Dynamic migration of workflows requires the notion of consistency for safe migration. The literature primarily covers consistency models based on the history of the workflow to be migrated. However, for several situations, the history based models are not enough to decide migratability of a state. The paper introduces lookahead models of consistency, which are based on the question of how the remaining part of the workflow is treated in the new process. Three lookahead models are described and are illustrated with the help of example cases of realistic migration scenarios. Moreover, in certain situations, even if there is a consistent lookahead migration possible, the tokens can not be directly migrated into the new net due to contradictory traces available in the new net. The paper also proposes an algorithm called Accept-Reject Branching to compute the contradictory segment of the new net. A detail case study of a library resource acquisition workflow is presented to highlight the contributions.
In an ever-changing business environment the business processes do not remain static. Instances of one workflow often need to follow the evolved business logic of a different, or a refined schema. When an instance migrates from the old process into the new process the issue of consistency has to be addressed. The notion of consistency ensures that a migrated instance finishes execution without encountering a runtime error or inconsistencies in application semantics.
One of the initial works discussing consistency in dynamic evolution of
workflows is by Ellis et al. [
Notable works using Petri net models of workflows, on the other hand, adopt
the notion of consistency defined on the basis of marking. In Petri net models
various process states are explicitly modeled by places. In this model a marking
represents the current state of the process. Consistent markings in the old and
the new workflow are decided based on the equivalence of states. This approach
is taken in the works by Van der Aalst [
History based consistency model derives its motivation in the need to
consider as done what is already accomplished and proceed exactly thereafter by
resuming the workflow as per the new logic. Therefore, a primary goal of
interest in history based migration is to ascertain the preconditions before migration
takes place. However, apart from the models of history and state based
consistency, dynamic workflow migration in the context of other business goals such
as resource optimization, incidental migration, and handling eventualities often
require a lookahead consistency criterion. Motivating examples of such dynamic
migration scenarios are presented in this paper, on the basis of which, we
develop the notion of lookahead consistency. A Petri net based modeling notation
called WF-net [
An algorithm for generating weak lookahead consistent migrations for workflow instances is presented. It is possible that newer paths may be available in the new net for a migrating instance. In order to enforce a stricter lookahead, these paths need to be blocked, which can be done by blocking the head-transitions of the contradictory segments. These blocking transitions are identified using an algorithm called accept/reject branching.
The paper is organized as follows. Section 2 briefly outlines the preliminaries of Petri net based workflow model. Section 3 discusses the related work and the contributions of the paper. Sections 4, 5 and 6 discuss the three lookahead consistency models with the help of realistic application scenarios. Section 7 lastly discusses the algorithms for lookahead consistency along with a case study. 2
In this section a brief background is provided for WF-net notation of Van der
Aalst [
The literature includes a variety of consistency criteria in the context of
runtime migration of workflows [
The only work in this context, where the possible lookahead parameters were
taken into account is the notion of inheritance of workflows by Van der Aalst
and Basten [
Consulting lookahead parameters in the context of dynamic web-service
protocol evolution has been identified as a necessary feature in the work of Ryu et
al. [
A benefit of these newly introduced models is that they can be used independently or in commune with the history based or state based consistency models as per the need of a particular workflow migration scenario. A lookahead based migration approach can then be applied considering the traces starting from the current state in the old workflow in the migration pair, and finding them in the new workflow to compute consistent migration.
The proposed lookahead models are demonstrated with the help of motivating cases. In the subsequent sections we define and illustrate three lookahead consistency models, which are strong lookahead consistency, accommodative lookahead consistency and weak lookahead consistency models respectively. The accommodative and the strong lookahead consistency models are specializations of the weak model, and the strong model is a specialization of the accommodative model.
In this model, consistent states in the old and the new workflows are mapped by equivalence between possible futures in both the workflows. States of the old and the new workflows are consistent if the schedules that are yet to be completed from the old workflow state are the only schedules that are possible in the new workflow after migration. The strong lookahead model does permit changes to the net as long as the set of possible future traces is the same. This model can be applied to handle migration situations in process re-engineering cases, in which, from the point of view of the current state of the migrating instance, a change should not be perceived as far as the traces, i.e. the choices and the sequences thereby are concerned. In practice, such a situation may arise due to maintenance and compatibility issues. One such situation is illustrated later through a case study of a food packaging workflow example.
