Work ow Modeling and Performance Evaluation with Colored Stochastic Petri Nets
Juliane Dehnert
Technische Universitat Berlin, Sekr. E-N 7 Einsteinufer 17, 10587 Berlin, Germany
[email protected]
Introduction
Jorn Freiheit
and
Armin Zimmermann
Technische Universitat Berlin, Sekr. FR 2-2 Franklinstr. 28/29, 10587 Berlin, Germany
[email protected]
Presenting the modeling approach
There is a need for modeling and performance evaluation techniques and tools for a fast and reliable design of work ow systems. The paper introduces a modeling methodology based on colored stochastic Petri nets. For describing a business process it is necessary to consider di erent aspects. Essential are functional (In what order?), organizational (By whom?) and information related aspects (Which items/documents are processed?). Aspects related to time gain more importance additionally. Business (re)engineering projects typically try to reduce turnaround times and improve execution durations in order to improve competitiveness and customer contentedness. These questions can be answered by an evaluation of the business process performance, necessitating the exact description of all timing aspects of the process. There are only few approaches (e.g. (Erwin 1998; Ellis, Keddara, & Wainer 1998; Ferscha 1994)) considering time, which o er analysis or simulation as a means to evaluate the behavior of the work ow model. Often the notion of time is limited to the functional view. Therefore these evaluation methods can only compute performance measures assuming independence of the work ow from the environment and other concurrent processes. Moreover it is limited to deterministic delays and time constraints. Stochastically distributed durations are often neglected. In the eld of work ow performance modeling, a mixture of both stochastic and xed (deterministic) durations are necessary. Fixed times are needed to model durations of automated processes, deadlines, and routine activities with previously known delay. Stochastic durations are necessary to model human activities, stochastic events like employee absence due to sickness or holidays, and other events with unknown duration. Consequently, deterministic and stochastic durations should be integrated into the model.
We introduce a methodology for the modeling and performance evaluation of work ow processes, which tries to overcome the above mentioned limitations. The approach is not limited to the functional aspects, but includes a resource description as well. All aspects are described using the same modeling technique, namely a dedicated class of colored stochastic Petri nets (Zimmermann & Hommel 1999) (called CSPNs in the following). The suitability of Petri nets for the description of business processes has been examined and discussed extensively in the literature (van der Aalst 1998; Oberweis 1996). Within CSPN's, delays can be expressed by assigning ring delay distributions to transitions. We distinguish stochastic, deterministic, or zero ring delays for transitions. To avoid a complex description, where elements related to di erent views are mixed in one model, the concept is based on independent models for the functional aspects and the resources. The resource model describes the abilities and work ow independent properties of the work ow management system resources, such as communication connections, sta , technical resources etc. The workplans specify the actual business processes that take place for every case, and describe the work ow dependent features of the system. Each workplan can be thought of as a path through the resource model. Later on, the di erent model parts are automatically merged resulting in a complete work ow model, which then includes both the resource constraints of the system and the synchronization of the work ow steps. The use of the same description technique together with an automatic compilation of the model parts provides evaluation facilities for the whole model. Time aspects are considered in detail, facilitating a realistic system speci cation. Deterministic and di erent types of stochastic delays are allowed for the description of durations of activities as well as times associated to resources.
c 2000, American Association for Arti cial InCopyright telligence (www.aaai.org). All rights reserved.
The proposed methodology is demonstrated using an example. The considered business process describes the
Example
handling of damages and losses in a transport company. A claim handling starts when a customer message arrives, informing about a new damage event, it passes inspection and some kind of repair and ends up with a closed le sent to the archive. The possible executions of a claim handling are described in the workplans. During its work o it passes di erent oces. In detail we describe three oces of the company, namely le administration, check/decision and the main damage event handling oce. As it is usual for Petri net models, transitions model activities of the system, while places are passive elements and contain tokens that model moving and/or state changing entities. Transitions with thick bars are called substitution transitions, acting as place holders for submodels describing their behaviour in more detail on a lower level of hierarchy. Places shown as dotted circles connect the submodel with its environment. Transitions depicted as a bar re immediately without delay. Transitions drawn as empty rectangles have an exponentially distributed ring time, while transitions with deterministic delay are depicted as lled rectangles. Two colour types are prede ned in the model class: Object tokens model les, orders, letters etc. inside the work ow management system, and consist of a name and the current state. Elementary tokens cannot be distinguished, and are thus equivalent to tokens from uncolored Petri nets. They are used to model states of the resources, for instance whether an employee is busy or not. Places can contain only tokens of one type. Therefore it is possible to graphically separate object places and arcs (drawn thick) as opposed to thinly drawn elements that correspond to elementary tokens. Textual descriptions needed in colored Petri nets for the de nition of variables and colour types can thus be omitted, and the speci cation of the types of places and arcs are implicitly given.
