Abstract
In this work, the modeling and stability problem for queueing systems with failures in their normal operation is considered. Two types of failures are contemplated. The first one due to server breakdown while the second due to consumer interruption while in service. Timed Petri nets is the mathematical and graphical modeling technique utilized. Lyapunov stability theory provides the required tools needed to aboard the stability problem for fault queuing systems modeled with timed Petri nets. Employing Lyapunov methods, a sufficient condition for stabilization is obtained. It is shown that it is possible to restrict the fault queuing systems state space in such a way that boundedness is guaranteed. However, this restriction results to be vague. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.
| Original language | English |
|---|---|
| Pages (from-to) | 373-384 |
| Number of pages | 12 |
| Journal | Neural, Parallel and Scientific Computations |
| Volume | 20 |
| Issue number | 3-4 |
| State | Published - Sep 2012 |
Keywords
- Fault queuing systems
- Lyapunov methods
- Max-plus algebra
- Timed Petri nets