orret exeution i foun to be untenble, we how how to n bet roximtion l n how to erive heuler for uh l. Thu we rovie n eetive men of moeling workow ytem n generting the heuling mehnim to mnge them. 1 Introution Workow ytem hve gine rominene in reent yer for lition in buine roee, hoitl minitrtion, ollbortion tehnologie, n mnufturing ontrol, mong other re. Workow re hrterize by tk whih e n mniulte hre t reoure, with lition-ei intertk eenenie. Thee tk my run on utonomou, heterogeneou ltform, involve intertion outie the omuting ytem, n emn ivere orretneonition with regr to their interleve exeution. In thi er we exmine hllenging roblem in workow, the eient n orret mngement heule for the tion n oertion tht rereent the exeution of the ytem. A n exmle, onier omuting ytem to it hoitl mngement n minitrtion. A tyil workow eribe for uh ytem my onit of everl tk uh entering the tient t into In Proeeing of Interntionl Workho on Avne Trntion Moel n Arhiteture (ATMA), e. E. Bertino, S. Jjoi n L. Kerhberg, 1996, 36{46. y Suorte in rt by NSF grnt CCR n ONR grnt N z Suorte in rt by ooertive fellowhi from IBM Toronto Lbortory. 1

2 tbe, obtining informtion on erlier viit n meil hitory, ertining inurne informtion, entering the meil ttennt' ignoti, reribing tretment meiine, eing ot n billing the tient. There my be reeene ontrint (e.g., initite rerition only fter ignoti re entere) or otentil t onit (e.g., hek reribe tretment gint llergie in the meil hitory) tht roribe ertin kin of interleve exeution mong the tk. Eh tk itelf my onit of everl tion n oertion whih re orere mong themelve. Furthermore, thee tk my exeute on ierent ltform n my hve utonomou exeution hrteriti, o ome of the oertion n tion within eh tk my be outie the ontrol of ny workow uerviion one the tk i initite. Dt my be onurrently hre mong ome of the tk tht re ermitte to exeute t the me time (e.g., the tk ertining to meil hitory n inurne). The bove erition houl inite tht mnging workow ytem ihllenging. Not only re there intr-tk orering (whih reumbly my be hnle utonomouly), but lo omlex intertk eenenie. Logil eenenie rie from the e to hre t reoure, n erformne ontrint rie from the eire to imoe the fewet retrition on the utonomou exeution. To omoun the roblem, ome of the tion within the iniviul tk my be unontrollble by n externl workow heuler. Our roh to the roblem of workow heuling roee follow. Firt we moel workow ytem irete event ytem. Eh tk in workow my be regre et of irete event orere to exeute in re-eie mnner, n the irete event ytem of the iniviul tkn be ombine to moel of the ytem whole. Seon, we ue tehnique from uerviory ontrol theory [RW89] for uh ytem to obtin orret n eient heuler tht mnge workow ytem. Our roh, though not the ne to ll workow roblem, goe te further in unertning n olving everl of the iultie eribe bove. We re in goo oition to tte unequivolly wht i oible, n how to hieve the oible, with the moel tht we eribe. In reent yer, there h been onierble work in the re of workow mngement (e.g. ee [GHS95, KR95, AAA + 96] ). Our work i relte to [ASSR93, ST94, Kle91, Gun93] in tht we re moeling tk in workow ytem nite tte utomt. Temorl logi [ST94] n nite-tte utomt [ASSR93] hve been ue to eify eenenie n heuling. Our metho i imilr to [ASSR93] in tht we moel tk nite-tte utomt, but ierent from it in tht we t the well-unertoo tehnique of uerviory ontrol theory to rovie frmework for workow ytem. Moreover, number of imortnt reult ertining to ierent kin of event (e.g., unontrollble, utonomou event) re lo hnle. 2 Deribing Workow In thi etion we introue the notion of workow n ome relte