The WF-net based definition of the strong lookahead consistency model is given below. We use relational operator ˛ between two markings to represent strong lookahead consistency between them. Subsequently relational operators :˛ and ˛ are used to represent the accommodative and the weak lookahead models. Definition 1 Let the old and the new workflows be modeled as WF-nets W and W 1 respectively, mf and m1f be the final markings in W and W 1 respectively, m σ be a marking in W , and m1 be a marking in W 1. Let Fm = tσ|m ÝÑ mf u, i.e. be the set of all firing sequences starting from marking m and reaching the final marking mf in the old net. Similarly, F m1 = tσ1|m1 ÝσÑ1 m1f u, i.e. be the set of all firing sequences starting from marking m1 and reaching the final marking m1f in the new net. Strong Lookahead consistency m ˛ m1 is defined by the following trace equivalence condition: (i) @σ P Fm, σ P F m1, and (ii) @σ1 P F m1, σ1 P Fm. In other words, m ˛ m1 is defined by the equality Fm “ F m1.
Old Workflow Instance New Workflow Instance in Optimized Schema
It can be noted that to satisfy the above criteria, the structure of the
downstream nets of the old and new workflows need not be the same. Intentionally
different designs resulting into the same behavior may also fit to the definition.
For example, a new net may be an alteration of its corresponding old net for
achieving an optimization in the design as shown in Fig 2. In this example, the
set of traces is tt2t3, t3t2u, which is same in both the nets. As the firings of
transitions in Petri net semantics (reachability graphs[
However, real-life workflows may have long duration tasks, in which, the
semantics of non-overlapping atomic executions may not be possible. In such
cases, the trace-based model can still be applied considering discrete events such
as commencements or completions. For example, in an academic setup, if
performing two courses in two consecutive semesters and performing them together
in parallel in one semester needs to be considered as equivalent, it can be done so
by considering the events marking the first lectures of the two courses. So, though
there is physical interleaving of the task actions, if an academic process believes
that the interleaving is acceptable as long as strong lookahead consistency is
maintained w.r.t. the courses, a migration of a student from one system to
another is possible. This assumption is useful in applying the lookahead models in
non-Petri net workflow models such as ADEPT2 [
Fig. 3 shows packaging workflows for milk-products, chocolate and dry-fruits respectively. The packaging company imports the food items in bulk from various food processing companies and delivers them to distributors after packaging. The activities of devanning, storing items in the warehouse, quality inspection, and transport for delivery are manual activities. The fourth task in the dryfruit packaging workflow is a manual task of inserting fruits by weight. Cutting of cheese and butter, food packaging in polythene or cardboard boxes, packet sealing and labeling are user assisted automated activities. As shown in the figure, in the case of dry-fruit, two kinds of packets are produced by the workflow using polythene packets or cardboard boxes. The workflow process is organized such that the packaging choice automatically alternates after regular intervals.
The packaging unit uses three different assembly-lines for the three food items. However, we can observe that polythene-based packaging of milk-products can use part of the assembly-line for the chocolate packaging once they reach the equivalent state (i.e. marking) p. Such an equivalent state is not available in the assembly-line of the dry-fruit packaging workflow due to the strictly alternating packaging designed feature. As the possible future execution sequences of the workflows for milk-products and chocolate packaging are exactly the same from the shown markings, a single assembly-line can take care of both of the packaging processes downstream the equivalent markings. The migration decision can be helpful when one assembly-line needs to be shut down for maintenance. Such a migration does not require any modification to the new process when strong Workflow for Butter and Cheese Packaging
Workoflw for Chocolate Packaging Workflow for Dry-fruit Packaging lookahead is established. As the alternating path of cardboard packaging in the dry-fruit assembly-line is not used for milk-products, the assembly-line is not suitable in this migration situation, in spite of the existence of the polythene packaging option inside the proposed new assembly.
The above example of dynamic workflow migration situation occurs in the context of resource maintenance, which is an assembly line in this case. It can be observed that the necessity of comparing the future of the running cases with the available assembly line is vital to finish the cases by dynamically migrating them. Clearly, history based consistency models do not serve a useful purpose, whereas a lookahead model captures the consistency requirement. 5
This class of lookahead consistency notion is a weaker one as compared to the earlier class. The accommodative lookahead consistency can be defined to permit new alternatives which are not found in the old net, in addition to the existing traces. In this model, if a trace is possible in the old workflow, it is also possible in the new workflow. However, the converse is not required.
Definition 2 Following the terms m, m1, mf , m1f , Fm, F m1 as used in Definition 1, Accommodative Lookahead Consistency m :˛ m1 is defined by the following trace equivalence condition: @σ P Fm, σ P F m1. In other words, Fm Ď F m1.
