Goal models represent interests, intentions, and strategies of di erent stakeholders in early requirements engineering. When capturing requirements of socio-technical systems, goal models evolve quickly to become large and complex. Hence, understanding and maintaining such goal models become more challenging. Software engineering metric-based approaches have shown good potential in measuring software designs. In this paper, we propose a structural metric to measure actor external dependencies in GRL (Goal-oriented Requirement Language) models. We illustrate our approach by applying our metric to a goal model describing undergraduate students' involvement in research activities.
Goal models have been introduced as a means to ensure that stakeholders'
interests and expectations are met in the early requirements engineering stages. As
goal models gain in complexity (e.g., large systems involving many
stakeholders and many dependencies), they become di cult to validate, maintain, and
comprehend. These challenges led to the development of many goal-oriented
metric-based approaches [1{4]. These approaches di er in their targeted
notation, their purpose, their analysis type (e.g., quantitative, qualitative), and
their scope (e.g., global, local). In order to support the assessment and
selection of Commercial O -The-Shelf (COTS) components, Franch and Maiden [
Many simple GRL metrics (e.g., number of goals, number of actors, etc.)
are captured using the jUCMNav [
The main motivation of this research is to provide a quanti cation of structural properties of GRL models. This paper aims to: { Propose a quantitative metric to measure the Actor External Dependencies (AED) in GRL goal models (i.e., local metric at the actor level). { Provide a basis for systematic assessment of goal models with respect to the interactions between the involved actors (i.e., global metric at the model level).
{ Provide a theoretical evaluation of the proposed AED metric. The remainder of this paper is organized as follows. Our proposed GRL actor external dependency metric is presented Sect. 2. In Sect. 3, we apply our proposed metric to a GRL model describing the involvement of students in research activities. A discussion of the bene ts and threats to validity of our approach is provided in Sect. 4. Finally, conclusions and future work are presented in Sect. 5. 2
Dependencies enable reasoning about how actor de nitions depend on each other
to achieve their goals. Dependencies between stakeholders can be classi ed as
explicit or implicit. Explicit dependencies are modeled as dependency links ,
while implicit dependencies are modeled using contributions and
decompositions crossing actor boundaries. Explicit dependency links can be used in
many types of con gurations according to the required level of detail [
In what follows, we propose the Actor External Dependency metric (AED) to measure the GRL external dependencies at the actor level. The metric tends to measure the level of which the actor depends on other services provided by other actors. We use the term \element" to denote a GRL intentional element of type goal, softgoal, or task. 2.1
Metrics de nitions Dependencies between intentional elements are counted as follows: { Explicit dependencies: Goal1 Goal2, denotes \Goal1 depends on Goal2".
Hence, the outgoing dependency link is counted as a dependency for Goal1. { Implicit dependencies: (1) Goal1 Goal2, denotes \G1 is contributing to the achievement of G2", meaning that G2 depends on G1. Hence, the incoming contribution is counted as a dependency for Goal2, (2) Goal1 (Goal2, Goal3), expresses the fact that \Goal2 and/or/xor Goal3 contribute to the realization of Goal1". Therefore, the two decomposition links are counted as two dependencies for Goal1.
To measure the Actor External Dependency metric for actor a having k elements, we de ne the AED metric as follows:
AED(a) =
Pi=k a(nAEDi) i=1 nSE k k where nAED (Number of Actor External Dependencies), denotes the number of external dependencies (incoming contribution and decomposition links, and outgoing explicit dependencies) for each element enclosed in actor \a", and nSE denotes the total number of intentional elements in the model.
In addition, we calculate the average model dependency for a GRL model with m actors as:
AM D =
Pnn==1m AED(n) m
Where AED(n) is the Actor External Dependency of actor \n". 2.2
AED theoretical validation
To validate the proposed metric theoretically, we use the properties proposed by
Kitchenham et al. [
As AED satis es these properties, then this metric is theoretically valid. 2.3
AED Interpretation AED metric computes a normalized value for the actor external dependency. A lower AED value means the actor does not depend much on the services provided by other actors and hence, it is more independent. The higher the AED value, the more dependent the actor. Since AED metric measures the external dependency only, the internal connections within actors are not considered, and hence do not a ect the metric value. 3
In this section, we apply the proposed AED metric to a GRL model (see Fig. 1) that describes undergraduate student involvement in research activities. The model involves two actors (Professor and Undergraduate Student) and describes one explicit dependency stating that \In order to ensure active involvement of students in research projects, professors depend on students to show their commitment to research activities". Research opportunities may take one of the following forms: (1) Perform programming duties, and (2) Perform experiments and data collection, (3) Perform engineering or scienti c design tasks, and (4) Perform mechanical oand/or electrical assembly tasks. They are described as four tasks contributing positively (i.e., using the GRL help contribution type) to the softgoal \active involvement of undergraduate students in research projects". Student commitment to research activities is subject to either getting an academic credit for their performed tasks or have a nancial support (through hourly wages) from professors.
The AED metric is calculated as follows:
AED(P rof essor) = 6 5 +
+ In general system design, dependencies are clearly undesirable. However, in a socio-technical context dependencies may be desirable. For instance, it might be appropriate to o oad a human actor by moving some of his responsibilities to a software actor (i.e., by implementing more automation), creating new external dependencies between the human and the software actors. Hence, specifying an adequate level of dependencies requires an expert judgment and the agreement of the intervening stakeholders. While a dependency metric helps the assessment of actor interactions within a GRL model, a theoretical framework is required to guide the model redesign.
A simplistic dependency metric would consider the number of outgoing connections regardless of how many elements an actor has, while the proposed AED metric considers the number of connections with respect to the elements an actor has, which tends to show the relative dependency.
Our metric and the illustrative example are subject to some limitations and threats to validity. These limitations and threats are related to the extent to which our results can be generalized. A possible threat is that we have considered all external relations to have the same weight. However, de ning a dependency weight will always be subjective and hence we have decided to ignore the weight factor. Another possible threat is that we only proposed the Actor External Dependency. Although, this metric by itself may not provide a complete picture to understand the system complexity or dependency, it seems to be a good indicator.
The quantitative Actor External Dependency (AED) metric described in this paper provides a basis for systematic investigation of socio-technical system dependencies expressed in the GRL language. We have validated theoretically our proposed metric and have applied it to a GRL example to demonstrate its applicability. As future work, we plan to propose a metric to measure the actor internal dependencies (i.e., between intentional elements within an actor) and another metric to measure actor stability.
The authors would like to acknowledge the support provided by King Fahd University of Petroleum & Minerals (KFUPM).