Direct Method

The interface to compute an approximation for the transient state probabilities based on [#!technicalreportespa!#], using a direct method, is shown in Figure . This method has computational advantages when the matrix has a special structure.

Figure: Point Probabilities Interface - Approximation Technique (Direct).

The input parameters are:

1. . The initial probabilities at time zero.
2. . The time points at which point probabilities will be calculated.
   • Final Time: this time is the last observation point.
   • Number of points: the total number of observation points in the given time interval.
   • erlang Stages: the total number of Erlang Stages to be used in the approximation (See [#!ross!#,#!PMCCS4!#] for more details about this parameter).
3. Block Set. The direct method assumes that the matrix is partitioned into $K$ blocks. The user has to define the initial state, the block size, and the number of blocks.
4. Measures of Interest
   • State Probability: with this option the point probability at time $t$ is obtained.
   • Probability of a set: with this option, the probability that the system is in a set of states at time $t$ is calculated. In this case the user has to specify the set of states using the global reward object Global_Rewards.sym . The states included in the set are those that satisfy the condition defined for the global reward.
   • Expected Value: with this option the expected value at time $t$ of one state variable is calculated. In this case the user has to specify in the model a with the value of the state variable.
5. State_var. This parameter is specified only if the ``Expected Value'' option is chosen.