terminology. We eribe n exmle whih we ue ubequently for illutrtive uroe. 2.1 Denition A workow i n orgnize et of tk. Tk re emntilly oherent unit of work whih my be exeute on ivere, heterogeneou ltform. Eh tk onit of event to be exeute in reene orer. An event i n tion to be rrie out on the ytem; e.g., tk initition or termintion, or t e or ute. Event notition re ent to the workow heuler, whih ontrol tk exeution by eletively llowing n reventing event from ourring. A workow heuler i therefore ive in nture, llowing tk to hooe the event they exeute but limiting their rnge of hoie. Some tk my involve event tht re outie the ontrol of the workow heuler. If heuler i notie of uh n event, it nnot revent it from ourring. A workow orgnize it tk by etblihing reltionhi between event of ierent tk. Thee intertk eenenie, like the truture of the tk themelve, re ene by the workow eigner. The 2

3 Debit Creit trt trigger trt reommit reommit bort ommit bort ommit ommit Figure 1: The T RANS workow. tk of heuler i to enure heule, or equene of event, tht tie both the tk eition n the intertk eenenie. 2.2 Exmle: the T RAN S workow Conier imle workow T RAN S, illutrte in Figure 1. T RAN S trnfer fun between bnk ount by ebiting one ount n reiting the other. The workow ontin tk ebit whih trigger tk reit. Both tk involve trt event, termintion event (either ommit or bort), n n intervening re-ommit event. Eh tk i require to be tomi: it mut either exeute to omletion or not exeute t ll. We ume tht the filure of reit i tolerte but not tht of ebit; no work houl be ommitte if ebit fil. Hene the tk reit n omlete uefully only if ebit omlete uefully. There re two intertk eenenie in thi workow. Firt, if ebit i to trt work, reit mut lo trt, with ebit reeing reit. Thi trigger eeneny involve both o-ourrene onition (i.e. if ebit trt, then reit trt) n temorl onition (i.e. if reit n ebit both trt, then ebit trt before reit). Seon, it mut be enure tht reit homlete or will omlete uefully before ebit i llowe to o o. Thiommit eeneny i imly o-ourrene onition (i.e. if reit ommit, then ebit mut hve ommitte or mut ommit lter). Let n rereent the trt n ommit event of reit, n let n rereent the trt n ommit event of ebit. We ene the reltion trigger n ommit whih hol between event. Then our eenenien be exree ( trigger ) ^ ( ommit ). 3 Suerviory Control of Direte Event In thi etion we reent relevnt mteril from [RW89] for irete event ytem n the reult from uerviory ontrol theory tht re relevnt to workow heuling. 3.1 Direte event ytem Direte event ytem (DES) re ynmi ytem in whih tte hnge re ue by intntneou ourrene of event. Thee event my emnte from outie or within the ytem, my or my not be ontrollble by the ytem, n my our t reitble or unreitble time intervl. Workown be urtely moele DES, ine the workow heuler reeive event notition in irete fhion. 3

4 3.1.1 Lnguge In workow heuling, we re interete in ontrolling the equene of event tht the ytem generte. We itinguih the tye of event tht n our in workow with lbel. The event et of the ytem i the et of ll uh lbel, n rereent the et of ll nite tring over inluing the emty tring. A lnguge over i imly ubet of. We n ene lnguge to rereent the et of ll event equene tht the ytem n generte n the et of ll legl equene tht heuler houl llow. If tring w i vli event equene, then ll event ub-equene generte before w re lo vli. We ue the onet of rex loure to rereent thi roerty. A tring u i rex of tring v 2 if for ome w 2, v = uw. The rex loure L of L i the et of ll rexe of tring in L: fu : (9v 2 )(uv 2 L)g. If L = L then L i rex-loe. The behvior of DES i moele