# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics
**Dr. Dmitry
Efrosinin**, Institut for Stochastic, JKU Linz,
will give a public talk (followed by a discussion) on **Wed, Jan. 12, 2011**
at **14:30 o'clock** at **HS 11**
on the topic of
"Controllable Queueing and Degradation Systems. Performance and Reliability Analysis"
. The organziers of the symposium,

Univ.-Prof. Dr. Gerhard Larcher

A.Univ.-Prof. Dr. Jürgen Maaß, and

die ÖMG (Österreichische Mathematische Gesellschaft),

hereby cordially invite you.

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

### Controllable Queueing and Degradation Systems. Performance and Reliability Analysis

Queueing and degradation systems belong to a class of dynamic stochastic systems with a given probabilistic law of motion. The queueing systems describe a service process of the customers that come randomly to the system and can be served in a random time. The degradation systems describe the behavior of the degrading unit that can completely fail in a random time by passing through different intermediate degradation states. The proposed systems are supplied by a controller or decision maker who controls the state transitions by taking a sequence of control actions according to a specified control policy. The dynamics of the systems is described by virtue of the multi-dimensional controllable Markov process.

The main goal is to find for each system with a defined cost structure an optimal control policy which minimizes the long-run average cost per unit of time and evaluate the main performance and reliability measures under given optimal control policy. We will distinguish the models where the control policy has a predefined threshold structure and the models where the structural property is unknown and must be found out. In the latter case the dynamic programming approach is applied to prove the monotonicity properties of the value function that in turn leads to the threshold property of the optimal control policy.