From the definition we can note that the accommodative lookahead consistency between m and m1, i.e. m :˛ m1, satisfies the trace equivalence condition (i) of Definition 1. Therefore, strong lookahead consistency between two markings implies accommodative lookahead consistency between them as well, i.e. m ˛ m1 ùñ m :˛ m1. Now we present a dynamic process migration scenario based on accommodative lookahead model.
Old and New Workflows for Two-year Masters Program
Old Subprocess for Each Semester
Foreign University Process
In an academic curriculum process depicted in Fig. 4, the old process in the migration situation represents a 4-semester masters program. Semesters are sequences of tasks involving orientation, registration, course work and grade reports. Course work comprises of credit courses in the first three semester, and a project in the last semester. The backlog credits are carried over into the next semester. In the process shown in the figure, the semester activities are firstly shown as single transitions of higher level, and they are expanded as a generic subprocess.
A migration situation arises when a student applies for an academic exchange program and joins a foreign university to replace a portion of her academics in the host institute. The student comes back and joins into the old process after completing the exchange credits.
The rules for the exchange program are outlined as follows: – One student can join an exchange program to study in the foreign university in her second or/and third semester. – The minimum cut-off CPI for availing the exchange program to join course work in a foreign university is 8.0. – During the study in the foreign university, a student must complete the courses equivalent to the core credit courses in the home university. – A student with CPI above 9.0 can join additional honors credit courses as electives.
The foreign subprocess that can replace sem-2 and/or sem-3 activities in the in the old 2-year program to avail the exchange program is highlighted in Fig. 4. It is only a part of a bigger process in the foreign university. A student is allowed to migrate if equivalent core credit courses are available in that semester. The list of courses offered at the foreign university website is to be consulted externally. Therefore, an application for migration are processed at states (markings) sem-1 completed or sem-2 completed. As the foreign university course work also offers the option of performing elective courses in addition to the core courses, the host institute permits the additional paths.
The above example brings us to the application of accommodative lookahead consistency at the point of migration. This migration scenario shows that a combination of past and lookahead parameters can also be used for deciding migratability. The set of new traces possible for a migrating student is a superset of the old. In this case, several historic or present parameters such as CPI, position in the academic calender are also used to determine the points of migration. 6
The third kind of lookahead consistency model is the weak model. A state of the old workflow is consistent with a state in the new workflow by the weak lookahead model if at least one of the possible future traces is retained in the future of the new net. However, the future of the new net may have additional alternative traces.
Definition 3 Following the terms m, m1, mf , m1f , Fm, F m1 as used in Definition 1, Weak Lookahead Consistency m ˛ m1 is defined by the following trace equivalence condition: For non-empty Fm, Dσ P Fm such that σ P F m1. For empty Fm, Fm “ F m1.
It can be observed that, quantifier @σ P Fm in Definition 2 is enough to find one such case required in Definition 3. Therefore, m :˛ m1 ùñ m ˛ m1. Moreover, we can obtain m ˛ m1 ùñ m ˛ m1 from the already established relation m ˛ m1 ùñ m :˛ m1.
Old Curriculum
New Curriculum
Fig. 5 depicts an example case of academic curriculum revision of a 4-semester masters program. In the old curriculum, credits for three groups of courses are to be completed in the first three semesters. Alternate branches with backlog credits are available. The allocation of a project-supervisor is arranged before the final semester project work. The program ends with project reporting. The revised curriculum emphasizes on the depth in course work rather than the extent of the covered syllabus, by reducing the number of compulsory credits for the under-performing students. After completing group-1 courses in the first semester, the students have to perform two groups of courses. They can take up group-2 and group-3 courses as per the old curriculum, or they have the option of a seminar and a mini-project course. The students having backlogs can not register for group-3 courses.
A student in the old curriculum can migrate from current state into a state in the new curriculum, the design makes available at least one path in the new which is exactly a path in the old. However, new alternatives are also open to the migrating student. One set of equivalent markings by this criteria is shown in the figure. It can be noted that for the single token in the old workflow, two tokens are generated in the new workflow, which together constitute the consistent mapping. The new workflow preserves the traces group2, group3, supervisor allocation, project, report and group2, group3, supervisor allocation, project+backlog, report from the old workflow and not the others. Some traces of the old workflow are suppressed in the new workflow. In this way, the weak lookahead model can be applied to define flexible but at least minimally compatible workflows.
