Recursion with Tangram messages

Imagining the Geometric_Bulk object from figure as a closed black box, all one can see is that it transforms a single message received by it into a new set of $X$ messages, where $X$ is a strictly positive geometric random variable. In order to accomplish that, it needs to perform a few tricks.

Figure: The Geometric_Bulk object.

The object has a reference to itself, denoted by the constant MYSELF declared with the Object type. Upon receiving a message at port PORT_IN, the object executes one of two possible actions:

• With probability $P$, it sends the final message in the bulk through PORT_OUT and stops.
• With probability $1-P$, it sends a message to the server and another one to itself at PORT_IN, which regenerates the process.

The keep ocurring until the state with the queue full is reached. From there, when a new message is generated by the bulk object, the model remains at the same state and Tangram stops the recursion.

If the server queue has a maximum size of $N$ customers, then the Tangram-II Markov chain generator explores the state space as depicted in figure .

Figure: The recursion tree generated by Geometric_Bulk object from the initial state.

In conclusion, we may notice that with the idea of recursive messages, Tangram-II can generate state spaces that, at first, may not be obvious how to model.