Transaction processing systems are judged by users to be correctly functioning not only if their transactions are executed correctly, but also if most of them are completed within an acceptable time limit. Therefore, we propose a definition of availability for systems for whom there is a notion of system failure due to frequent violation of response time constraints. We define the system to be available at a certain time if at that time the fraction of transactions meeting a deadline is above a certain user requirement. This definition lends to very different estimates of availability measures such as system downtimes as compared with more traditional measures. We conclude that for transaction processing systems, where the user's perception is important, our definition more correctly quantifies the availability of the system.

Stochastic Petri net models of large systems that are solved by generating the underlying Markov chain pose the problem of largeness of the state-space of the Markov chain. Hierarchical and iterative models of systems have been used extensively to solve this problem. A problem with models which use fixed-point iteration is the theoretical proof of the existence, uniqueness and convergence of the fixed-point equations, which still remains an "art". In this paper, we establish conditions, in terms of the net structure and the characteristics of the iterated variables, under which existence of a solution is guaranteed when fixed-point iteration is used in stochastic Petri nets. We use these conditions to establish the existence of a fixed point for a model of a priority scheduling system, at which tasks may arrive according to a Poisson process or due to spawning or conditional branching of other tasks in the system.

We discuss the role of modeling in the design and validation of life-critical, real-time systems. The basics of Markov, Markov reward, and stochastic reward net models are covered. An example of a nuclear power plant cooling system is developed in detail. Multilevel models, model calibration, and model validation are also discussed.>

Presents a performance analysis of a heterogeneous multiprocessor system where tasks may arrive from Poisson sources as well as by spawning and probabilistic branching of other tasks. Non-preemptive priority scheduling is used between different tasks. Stochastic reward nets are used as the system model, and are solved analytically by generating the underlying continuous-time Markov chain. An approximation technique is used, that is based on fixed-point iteration to avoid the problem of a large underlying Markov chain. The iteration scheme works reasonably well, and the existence of a fixed point for the iterative scheme is guaranteed under certain conditions.>