  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.
