Discrete Event Dynamic Systems: Theory and Applications 3, (1993): 219-247 9 1993 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. Specification Techniques for Markov Reward Models* BOUDEWIJN R. HAVERKORT University of Twente, Tele-lnformatics and Open Systems, 7500 AE Enschede, the Netherlands KISHOR S. TRIVEDI Duke University, Department of Electrical Engineering, Durham NC 27708-0291 Received September 5, 1992; Revised February 25, 1993 Abstract. Markov reward models (MRMs) are commonly used for the performance, dependability, and perfor- mability analysis of computer and communication systems. Many papers have addressed solution techniques for MRMs. Far less attentionhas been paid to the specification of MRMs and the subsequent derivationof the underlying MRM. In this paper we only briefly address the mathematical aspects of MRMs. Instead, emphasis is put on specification techniques. In an application independent way, we distinguish seven classes of specification techni- ques: stochastic Petri nets, queuing networks, fault trees, production rule systems, communicating processes, specialized languages, and hybrid techniques. For these seven classes, we discuss the main principles, give ex- amples and discuss software tools that support the use of these techniques. An overview like this has not been presented in the literature before. Finally, the paper addresses the generation of the underiying MRM from the high-level specification, and indicates important future research areas. Key Words: dependability, Markov reward models, performability, performance, specification techniques, stochastic Petri nets 1. Introduction Markov reward models have become popular for the analysis of the performance, depen- dability, i.e., the reliability and/or availability [Laprie 1985], and performability of com- puter and communication systems. This is due to the nice features of MRMs in general, but also to the increased capacity (both in terms of computational speed and memory size) of modern day workstations. Many papers have addressed the numerical techniques for the analysis of possibly large MRMs, both for their steady state and transient behavior. In special cases, MRMs exhibit closed-form solutions for their steady-state probabilities; however, closed-form expressions for the transient state probabilities are rare. In case explicit solutions (often called analytical solutions) are not feasible, MRMs with finite state space can be solved numerically. ~ Apart from the use of numerical techniques, MRMs can also be solved by using discrete event simulation (DES). DES has an advantage that the MRM need not be available explicitly before the actual analysis starts. This feature is necessary when dealing with infinite state *This work was supported in part by the Naval Surface Warfare Center under contract N60921-92-C-0161 and by the National Science Foundation under grant CCR-9108114.