Non-Markovian Models

The tool allows the solution of a class of non-Markovian models. Presently, the models that can be solved are restricted to those in which at most one deterministic event is enabled at any one time. The deterministic events may be enabled by any event and disabled by exponential events.

In this method an embedded Markov chain is constructed at special time points (embedded points). In any interval between embedded points, there may be either zero or a single deterministic event enabled. For instance, assume that the model consists of a single-server queue with deterministic service times. The embedded points are the service completion instants and the beginning of a busy period. Once the embedded points are determined, the transition probabilities between them are found, and then the measures of interest (see [#!embed95!#] for details on the solution technique).

To use this method, choose the button Analytical Model Solution and then click on Non-Markovian models. The interface is shown in .

Figure: Non-Markovian Models.

The following parameters must be specified :

Measures of Interest

The measures of interest are the marginal probabilities that the system spent in the specified states (see chapter for details).

Solution Methods

Steady-state solution for solving the embedded chain (Methods :, Power, or SOR).

Precision

Max number of iterations

as defined for Iterative Methods.

During the intervals in which a deterministic event is enabled, a group of objects may evolve independently of other groups in the model. The solution technique we employ can take advantage of this behavior to reduce the computational costs of calculating the transition probabilities between embedded points.

NOTE: It is not allowed to run PMF when the file selected is from a non-Markovian solution.

NOTE: Every non-Markovian model must have an independent_chains object. This object specifies the deterministic event, a set of ``chains'', and associated objects. A set of objects associated with a chain must evolve independently of other objects associated with another chain. This special object can be found in the library (Domain TANGRAM2_OBJECTS). In the ``Model with Deterministic Server'' example (chapter ), we show an example of the use of the independent_chains object.

WARNING: The order of the objects in any chain must be exactly the same as the order of the list of objects in the Mathematical Model Module window.

WARNING: The specification of the ``independent chains'' is for the sophisticated user who is familiar with the solution technique. If the user is not familiar with that technique, he should associate all objects with a single chain for each deterministic event.