Step 2: Generating the State Space

Once the model has been created , it can be solved either analytically or via simulation. Since all events are exponential in the M/M/1/k model, it is possible to generate the Markov chain and to solve it analytically. (The tool allows a class of non-Markovian models to be solved analytically as well. See chapter for details.)

To generate the state space, click on ``Mathematical Model Module''. Figure shows the corresponding graphical interface.

Figure: The Mathematical Model Module.

The parameter Max number of states limits the total number of states that will be generated by the program. If we set it to zero, no limit is used. This limit is useful during the debugging of the model, and it is advisable to explicitly set this parameter to avoid generating an unexpected very large state space due to specification errors.

In the next step, we must specify. This information is useful for the hash function used by the search engine. Note that only a rough upper bound on the value of each state variable is needed, not a precise value. If we click on the Extract button, the name of the state variables are extracted from the model and displayed in the interface. The maximum values can then be set.

In our example model, the Server_Queue is limited to $100$ and so the maximum value of the state variable queue (Server_Queue object) should be at least $100$. Then

Variable Name                Max Value
Server_Queue.queue              100

Now we are able to generate the state space of the model. To run the generator program, click on the Generate button.

Several files are generated after this process is over. These files give the following information: the infinitesimal generator matrix of the model, the corresponding transition probability matrix of the model (if the matrix is uniformized), the state space of the model, and other information that will be used as input for other modules of the TANGRAM-II tool.

Now we are able to solve for the steady state of the model.