rex-loe lnguge L over n event et Lnguge genertor We n rereent the behvior of workow in term of lnguge genertor G. G i nite tte utomton (FSA) (Q; ; ; i; M) oniting of nite tte et Q, nite event et, rtil trnition funtion : Q! Q, n initil tte i 2 Q, n et of mrke tte M Q. The behvior of the ytem iture by oniering ll equene of trnition tht n be tken from the initil tte. We exten the funtion to tring of event: if q 2 Q, then (q; ) = q n for ll w 2 ; 2, (q; w) = ((q; w); ). We ene the behvior of G to be L(G) = fw 2 : (i; w) efineg. The genertor' mrke tte M rereent tte of tiftory omletion. We ene the mrke behvior of G to be L M (G) = fw 2 : (i; w) 2 Mg. It i lwy the e tht L M (G) L(G), but it i lo eirble tht L M (G) = L(G). Thi men tht every equene of event generte by G n be extene to rrive t tte of tiftory omletion. When thi i the e, we y tht G i nonbloking. Given genertor A n B, we n rereent the onurrent exeution of the genertor by the hue rout G = A k B of thee genertor. The tte of G onit of ir of tte A B, the event et i A [ B, the initil tte i the ir (i A ; i B ), n the mrke tteonit of ll ir f(; t) : 2 M A ^ t 2 M B g. The trnition funtion i ene follow: 8 ( A (q; ); B (r; )) if A (q; ) n B (r; ) re ene; >< G ((q; r); ) = ( A (q; ); r) if A (q; ) ene n B (r; ) unene; >: (q; B (r; )) if A (q; ) unene n B (r; ) ene 3.2 Suerviory ontrol In thi etion we iu how ontroller or uervior n enfore orretneonition on DES. A ontrolle ytem i moele feebk loo between genertor n uervior. At eh event ourrene, the uervior ontrol the et of oible event by ibling ertin event (reventing them from ourring). The event et i rtitione into et of ontrollble event (thoe whih n be ible) n et u of unontrollble event Feebk loo of ontrol A illutrte in Figure 2, when n event our, the genertor G move from iturrent tte q to tte G (q; ) n notie it uervior of the event' ourrene. After eh event ulie by G, the uervior en et of event, the ontrol inut, to G. Thee re the event enble in G' new tte G (q; ). Unontrollble event re lwy enble: u. The event generte by G re ontrine by the ontrol inut; eh event ent from G to the uervior ihoen from the urrent vlue of. We moel the uervior DES, n in rtiulr n FSA S. The uervior'ontrol tion re then etermine by the trnition truture of S. The uervior n genertor run in rllel. If G i in 4

5 Suervior Genertor Figure 2: Feebk loo of ontrol. tte q n S i in tte r, then event i enble if n only if G (q; ) n S (r; ) re ene. If both re ene, then G move to tte G (q; ) n S move to tte S (r; ) Controllbility We my k wht lngugen be relize by uerviory ontroller of the tye eribe bove. If ll event re ontrollble, the ontrol roblem i trivil, n ny lnguge generte by n FSA (i.e. ny regulr lnguge) n be relize; t eh tte, the uervior n ible the event for whih it utomton h no trnition ene. Controller eign i more omlite if there re unontrollble event, the uervior my not be ble to ible ertin event tht le outie it trnition truture. For lnguge K to be ontrollble, eh unontrollble event mut le to th from whih ome tring in K n be ttine. In rtiulr, K iontrollble if K u \ L(G) K; for ny rex of tring in K, if n unontrollble event i e, the reult i till rex of tring in K. For workow heuling, we wnt olution tht i not only ontrollble but lo nonbloking. The uervior mut enure tht mrke tte i lwy rehble. To hrterize the onition uner whih nonbloking olution i oible, we introue the notion of L M (G) loure. A lnguge K L M (G) i L M (G)-loe if K \ L M (G) = K. To ttin L M (G) loure, we mut enure ll the tring in K re in L M (G) n tht ny mrke rex of tring in K i itelf in K. To voi