Modeling computer systems evolutions: non-stationary processes and stochastic Petri nets-application to dependability growth

Stochastic Petri nets (SPNs) have emerged over the years as a favored approach for performance and dependability modeling and evaluation. Their usual utilization assumes that systems specification and design do not evolve, in opposition to real-life. This paper is aimed at a preliminary exploration of how to take advantage of the existing body of results on SPNs for modeling the evolution of computer systems, i.e. to model non-stationary stochastic processes. It focuses on dependability evolutions which result from successive releases. Introduction Modeling and evaluating computer systems, with respect to either or both performance and dependability, is undoubtedly a flourishing domain. Modeling and evaluation of performance, or of dependability with respect to physical faults, has largely focused on the influence of system structure, together with a) workload when performance is of interest, b) fault occurrence and manifestation for dependability, and c) both workload and faults when performance and dependability, i.e. performability is of interest. Out of the corresponding methods and techniques, stochastic Petri nets (SPNs) and their many flavors (generalized SPNs, extended SPNs, deterministic and stochastic Petri nets, stochastic activity networks; see [2] for a recent survey) have emerged over the years as a widely favored approach. From a system modeler viewpoint, SPNs enable attention to be focused on the logic of the system, especially on the interactions and dependencies (either functional or stochastic, or both) between classes of components, and to handle in a modular way the number of components within each class. Over the The work reported in this paper has been partially supported by the ESPRIT Basic Research Action PDCS-2 (Predictably Dependable Computing Systems, Action no. 6362). years, the underlying stochastic processes which can be handled by SPNs (see e.g. [3]) have evolved from homogeneous Markov processes, to semi-Markov processes, and more recently to Markov regenerative processes, without leaving aside the transformation of nonMarkov situations into Markov processes via the device of stages, also called “phase-type expansion”. Keeping the above-mentioned essential property of expressing the system logic, the handling of non-Markov situations, and thus of the influence of the past history on the future system behavior, is expressed at the Petri net level. This increase in the expressiveness power of the SPNs has been accompanied by important developments in the processing of the SPNs for evaluating the performance, dependability or performability measures for complex SPNs, either via direct simulation of the net (for instance thanks to the variance reduction techniques), or via the processing of the Markov chain isomorphic to the reachability graph (for instance thanks to the randomization techniques). The net result of the evolution briefly recalled above, is that SPNs have reached a degree of maturity such that they can handle realistically the current complex computer systems; the corresponding models can be built and processed under less and less strong assumptions, and powerful software packages are available to assist the modeler, such as ESPN, GreatSPN, SPNP, SURF-2, TOMSPIN, UltraSAN, etc. However, a strong implicit assumption is that the modeled system is not evolving over time, i.e. its specification and design do not change. In terms of the underlying stochastic processes, this means that all those studies are concerned with stationary processes, be the performance or dependability measures evaluated for transient or steadystate situations. On the other hand, modeling and evaluation of dependability with respect to design faults has naturally focused on non-stationary processes, mainly devoted to software reliability evaluation. A large number of reliability