In the previous sections, we have developed the lookahead consistency models and illustrated their applicability in several dynamic workflow migration situations. In this section, we first discuss the computation of weak lookahead consistent markings in the new net. Further, we discuss the approach of enforcing lookahead consistent execution on migrating instances in situations in which a weaker model is available in the new net. The accept/reject branching algorithm is then presented to support the lookahead consistency enforcement approach. The workflow nets considered in the following algorithms are considered to be acyclic. Moreover, all transition labels in the nets are assumed to be unique. 7.1
Algorithm 1 computes the weak lookahead consistent markings in the new net by replaying the lookahead traces possible in the old net. As only acyclic nets are considered, the set T races of lookahead traces is finite. For a set of computed traces in the old net, all of them may not replay in the new net. The algorithm finds out the markings in the new net each of which can replay at least one of the traces. The outputs of the algorithm are set S of weak lookahead markings and set L containing the preserved lookahead traces in the new net.
Algorithm 1: Computation of Weak Lookahead Consistent Marking Input: Old WF-net N “ pP, T, F q, Marking M in N , New WF-net
N 1 “ pP 1, T 1, F 1q
Result: Set of Markings S in N 1, Set of Preserved Lookahead Traces L 1 Let Mf and Mf1 are the terminal markings in N and N 1 respectively σ 2 T races Ð tσ | M ÝÑ Mf u 3 if T races “ tu then 4 S Ð Mf1 5 L Ð tu 6 return 7 T racesr Ð tσr | σr is reverse of σ, σ P T racesu 8 Fe1dit Ð tpx, yq | py, xq P F 1u 9 Ne1dit Ð pP 1, T 1, Fe1ditq 10 S Ð tu, Lr Ð tu 11 while T racesr ‰ tu do 12 Let σr be a member of T racesr 17 L Ð tσ | σ is reverse of σr, σr P Lru
First it computes T races, the set of lookahead traces in the old net. If set T races is empty, it indicates that the old net is already terminally marked. Therefore, the only lookahead consistent marking in the new net is the terminal marking Mf1 . Also, since there is no lookahead trace in the old instance, the set of preserved lookahead traces in the new net is also empty. Therefore, the algorithm terminates here after computing these boundary outputs. Lines 3-6 handle this boundary case.
For non-empty T races, it flips the member traces and stores them into set T racesr. Lines 8-9 reverse the arcs directions in the new net N 1 and stores the reversed net as Ne1dit. For each of the traces in T racesr, the algorithm looks for its occurrence in N 1
edit. Finally, set L contains those original lookahead traces that can be replayed in N 1, and set S contains the weak lookahead consistent markings in N 1.
The algorithm thus looks for all traces starting from the current marking in the old net, collecting all new markings corresponding to these traces in set S. Since, this collection is a set, a marking appears only once even though it can trigger more than one lookahead traces due to fork-join patterns. The set S can however have multiple markings in certain configurations as given in Fig. 6. For the example given in this figure, the algorithm starts with T races “ tt1t3, t2t3u and ends with computing S “ ttp11u, tp12uu, L “ tt1t3, t2t3u.
The motivation behind enforcing lookahead consistency is as follows. Given a marked old net and a new net schema, even though the lookahead consistent marking is supported in the new net, due to the generality of the new net, the tokens can not be guaranteed to follow the execution path as prescribed by the old model. For example, consider two consistent markings are shown in the milkproduct packaging and dry-fruit packaging workflows of Fig. 3 as per the weak or accommodative consistency model. As noted out earlier, since they do not satisfy the strong model, the assembly line of dry-fruit packaging can not take over the task of milk-product packaging. However, if we disable the traces in the new workflow which violate strong lookahead, the same can still be ensured for conforming to the desired post-migration paths. As a result, this approach achieves stricter consistency as intended for the migrating instance, which is not otherwise enforced by the new schema.
For the marking given in the milk-product packaging workflow in Fig. 3, Fig. 7 depicts the consistent marking and transition to be blocked to enforce strong lookahead consistency for the instance migrating into the dry-fruit packaging workflow. The only transition to be blocked in this case is shown as a box with thick border.
Next, the accept/reject branching algorithm given in Algorithm 2 identifies such transitions that need to be blocked to enforce the consistency preserving lookahead executions. It is assumed that a suitable implementation mechanism for disabling the transitions is available in the workflow management system.