bloking, we mut not exlue ny mrke rex tht le to eire tring k, ele there will be no wy to reh k. Note tht our roh enure tht the workow heuler mintin heule tht i lwy extenible to orret one. Therefore, tte from whih no legl trnition re vilble never rie. The reult for ontrollbility, tken from [RW87b], re ummrize follow. Fix genertor G tht generte lnguge L(G) n mrke lnguge L M (G). For nonemty K L(G) there exit uervior S relizing K if n only if K i rex-loe n ontrollble. For nonemty K L M (G) there exit uervior S relizing K it mrke lnguge, n the ytem i nonbloking if n only if K iontrollble n L M (G)-loe Controllble ublnguge If given lnguge K i foun to be unontrollble, we woul like to n ontrollble lnguge K tht i loe n roximtion to K oible. In workow heuling, thi men ning ontroller tht llow mny vli heule oible while not llowing ny invli heule. It i not obviou riori whether unique, otiml (in term of the lrget number of etble heule) roximtion lwy exit, or how to n it if it oe exit. Neverthele, it i the e tht the l C(K) of ontrollble 5

6 ublnguge of K iloe uner et union n h unique ureml element K " uner et inluion [WR88b]. If, in workow heuling, we mut ontrol the ytem o tht the ontrint imliit in K re never violte, then K " i the bet olution oible. Furthermore, if we moel the genertor n uervior FSA, n lgorithm i vilble to omute K " tht i of omlexity O(mn), where m n n re the number of tte of the genertor n uervior Moulr ynthei of ontroller Sheuling workow involve enforing et of intertk eenenie imultneouly. If eh eeneny n be exree in term of n FSA, uervior n be hieve by tking the rout of ll the eeneny utomt. The reult however my uer from n exonentil tte e inree. For exmle, the rout of n eeneny utomt with m tte eh my hve mny m n tte. A wy of voiing thi roblem i to introue itionl truture into the moel, moulrizing the uervior into et of ineenent ontrint enforer. The eeneny utomt in D re run in rllel, n the ontrol inut i the interetion of the ontrol inut of ll the utomt. A moulr uervior i obviouly eirble, the quetion rie to when uh uervior i oible. The nwer een on whether the ontrint lnguge re non-oniting. Lnguge K 1 n K 2 re non-oniting if K 1 \ K 2 = K 1 \ K 2 ; for every rex tht K 1 n K 2 hve in ommon, there mut be wor they hve in ommon tht ontin thi rex. If the eire lnguge i not ontrollble, we nee to ue n roximtion. A before, we n ue the oertion " to n n otiml olution. In the e of non-oniting ontrint lnguge, the " oertor ommute with the interetion oertor. Thi men tht n otiml uervior (in term of the mximum number of etble heule) n be hieve eiently by lying the " oertor to eh eition lnguge n intereting the reult. We ummrize the bove reult, tken from [RW87, WR88]: If K 1 ; : : : K n re non-oniting, L M (G)-loe n ontrollble, then K 1 \ : : : \ K n i L M (G)-loe n ontrollble. If K " 1 ; : : : K" n re non-oniting, then K " 1 \ : : : \ K" n = (K 1 \ : : : \ K n ) ". 4 Alying Suerviory Control to Workow We now ue the enition n reult of the reviou etion to frme workow heuling uerviory ontrol roblem. We ene our DES moel of workow, uing our T RANS workow n exmle, n then ly the reult of uerviory ontrol theory to n the otiml moulr olution. 4.1 Workow irete event ytem Eh tk in workow eie eenenie between it event. The workow to thee et of eenenie tht hol between event of ierent tk. We ene workow W to be ir (T ; D), oniting of et T of tk (eh eifying et of intr-tk eenenie) n et D of intertk eenenie. Both tk n intertk eenenie re moele DES, n in rtiulr FSA Tk Eh tk T in T i n FSA (Q T ; T ; T ; i T ; M T ). Q T i nite et of tte, T i nite event et, T i rtil funtion Q T T! Q T, i T 2 Q T, n M T Q T. The event et of eh tk re ijoint: (8T; U 2 T ; T 6= U)( T \ U = ;). We n moel the unontrolle workow by k T 2T T, the rout of ll the tk in the workow. We ume tht the workow heuler n itinguih between event in tk, o eh event ourrene i unique within tk: (8q; r 2 Q T )(8 2 T )[( T (q; ) efine ^ T (r; ) efine)! (q = r)]. 6

