Transient analytical solvers

In many cases, the modeler is interested in calculating measures for a relatively ``short'' interval, and so the results obtained from the steady state solution $(t \rightarrow \infty)$ are not good approximations for the desired measures.

There are many examples which show the importance of determining the transient behavior of the system being modeled. For instance:

1. In the analysis of systems that have to remain operational in a given interval of time (usually called the system mission time), such as on-board aircraft computers, satellite systems, etc. In these cases, possible questions to be answered are related to the probability that the system will fail during the mission time. A failure in the system can be catastrophic or can cause considerably loss of revenues.
2. Consider a model of a data communication channel with limited buffer. There are many important questions to be answered such as: ``what is the probability that a packet is lost due to buffer overflow, during a given interval of time ?'' Or ``how long does it take until a packet is lost ?''
3. Transient analysis is also useful to determine equilibrium results in many models. For instance, the steady-state behavior of regenerative processes may be characterized by the behavior of the process over a cycle (finite time between two regeneration points).

See [#!transol2000!#] for a survey on .

The interface for transient analysis is shown in Figure . It can be seen from the figure that we can obtain three types of transient measures: , Distributions, and Expected Values (see also Figure .

Figure: The Transient Methods.

Most of our transient solution methods are founded on the technique (see references [#!SouG86!#,#!SouG96!#,#!transol2000!#,#!SouG96!#,#!billy-book!#,#!book-escola92!#].)