Algorithm 2: Accept/Reject Branching
Input: WF-Net N “ pP, T, F q, Marking M in N , Set of lookahead traces Σ Result: Set of transitions Tblock 1 let pathpe0, e0q = TRUE 2 let pathpei, ejq be a boolean function indicating the existence of directed path from net element (place or transition) ei to net element ej 3 Pexchoice Ð t p | pp, tiq, pp, tjq P F , i ‰ j, Dp0 such that M pp0q “ 1, pp0, pq =
TRUE u 4 Tpotential Ð t t | t P T, p P Pexchoice, pp, tq P F u 5 Tlookahead Ð t t | σ P Σ, t P Tpotential, t P σ u 6 Tblock Ð Tpotential ´ Tlookahead
The inputs to the algorithm is a marking in the new net and the set of desired lookahead traces Σ which is set to L, the output of Algorithm 1. As output it produces the set of transitions Tblock which can be blocked to disable all the lookahead traces that are not in Σ.
First the algorithm identifies the choice gateways which are not yet traversed by the tokens in the new net. In a sequence, disabling the head-task prevents the whole sequence. Paths following exclusive-choice gateways are sequences with head-tasks as the first tasks after the choice. The algorithm finds out the set of tasks Tpotential which holds all the head-tasks following the choice gateways in the new net. Discarding those tasks from Tpotential which are not in the lookahead traces gives the remainder portion of the net which should be left as active. In this way, the algorithm finds out the tasks to be blocked as the set Tblock, which is Tpotential ´ Tlookahead.
It can be noted that blocking of lookahead transitions for the migrated instances may not be an appropriate solution in a given application. For instance, consider the case of migrated instance in Fig. 8 of the academic workflow process shown in Fig. 5. The blocked transitions are shown as boxes with thick border. As a result of blocking these transitions, the migrating student can proceed only through group2 and group3 courses. However, due to the additional constraint of the university that a student having backlogs can not register for group3 courses, such students can not be migrated since there is no path left for them in the new net. Also, migrating students can not take seminar and mini-project courses available in the changed curriculum. Therefore, with reason of retaining flexibility, blocking of transitions is not suitable for this situation. On the contrary, the approach of blocking transitions is suitable for those cases where migration is inevitable, and yet sticking to the old execution paths is necessary for application semantics. A case study of a library resource acquisition workflow given in Section 7.3 describes one such suitable migration scenario for accept/reject branching.
The following conditions summarize the inferences regarding the class of lookahead consistency that can be drawn from the outputs of the two algorithms. 1. L ‰ tu confirms weak lookahead consistency. (Algo. 1) 2. In addition, |S| “ 1 and L “ T races confirms accommodative lookahead consistency. If S contains more than one markings, no single marking can fire all lookahead traces since there are no duplicate transitions. Hence, the condition |S| “ 1. (Algo. 1) 3. In addition, Tblock “ tu confirms strong lookahead consistency. (Algos. 1, 2) 4. S “ tu implies absence of lookahead consistency. 5. If Tblock ‰ tu, blocking of the transitions in set Tblock is a mechanism to enforce the desired lookahead traces. This converts accommodative lookahead to strong lookahead. In the case of weak lookahead, the lookahead traces found can indeed be enforced by blocking these transitions.
A library resource acquisition workflow case is considered for this case study. Processes in this system are orders of the kind firm orders . (There are other types of library acquisitions such as serial subscriptions, standing orders and blanket orders which are not considered in the case study.) In the old system, the institute has separate processes of resource acquisition for the academic departments and for the central library as shown in Fig. 9a and Fig. 9b respectively. It is proposed to merge these processes into a single one. We first describe the old processes after which the new process is outlined. After this, a consistent lookahead based migration solution is worked out.
The Old Departmental Process The departmental process can be followed only for acquisition of hard-copies. First the bibliographer has to prepare the list of books to be purchased. The overall expense is then estimated and an application is sent next to the department office for approval of the budget. Arrival of the funding approval initiates the negotiation procedure with the vendors. In the case of rejection of the funding application from the department office, the workflow can proceed in one of the two ways. If the applicant can arrange money from her/his project funds, the workflow can proceed to join the flow of usual acquisition process by initiating the price negotiation. Otherwise, in the case of unavailability of funding, the acquisition case is dropped. Next, the payment is carried out for the agreed price as a confirmation of the purchase order to the vendor. Delivery of the books along with the invoice completes the resource acquisition. The workflow finishes after recording the acquisition details in the department resource database and with cataloging of the acquired resources. The Old Central Library Process The central library workflow follows similar logic for hard-copy resource purchase, though the funding agencies are different. All acquisition requests are sent to the academic office for funding approval. (a) Departmental Workflow
(b) Workflow of Central Library
Fig. 9. Library Workflows for Resource Acquisition In the case of rejection, either the Industrial Research and Consultancy Center (IRCC) supports the funding issues, or the case has to be dropped. In addition to the above, the central library workflow supports purchases of e-resource. In the case of e-resource acquisition, additional activities for license negotiation and agreement are incorporated in the workflow. Once the license is signed, its copy is received by the library which is recorded in the central library database. After payment, the e-resource is activated. According to the license agreement, this step can involve storing a local copy of the resource or enabling password protected access of the document residing on its remote host. Cataloging of the resource is performed on the central library database, which wraps up the process.