7 G : G : Figure 3: Tkreit n ebit moele FSA. G : Figure 4: Conurrent exeution of reit n ebit moele n FSA. Eh tk begin with trt event n terminte with ommit event or n bort event. In ition there i re-ommit event tht reee termintion. A eh tk i tomi, it mut run to omletion or not t ll. Therefore the initil tte n the tte following termintion re the mrke tte. The tkreit n ebit re moele erte utomt G n G in Figure 3 n ingle utomton G = G k G in Figure Intertk eenenie Eh eeneny D in D i DES, n in rtiulr n FSA. Unlike the tk utomt, eeneny utomton h no rivte event et; rther, it event et onit of ll the event et of the tk utomt. Let = S T 2T T ; then D i n FSA (Q D ; ; D ; i D ; M D ), where Q D i nite, D i rtil funtion Q D! Q D, i D 2 Q D, n M D Q D. The T RANS workow h the intertk eenenie ( trigger ) ^ ( ommit ); we n rereent thee ontrint by the utomt D n D hown in Figure Suerviory ontrol of workow We re rey to ly the reult of Suerviory ontrol theory to our moel of the T RANS workow. We begin by ening our eition lnguge of orret heule. We then tet for ontrollbility n 7

8 D : trigger D : ommit {, } { } {, } { } { } Figure 5: Automt rereenting the intertk eenenie of T RAN S Figure 6: Genertor for eition lnguge K. bloking of thi lnguge, generte n otiml (in term of the mximum number of etble heule) ontrollble nonbloking lnguge n tet thi lnguge for moulrity Seition lnguge From the eition of the genertor G n the eenenie D n D we wih to ene the legl lnguge K of the workow ytem. K mut be ubet of eh of the lnguge L(D ) n L(D ) generte by the eeneny utomt, n it mut be ubet of the lnguge L(G). The eire lnguge i K = L(G) \ L(D ) \ L(D ), n the eire mrke lnguge i K M = L M (G) \ L M (D ) \ L M (D ). The hue rout G k D k D, generting K with mrke lnguge K M, i illutrte in Figure Controllbility We ue the reult reente in etion to etermine whether K M iontrollble. We n how tht K M i not ontrollble (i.e. K M u \ L(G) 6 K M ) by the following ounterexmle. Conier the 8

9 () 11 (b) Figure 7: Contrution of genertor for K " M : () genertor H 1, (b) genertor H 2. tring k = K M. If we exten thi tring by ing the event 1 2 u, we get the tring K M. Intuitively, thin be exline follow. The tring k rereent heule in whih the reit tk i llowe to ommit without the ebit tk hving ommitte erlier. For the ommit eeneny to hol between reit n ebit, the ebit tk mut then ommit. Thi however nnot be gurntee, ebit my bort inte (e.g. ue to filure of the ite where ebit i running), n event outie the ontrol of the workow heuler Contrution of otiml ontroller Sine the lnguge K M i not ontrollble, K " M 6= K M, o n otiml uervior in the ene of etion will only be ble to llow ubet of K M. We ue the lgorithm of [WR88b] iue in etion to ontrut genertor for K " M with mrke lnguge K" M. We trt with n FSA H 0, ub-utomton of G tht generte K with mrke lnguge K M. H 0 i imly the hue rout G k D k D, hown in Figure 6. We tke the trim of thi FSA, removing ll tte tht re unrehble from the initil tte or from whih mrke tte i unrehble. Thi remove tte 21, 31, 41, 51 n 45. The reulting FSA H 1 i hown in Figure 7. We now omre the unontrollble trnition of H 1 with thoe of G. If there i n unontrollble trnition (q; ) in G whih le from tte q in H 1 to tte r not in H 1, we mut remove q from H 1. There i uh trnition, (43; ), o we remove tte 43 n ll trnition to n from it. We then tke the trim, removing tte 42. The reult H 2 i hown in Figure 7. Comring H 2 with G, we n no unontrollble trnition in G tht le from tte in H 2 to tte 9

