Abridged Petri Nets

A new graphical framework, Abridged Petri Nets (APNs) is introduced for bottom-up modeling of complex stochastic systems. APNs are similar to Stochastic Petri Nets (SPNs) in as much as they both rely on component-based representation of system state space, in contrast to Markov chains that explicitly model the states of an entire system. In both frameworks, so-called tokens (denoted as small circles) represent individual entities comprising the system; however, SPN graphs contain two distinct types of nodes (called places and transitions) with transitions serving the purpose of routing tokens among places. As a result, a pair of place nodes in SPNs can be linked to each other only via a transient stop, a transition node. In contrast, APN graphs link place nodes directly by arcs (transitions), similar to state space diagrams for Markov chains, and separate transition nodes are not needed. Tokens in APN are distinct and have labels that can assume both discrete values ("colors") and continuous values ("ages"), both of which can change during simulation. Component interactions are modeled in APNs using triggers, which are either inhibitors or enablers (the inhibitors' opposites). Hierarchical construction of APNs rely on using stacks (layers) of submodels with automatically matching color policies. As a result, APNs provide at least the same modeling power as SPNs, but, as demonstrated by means of several examples, the resulting models are often more compact and transparent, therefore facilitating more efficient performance evaluation of complex systems.Comment: 17 figure

Separation of Circulating Tokens

Self-stabilizing distributed control is often modeled by token abstractions. A system with a single token may implement mutual exclusion; a system with multiple tokens may ensure that immediate neighbors do not simultaneously enjoy a privilege. For a cyber-physical system, tokens may represent physical objects whose movement is controlled. The problem studied in this paper is to ensure that a synchronous system with m circulating tokens has at least d distance between tokens. This problem is first considered in a ring where d is given whilst m and the ring size n are unknown. The protocol solving this problem can be uniform, with all processes running the same program, or it can be non-uniform, with some processes acting only as token relays. The protocol for this first problem is simple, and can be expressed with Petri net formalism. A second problem is to maximize d when m is given, and n is unknown. For the second problem, the paper presents a non-uniform protocol with a single corrective process.Comment: 22 pages, 7 figures, epsf and pstricks in LaTe

Modelling Requirements for Content Recommendation Systems

This paper addresses the modelling of requirements for a content Recommendation System (RS) for Online Social Networks (OSNs). On OSNs, a user switches roles constantly between content generator and content receiver. The goals and softgoals are different when the user is generating a post, as opposed as replying to a post. In other words, the user is generating instances of different entities, depending on the role she has: a generator generates instances of a "post", while the receiver generates instances of a "reply". Therefore, we believe that when addressing Requirements Engineering (RE) for RS, it is necessary to distinguish these roles clearly. We aim to model an essential dynamic on OSN, namely that when a user creates (posts) content, other users can ignore that content, or themselves start generating new content in reply, or react to the initial posting. This dynamic is key to designing OSNs, because it influences how active users are, and how attractive the OSN is for existing, and to new users. We apply a well-known Goal Oriented RE (GORE) technique, namely i-star, and show that this language fails to capture this dynamic, and thus cannot be used alone to model the problem domain. Hence, in order to represent this dynamic, its relationships to other OSNs' requirements, and to capture all relevant information, we suggest using another modelling language, namely Petri Nets, on top of i-star for the modelling of the problem domain. We use Petri Nets because it is a tool that is used to simulate the dynamic and concurrent activities of a system and can be used by both practitioners and theoreticians.Comment: 28 pages, 7 figure

Artifact Lifecycle Discovery

Artifact-centric modeling is a promising approach for modeling business processes based on the so-called business artifacts - key entities driving the company's operations and whose lifecycles define the overall business process. While artifact-centric modeling shows significant advantages, the overwhelming majority of existing process mining methods cannot be applied (directly) as they are tailored to discover monolithic process models. This paper addresses the problem by proposing a chain of methods that can be applied to discover artifact lifecycle models in Guard-Stage-Milestone notation. We decompose the problem in such a way that a wide range of existing (non-artifact-centric) process discovery and analysis methods can be reused in a flexible manner. The methods presented in this paper are implemented as software plug-ins for ProM, a generic open-source framework and architecture for implementing process mining tools