On the existence of uni-instantaneous Q-processes with a given finite mu-invariant measure

Let S be a countable set and let Q = (q(ij), i, j is an element of S) be a conservative q-matrix over S with a single instantaneous state b. Suppose that we are given a real number mu >= 0 and a strictly positive probability measure m = (m(j), j is an element of S) such that Sigma(i is an element of S) m(i)q(ij) = -mu m(j), j 0 b. We prove that there exists a Q-process P(t) = (p(ij) (t), i, j E S) for which m is a mu-invariant measure, that is Sigma(i is an element of s) m(i)p(ij)(t) = e(-mu t)m(j), j is an element of S. We illustrate our results with reference to the Kolmogorov 'K 1' chain and a birth-death process with catastrophes and instantaneous resurrection.

Functional analysis of a real-time protocol for networked control systems

Traditional real-time control systems are tightly integrated into the industrial processes they govern. Now, however, there is increasing interest in networked control systems. These provide greater flexibility and cost savings by allowing real-time controllers to interact with industrial processes over existing communications networks. New data packet queuing protocols are currently being developed to enable precise real-time control over a network with variable propagation delays. We show how one such protocol was formally modelled using timed automata, and how model checking was used to reveal subtle aspects of the control system's dynamic behaviour.

Towards platform-independent real-time systems

Real-time software systems are rarely developed once and left to run. They are subject to changes of requirements as the applications they support expand, and they commonly outlive the platforms they were designed to run on. A successful real-time system is duplicated and adapted to a variety of applications - it becomes a product line. Current methods for real-time software development are commonly based on low-level programming languages and involve considerable duplication of effort when a similar system is to be developed or the hardware platform changes. To provide more dependable, flexible and maintainable real-time systems at a lower cost what is needed is a platform-independent approach to real-time systems development. The development process is composed of two phases: a platform-independent phase, that defines the desired system behaviour and develops a platform-independent design and implementation, and a platform-dependent phase that maps the implementation onto the target platform. The last phase should be highly automated. For critical systems, assessing dependability is crucial. The partitioning into platform dependent and independent phases has to support verification of system properties through both phases.