10 Figure 8: Genertor for K " n K ". not in H 2. A thi itertion leve H 2 unhnge, xoint i rehe, o the lgorithm terminte. H 2 generte K " M with mrke lnguge K" M Moulr olution While the ontroller olution in the reviou etion oe not uer from lrge tte e, we n till tet whether moulr olution of the tye eribe in etion i oible for our exmle. Let K n K be the lnguge generte by the eeneny utomt D n D. We n ontrut genertor for K " n K " uing the lgorithm of [WR88b]; the genertor re hown in Figure 8. Our gol i to ue thee genertor in ontroller for the lnguge K " = (K \ K ) ". The lnguge reulting from the rllel ue of thee genertor, eribe in etion 3.2.4, i K " \ K". Next, by inetion, we ee tht K " n K " re non-oniting, i.e. K \ K = K \ K. Thi imlie tht K " \ K" = (K \ K ) ", n hene tht the moulr roh roue the eire lnguge K. 5 Conluion In thi er, we hve ree iue in heuling utonomou tk in workow environment. We hve rovie frmework te from the well-unertoo omin of irete event ontrol ytem theory. Our frmework i be on nite-tte utomt n rovie rtil mehnim for eifying eenenie mong the tk. Given et of eenenie, we re ble to reon bout the exitene of heuler n to relize heuler when they exit. Furthermore, we rovie the men to imoe intertk eition by regulr lnguge whih filitte lition-ei eenenie to be mnte eily. There re everl iue within our frmework tht nee to be reolve. Thee inlue filure reovery, hnling intrtbility roblem tht my rie, imlementtion tehnique, et. Severl imle toolkit exit for the eition n mniultion of irete event ytemontrol, n we exet to ue them with our roh to it in the eveloment of workow mngement ytem. Referene [AAA + 96] G. Alono, D. Agrwl, A. El Abbi, M. Kmth, R. Gunthor, n C. Mohn. Avne trntion moel in workow ontext. In Proeeing of the Twelfth Interntionl Conferene 10

11 on Dt Engineering, [ASSR93] P.C. Attie, M.P. Singh, A. Sheth, n M. Ruinkiewiz. Seifying n enforing intertk eenenie. In Proeeing of the Nineteenth Interntionl Conferene on Very Lrge Dt Be, ge 134{145, [GHS95] D. Georgkooulo, M. Hornik, n A. Sheth. An overview of workow mngement: from roe moeling to workow utomtion infrtruture. Ditribute n Prllel Dtbe, 3:119{153, [Gun93] R. Gunthor. Extene trntion roeing be on eeneny rule. In Proeeing of RIDE-IMS, ge 207{214, [Kle91] J. Klein. Avne rule riven trntion mngement. In Proeeing of the Thirty-ixth IEEE Comuter Soiety Interntionl Conferene, ge 562{567, [KR95] M. Kmth n K. Rmmrithm. Moeling, orretne n ytem iue in uorting vne tbe lition uing workow mngement ytem. Tehnil Reort 95-50, Univerity of Mhuett, [RW87] [RW87b] [RW89] [ST94] [WR88] [WR88b] P.J. Rmge n W.M. Wonhm. Moulr feebk logi for irete event ytem. SIAM Journl of Control n Otimiztion, 25(5):1202{1218, My P.J. Rmge n W.M. Wonhm. Suerviory ontrol of l of irete-event roee. SIAM Journl of Control n Otimiztion, 25(1):206{230, Jnury P.J. Rmge n W.M. Wonhm. The ontrol of irete event ytem. Proeeing of the IEEE, 77(1):81{98, Jnury M.P. Singh n C. Tomlinon. Workow exeution through itribute event. In Proeeing of the Sixth Interntionl Conferene on Mngement of Dt, W.M. Wonhm n P.J. Rmge. Moulr uervior ontrol of irete event ytem. Mthemtil Control, Signl, n Sytem, 1(1):13{30, Jnury W.M. Wonhm n P.J. Rmge. On the ureml ontrollble ublnguge of given lnguge. SIAM Journl of Control n Otimiztion, 25(3):637{659, My