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Introduction
Workflow Analysis
Conclusions and Future Research
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Computer Science
Information Systems

Modeling and Analysis of Workflows Using Petri Nets

Profile image of Nabil AdamNabil Adam

1998, Journal of Intelligent Information Systems

https://doi.org/10.1023/A:1008656726700
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28 pages

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Abstract

A workflow system, in its general form, is basically a heterogeneous and distributed information system where the tasks are performed using autonomous systems. Resources, such as databases, labor, etc. are typically required to process these tasks. Prerequisite to the execution of a task is a set of constraints that reflect the applicable business rules and user requirements.

Figures (10)
Table 1. Some dependencies and their classification
Table 1. Some dependencies and their classification
Figure 1. A Travel Reservation workflow
Figure 1. A Travel Reservation workflow
The input and output sets of the places and transitions are as follows: et; ={pj, po}, et2 = {po}, tie = {ps}, toe = {pa}, eps = {ti}, eps = {to}, pie = {ti}, and poe = {ti, to}. The initial state of the PN is shown in Figure 2(a) (i.e., time =0) where p, and po are marked with one token each. Since both places in the input set of ¢; are marked (i.e., both m(p1), m(p2) > 0), ty is enabled. Similarly, tz is also enabled as m(p2) > 0. Although both ¢; and tz are enabled, firing one transition will disable the other. Thus, this net will result in two different firing sequences. Suppose ¢, fires first, it results in a new marking where the tokens from p, and p2 are removed and a token is placed in ps, as shown in Figure 2(b). Since p2 is empty, t2 is now disabled. The second firing sequence would result in by firing tz first. It removes one token from p2 and deposits one into 4, thus resulting in a marking as depicted in Figure 2(c). Since pz is empty, t, is disabled. Because there are no more transitions to fire after firing either t, or t2, the PN stops (said to be not live).
The input and output sets of the places and transitions are as follows: et; ={pj, po}, et2 = {po}, tie = {ps}, toe = {pa}, eps = {ti}, eps = {to}, pie = {ti}, and poe = {ti, to}. The initial state of the PN is shown in Figure 2(a) (i.e., time =0) where p, and po are marked with one token each. Since both places in the input set of ¢; are marked (i.e., both m(p1), m(p2) > 0), ty is enabled. Similarly, tz is also enabled as m(p2) > 0. Although both ¢; and tz are enabled, firing one transition will disable the other. Thus, this net will result in two different firing sequences. Suppose ¢, fires first, it results in a new marking where the tokens from p, and p2 are removed and a token is placed in ps, as shown in Figure 2(b). Since p2 is empty, t2 is now disabled. The second firing sequence would result in by firing tz first. It removes one token from p2 and deposits one into 4, thus resulting in a marking as depicted in Figure 2(c). Since pz is empty, t, is disabled. Because there are no more transitions to fire after firing either t, or t2, the PN stops (said to be not live).
The PN representation of a strong-causal control flow dependency between two tasks tw; and tw; employs a buffer place bf? with an input arc from pr; and an output arc going to pr;, as shown in Figure 5. Thus, ensuring that pr; fires only if pr; fires.
The PN representation of a strong-causal control flow dependency between two tasks tw; and tw; employs a buffer place bf? with an input arc from pr; and an output arc going to pr;, as shown in Figure 5. Thus, ensuring that pr; fires only if pr; fires.
Figure 8. Multiple dependencies with logic relations Figure 7. PN modeling for external dependencies
Figure 8. Multiple dependencies with logic relations Figure 7. PN modeling for external dependencies
Figure 6. A PN representation of a precedence type control-flow dependency
Figure 6. A PN representation of a precedence type control-flow dependency
€j1,--+;€im) depends on the resultant value of the task. Value dependencies between two tasks tw; and tw, can be modeled similar to the control flow dependencies by introducing a buffer bf, between the appropriate values of tasks tw; (1.¢., ei1,..., ein in Figure 9) and tw; (prj).
€j1,--+;€im) depends on the resultant value of the task. Value dependencies between two tasks tw; and tw, can be modeled similar to the control flow dependencies by introducing a buffer bf, between the appropriate values of tasks tw; (1.¢., ei1,..., ein in Figure 9) and tw; (prj).
Figure 10. The Main Data Entry Screen of IDEF2
Figure 10. The Main Data Entry Screen of IDEF2
Figure 11. An example showing the working of TC PN
Figure 11. An example showing the working of TC PN

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