Measures of Interest

For this model we will pay special attention to how to use the Measures of Interest module. Click on the Measures of Interest module. The interface is shown in Figure .

Figure: The Measures of Interest module.

For any measure of interest, we must select a file that contains the steady-state or transient probabilities of the model. This file is generated by the solution method chosen in the Analytical Model Solution module. In this example, we use the file generated by the no block Method. We also have to specify the file to store the results that we want to obtain (calculated measures of interest). The Measures of Interest module has three different sections:

- In this section we are able to calculate the probability mass function of one or more state variables. For this, it is necessary to choose the variable of interest in the Choose Variables box. If we want to obtain conditional probabilities, we must select the Conditional box. Then the conditional pmf of the selected state variables will be calculated. Suppose that we want to obtain

1. PMF of the Switch_2x2.queue_1 - Choose the Switch_2x2.queue_1 variable, select a name for the measure of interest file and click on the Evaluate button. To see the result, click on the Plot button, select the file generated, and click on the GNUPlot button. Figure shows the result.

   Figure: The PMF of the Switch_2x2.queue_1 object.

   
2. PMF of the Switch_2x2.queue_1 conditioned on the state of the On_Off_Source_1 and of the On_Off_Source_2 - To calculate the PMF of Switch_2x2.queue_1 conditioned on the On_Off_Source_1 and the On_Off_Source_2 being in the ON state, specify the condition
   (On_Off_Source_1 = 1) & (On_Off_Source_2 = 1)
   IMPORTANT: We must use parentheses to specify functions. If parentheses are not employed carefully, wrong results may be generated.

- Suppose we want to calculate the probability of a function of two or more state variables. For example, we may be interested in the probability that a state variable is equal to three times the value of another state variable. To specify the appropriate function we select the corresponding tabbed pane in Figure . As another example, suppose that we have two objects in the model with their respective state variables and we want to obtain the probability that the sum of these two state variables is less than a specific value. To do this, we must specify the function (state_variable_1_name) + (state_variable_2_name) < value.
If we select the Conditional option, the conditional probability of this function of the state variables is computed.
Other examples:

• If we want to obtain the probability that the sum of Switch_2x2.queue_1 and Switch_2x2.queue_2 is equal to 2, we have to specify the following function: (Switch_2x2.queue_1 + Switch_2x2.queue_2) = 2. We can also calculate the probability that Switch_2x2.queue_1 equals twice
  Switch_2x2.queue_2. This measure is specified by
  (Server_Queue_1.queue) = 2*(Server_Queue_2.queue).
• Conditional Behavior of Queues 1 and 2 - Suppose that we want to obtain the probabilities above, conditioned on the On_Off_Source_1 being ON. In this case it is necessary to click on the Conditional option and construct the function
  (On_Off_Source_1.status = 1).

- This section is used when we want to obtain the probability of a set of states. We can also use the Conditional option as in the previous sections. For example, suppose that we want to obtain the probability that the size of Queue 1 is 2 and the size of Queue 2 is 3, given that Source 2 is ON. To do this we specify the function (Switch_2x2.queue_1 = 2) & (Switch_2x2.queue_2 = 3). The condition is (On_Off_Source_1 = 1).

Average Rate Reward

- This section is used when we want to obtain the average at time $t$ or in steady-state. In fact, it is computed as an inner product of the reward vector and the probability vector.

Average Impulse Reward

- This section is used when we want to obtain the average at time $t$ or in steady-state. We consider the probability that the model is in a state, say $s_i$, multiply by the probability that occurs an transition to a other state, say $s_j$, and multiply by the impulse reward. Then we sum over all possible combinations.
NOTE: In ``PMF of one or more state variables'', ``Function of state variables'', and ``Probability of a set'', we can select more than one state probabilities file. In this case, the will generate a specific file for each time interval and a file with the interest measure for all time intervals.