Process Re-engineering A process re-engineering team decides to merge all the departmental workflows with the central library workflow due to the following reasons. – A consolidated storage of the library resources across all the academic departments can achieve better resource sharing among several departments, to the benefit of multi-disciplinary studies and projects. – E-resource acquisition can be performed using the departmental or individual project funds introducing a level of flexibility. – Individual departments can leave the responsibilities of library-staff recruitment and related activities to the central library authority reducing the redundant efforts in the old system.
As a result, the department resource databases has to be merged with the central library database. Secondly, the running instances need to be migrated in a consistent way by applying appropriate models as per the needs of individual old cases. It is observed that the task record acquisition details & catalog in the old process updates department resource database, whereas, in the new merged process it updates the central library database. This requires migration of all old incomplete instances into the new schema.
shows such an on-going workflow instance that is in state funds available. The migration scenario requires weak lookahead consistency criterion for the safe migration of the running instances in order to complete the hard-copy acquisition process from the department. The merged workflow schema and the migrated marking is shown in Fig. 10b.
In addition to the migration, the situation requires that the same path be enforced for the migrating instance without giving the additional flexibility of the alternative of e-resource purchase. Therefore, the execution of these running cases must be prevented from traversing the path for e-resource purchase, which is achieved by blocking the transitions which are output of the accept/reject branching algorithm. The traces of both the algorithms are given below. – T races “ t negotiate price, payment, recv. delivery & invoice, record acquisition details & catalog u. – L “ t negotiate price, payment, recv. delivery & invoice, record acquisition details & catalog u. – S = t funds available u. – Pexchoice “ t funds available, payment complete u. – Tpotential “ t negotiate price, negotiate price and license, recv. delivery & invoice, activate e-resource u. – Tlookahead “ L. – As a result, Tblock “ t negotiate price and license, activate e-resource u. – It can be noted that, L ‰ tu ensures weak lookahead consistency. Further, |S| “ 1 and L “ T races ensures accommodative lookahead consistency. However, Tblock ‰ tu implies that strong consistency is not supported by the modified workflow schema.
The transitions in set Tblock are shown as boxes with thick border in Fig. 10b. These transitions can be blocked in the new workflow execution environment (a) Old Instance in-progress (b) Migrated Instance in Merged Workflow
Fig. 10. Instance Migration into the Re-engineered Workflow only for this migrating instance to enforce its required lookahead consistency as discussed above. 8
In the literature, execution history based consistency notions are widely adopted wherever dynamic evolution and adaptation of workflows are considered. The proposed new model of lookahead consistency uses the remainder of the workflow instead of the completed history in defining consistency between states in a migration scenario. Three broad classes of the lookahead consistency were brought out with illustrative examples. The weak lookahead model looks for preservation of at least one lookahead trace of the old instance across the new net. For accommodative lookahead model, preservation of all lookahead traces of the old instance is necessary. The strong model requires the lookahead traces of the old instance and its migrated marking in the new net to be same. Strong lookahead implies accommodative lookahead, which in turn implies weak lookahead consistency.
Besides their usefulness and the inter-relationships among the models, two related algorithms were also presented for deciding lookahead consistency, computing token transfer, and for lookahead trace enforcement. The new set of lookahead models provide future-centric approaches of varying flexibility for token transfer in dynamic migration scenarios with applications to process re-engineering and maintenance. A case study of library resource acquisition workflow demonstrated the relevance of the approach.
As the past execution traces are not taken into account in the context of
lookahead based consistency models, these can not be used stand-alone in
situations requiring history equivalence. However, the lookahead models can also
be applied in combination with history equivalence as per the needs of business
goals. The algorithms for acyclic nets were implemented in GNU Octave [