The concept of rainflow cycles is often used in fatigue of materials for analyzing load processes. Methods are developed for computation of the rainflow matrix for a random load that is changing properties over time due to changes of the system dynamics; for example, for a random vehicle load it could reflect different driving conditions. The random load is modeled by a switching process with Markov regime; that is, the random load changes properties according to a hidden (not observed) Markov chain.

An algorithm is developed for a switching process where each part of the load is modeled by a Markov chain. As only the local extremes are of importance for rainflow analysis, another approach is to model the sequence of turning points by a Markov chain. The main result of this paper is an algorithm for computation of the rainflow matrix for a switching process where each part is described by a Markov chain of turning points. The algorithms are illustrated by numerical examples.

We consider a discounted cost Markov decision process with a constraint. Relating this to a vector-valued Markov decision process, we prove that there exists a constrained optimal randomized semistationary policy if there exists at least one policy satisfying a constraint. Moreover, we present an algorithm by which we can find the constrained optimal randomized semistationary policy, or we can discover that there exist no policies satisfying a given constraint.

The paper treats data compression from the viewpoint of probability theory where a certain error probability is tolerable. We obtain bounds for the minimal rate given an error probability for blockcoding of general stationary ergodic sources. An application of the theory of large deviations provides numerical methods to compute for memoryless sources, the minimal compression rate given a tolerable error probability. Interesting connections between Cramer's functions and Shannon's theory for lossy coding are found.

We consider several models of computer disk access and show that in many cases greedy policies, such as the nearest server policy, minimize the process of distances traveled by heads on circular, spherical, or linear data media. This minimization is in the joint stochastic or lower orthant sense.

This paper deals with evaluation and optimization of polling systems with time limits. Performance measures are evaluated with the power-series algorithm, a flexible technique for computing performance measures for multiqueue systems. The constant time limits are approximated by Erlang distributed variables. The algorithm is extended to compute derivatives of performance measures. This allows for optimization of cost functions with respect to the mean values of the time limits by gradient methods. Several properties of the optimal time limits are revealed by the numerical solution of various optimization problems.

We consider a monotone multistate system with conditionally independent components given the component reliabilities, and random component reliabilities. Upper and lower bounds are derived for the moments of the random reliability function, extending results for binary systems. The second moment is given special attention, as this quantity is used to calculate the standard deviation of the system reliability estimate. The motivation for the paper is to establish a basis for uncertainty analysis and Bayesian estimation in connection with multistate systems.

This paper presents an exact derivation of the statistical distribution of the signal to interference-plus-noise ratio (SINR) for optimum linear combining in wireless systems with multiple cochannel interferes, Rayleigh fading, and additive white Gaussian noise. The distribution of the SINR is shown to be remarkably simple and leads to bounds on the bit error rate and outage probabilities which are tighter, simpler, and more robust than any previous results. The simplicity of the SINR distribution permits extremely fast computation of outage probabilities for any number of interference channels and diversity levels. Hence for wireless systems it enables performance studies to be performed over a much wider range of conditions, such as shadow fading, specific channel allocation methods, etc. Previously such studies were extremely limited due to the intensive computational requirements of simulating these systems.