For the effective modelling, Alvis communication diagrams enable distributing parts of a diagram across multiple subdiagrams called pages. Pages are combined using the so-called substitution mechanism. An agent on one level can be replaced by a page on the lower level. Such a substituted agent is called hierarchical one. On the other hand, a part of a communication diagram can be treated as a module and represented by a single agent on a higher level. Thus, communication diagrams support both top-down and bottom-up approaches.

The substitution mechanism is based on a binding function π that maps ports of a hierarchical agent to ports with the same names (called join ports) on the corresponding page. If the function is a bijection the substitution is called a simple one.

Page D1 with hierarchical agents.

Subpage D2 for agent B.

A hierarchical agent can be replaced with its subpage using the following algorithm (for the considered example):

1. Remove the agent B from the page D1 with all its connections.
2. Move the contents of the page D2 onto the page D1.
3. Add connections - If after removing of the agent B, from the page D1, it has been removed a connection between ports B.a (port a of agent B) and X.p, then we add a connection between ports X.p and π(B.a) with the same direction as the removed one.

Page D1' with agent B replaced with its subpage.

A port of a hierarhical agent may have assigned more than one join port on the subpage. In such a case the binding function π is not a bijection and the substitution is called an extended one. Of course all join ports that are connected with a port of the corresponding hierarchical agent must have the same names, and thus they must belong to different agents.

The following figures present the communication diagram for a model of the well-known readers-writers problem. We have two kinds of agents called readers and writers respectively that use a shared resource called library here. At most, one writer can use the library at any time, but a few readers can use it at the same time. The considered model contains four readers and two writers.

Page System.

Page Readers.

Page Writers.

To present the way such pages are connected the so-called page hierarchy graph is used. Edges of a page hierarchy graph are labelled with names of hierarchical agents, while nodes represent pages in the corresponding model. The System node represents the top level page (so-called primary page) of the considered model. If a hierarchical communication diagram contains only one primary page it is a tree. Otherwise, it is a forest.

Page hierarchy graph.

The result of replacing of agents Readers and Writers with their subpages is presented in the following figure.

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