2 Modeling primitives


A. Törn - Contents - - Previous chapter - Next chapter - - Previous page - Next page

2.3 Hierarchical modeling

Large systems are not possible to model in one piece, some hierarchical approach is needed. This means that we start with a crude design containing the most important parts (transitions and places which may be sub-systems) and that these transitions and/or places may later be refined to model the system in greater detail. If possible we will use the arcs described in the previous sections, but sometimes this is not possible and then we will use arcs without any heads to just show dependencies. We use the one-arrival, single-server system to illustrate such modeling.
             Arrival                            Served
             Generation    Queue   Service      Items
             ___________           __________
            |___________|-->( )-->|__________|-->( )
                             Q                    SI
We now refine Arrival Generation and Service:
   ____________________
   |Arrival Generation |
   |          ______   |
   |  (•)<-->|______|----->( )
   |   G       Gen     |    Q
   |___________________|
                           ______________
                          |Service       |
                          |    ____ Serv |
                     ( )----->|____|--------->( )
                      Q   |      ^       |     SI
                          |      |       |
                          |      v       |
                          |   S (•)      |
                          |______________|
                          

The refined transitions must of course have arcs to the same places as in the crude graph. The refinements are nets on their own. It is also possible to refine places, but as this does not not add anything new, we recommend to only refine transitions.

In the arrival generation above the use of G is not clear. We could have left out G and this would not change the logic of the net. However, if transitions take time to execute, then it makes a difference.