The resource model
The resource model contains all used resources, like employees, computers, data bases, etc. and abstract possible actions of the resources, even if they are not used for the processing. Figure 1 shows the highest level of the hierarchical colored resource model. Its structure follows the layout of the modeled organization, which makes it easier to understand. Places model possible locations of objects, like les, orders, letters etc. All oces exchange documents via distributor. The input and output places model inand outgoing matters of the corresponding oces. Figure 2 shows the resource submodel of the le administration oce in more detail. The model has two parts. The transitions and places connected by thin arcs describe the behaviour and states of the employees working in this oce. The places and transitions connected by thick arcs describe the behaviour of objects like documents or memos.
check/decision check/decision_output
file_administration_input check/decision_input distributor
file_administration
damage_event_ handling_input file_administration_output
damage_event_ handling_output
damage_event_handling
Figure 1: Structure model of the damage event handling system example admonition
file_stack
begin_of_process processing file_administration_output file_administration_input employee_available in_process
interrupt_process
new_file
work_off employee_holiday end_of_work
interruption employee_working work_on
Figure 2: Structure submodel of the le administration oce The places
and connect the submodel
file administration input file administration output
with its environment.
The work ow models
In the resource model the structure of the system and possible ways of communication is summarized. The work ow model now describes the actual processes using the resources described in the resource model. Figure 3 shows the top level work ow model of the example. The work ow models describe paths through the resource model (see Figure 1). In the work ow model the arcs are inscribed by the tokens which ow through the arcs.
distributor
file_administration_input
damage_event_ message.arrived
file_administration
damage_event_ message.arrived
distributor
file_administration_output
customer.informed + central_office.informed + check/decision.ordered + damage_event_handling.ordered
check/decision.ordered distributor damage_event_handling.ordered
check/decision.ordered
damage_event_handling_input
check/decision_input
damage_event_handling.ordered
check/decision.ordered
check/decision
damage_event_handling
recourse.decided
event_list.found
damage_event_handling
check/decision_output
event_list.found
recourse.decided
distributor
distributor event_list.sent recourse.decided recourse.decided + event_list.sent file_administration_input
insurance.ordered file_administration
insurance.ordered
file_administration_output
distributor
Figure 3: Part of the top level work ow model of damage event handling
Tool support
To support the proposed methodology, a software tool is necessary. Throughout this paper the tool TimeNET is used. A recent enhancement of this tool is a modeling and evaluation environment originally intended for manufacturing systems (Zimmermann et al. 2000). We found that due to the similarities to business processes it is possible to adapt the tool for the modeling and evaluation of work ows as well. This is especially the case for strongly structured work ows like productionoriented and administrative work ow systems (van der Aalst 1998).
Evaluation
Evaluation of the performance is facilitated by associating stochastic, deterministic, or zero ring delays with transitions. Basic quantitative measures like the throughput, utilization, queue length, processing time, and others can be computed either by direct numerical analysis or discrete event simulation. This can be done using methods developed for extended deterministic and stochastic Petri nets (eDPSNs) (German 1994), because the stochastic process underlying both model types belongs to the same class. For the realistic description of times for the process steps, exponentially distributed ring delays have been associated with the normal oce tasks, while transitions modeling deadlines and in-house communication re after a xed (deterministic) delay. Therefore the
structural restriction of not more than one enabled transition with non-exponentially distributed ring delay (German 1994) is violated, forbidding the use of the direct numerical analysis methods. The simulation component of the tool TimeNET is thus used for the performance evaluation of the application example. The evaluation of the model can be used to answers questions like How many documents can be processed per week with the modeled organization? What is the mean time for a case to be nished? How big is the utilization of the resources? What are the bottlenecks? How much time does a document spend during processing, waiting, or being transported? How will the above numbers change if the available sta decreases e.g. due to holidays?
References
Ellis, C.; Keddara, K.; and Wainer, J. 1998. Modeling and Analyzing Timed Changes within Work ow Systems. Technical Report CU-CS-869-98, Department of Computer Science, University of Colorado at Boulder. Erwin, T. 1998. Leistungsbewertung von Geschaftsprozessen durch Auswertung halbgeordneter Petrinetz-Ablaufe. Master's thesis, Universitat Karlsruhe. Ferscha, A. 1994. Qualitative and Quantitative Analysis of Business Work ows using Generalized Stochastic Petri Nets. In Chroust, G., and Benczu, A., eds., CON'94: Work ow Management - Challenges, Paradigms and Products, 222 { 234. Oldenbourg Verlag. German, R. 1994. Analysis of Stochastic Petri Nets with Non-Exponentially Distributed Firing Times. Dissertation, Technische Universitat Berlin. Oberweis, A. 1996. Modellierung und Ausfuhrung von Work ows mit Petri-Netzen. Teubner-Reihe Wirtschaftsinformatik. Stuttgart, Leipzig: B. G. Teubner Verlagsgesellschaft. van der Aalst, W. 1998. The Application of Petri Nets to Work ow Management. The Journal of Circuits, Systems and Computers 8(1):21{66. Zimmermann, A., and Hommel, G. 1999. Modelling and Evaluation of Manufacturing Systems Using Dedicated Petri Nets. Int. Journal of Advanced Manufacturing Technology 15:132{137. Zimmermann, A.; Freiheit, J.; German, R.; and Hommel, G. 2000. Petri Net Modelling and Performability Evaluation with TimeNET 3.0. In 11th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation (TOOLS'2000).
