QoS Analysis of Weighted Multi-state Probabilistic Networks via Decision Diagrams Roberta Terruggia and Andrea Bobbio Dipartimento di Informatica, Universit`a del Piemonte Orientale, 15121 Alessandria, Italy {roberta.terruggia,bobbio}@mfn.unipmn.it Abstract. Network reliability analysis is usually carried out under the simplified hypothesis that the elements of the network are binary entities that can be in one of two mutually exclusive states, perfect functioning or failed. The present paper enlarges this view from two points of view. The elements of the networks are described by multiple states that can represent a variety of different situations, like degradation levels or mul- tiple failure modes. Furthermore, in order to increase the description power of the model, we assign to each state a weight describing a perfor- mance attribute of the element in that state. The weights may assume different physical meanings so that different Quality of Service (QoS) indicators may be evaluated. We show that the QoS analysis of a multi- state weighted probabilistic network can be performed by resorting to data structures called Multi-valued Decision Diagrams. Several exam- ples illustrate the methodology. 1 Introduction Most works in reliability theory are based on the traditional binary concept of reliability models allowing only two possible states for a system and its compo- nents, perfect functionality or complete failure. A variety of different algorithms for system reliability evaluation of binary systems have be presented in the liter- ature, but in the last years, methods based on Binary Decision Diagrams (BDD) have become predominant [7,1]. However, many real-world systems are composed of multi-state components, with different performance levels and several failure modes with various effects on the system’s entire performance. Such systems are called Multi-State Sys- tems (MSS). Under multi-state assumption, the relationship between component states and system states is much more complicated and the analysis becomes more complex [11,19]. Even the term ”reliability” becomes inappropriate, since the combination of different states for the components may provide different levels of performance for the whole system. In this case, a more appropriate and meaningfull measure is to evaluate the level of the Quality of Service (QoS) provided by the system as a combination of the states of its components. The definition and formalization of MSS can be traced long back in the reliability literature [8] but only recently, various extensions of Decision Diagrams have E. Schoitsch (Ed.): SAFECOMP 2010, LNCS 6351, pp. 41–54, 2010. c  Springer-Verlag Berlin Heidelberg 2010