A large class of stochastic optimization problems can be modeled as minimizing an objective function f that depends on a choice of a vector x ∈ X, as well as on a random external parameter ω ∈ Ω given by a probability distribution π. The value of the objective function is a random variable and often the goal is to find an x ∈ X to minimize the expected cost Eω[fω(x)]. Each ω is referred to as a...

Using the Wiener–Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Lévy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Lévy process versions of many known results about the large-time behavior of random walks. This is illustrat...

in this study, a robust controller is designed for fuzzy network control systems (ncss) using the static output feedback. delay and data packet dropout affect on the stability of network control systems, and therefore, the asymptotic stability condition is established considering delay and data packet dropout. delay is time-varying while the lower and upper bounds for delay is defined, and the ...

Performance evaluation of complex systems is a critical issue and bounds computation provides confidence about service quality, reliability, etc. of such systems. The stochastic ordering theory has generated a lot of works on bounds computation. Maximal lower and minimal upper bounds of a Markov chain by a st-monotone one exist and can be efficiently computed. In the present work, we extend sim...

The computing of stochastic bounds has become an efficient technique to obtain performance predictions for computer systems by the mean of Markovian models. However, the quality of these bounds may be affected by several properties related not only to how to use the technique but also to the Markovian model itself. On the other hand, multiprocessor systems have become an efficient and widely us...

Resource allocation is a widely studied class of problems in Operation Research and Artificial Intelligence. Specially, constrained stochastic resource allocation problems, where the assignment of a constrained resource do not automatically imply the realization of the task. This kind of problems are generally addressed with Markov Decision Processes (mdps). In this paper, we present efficient ...

We consider the domination number for on-line social networks, both in a stochastic network model, and for real-world, networked data. Asymptotic sublinear bounds are rigorously derived for the domination number of graphs generated by the memoryless geometric protean random graph model. We establish sublinear bounds for the domination number of graphs in the Facebook 100 data set, and these bou...

The exact order of deterministic, stochastic and average error bounds of multidimensional quadrature formulas for anisotropic Sobolev class W r pðIÞ; Nikolskii class H pðIÞ and their periodic analogue is obtained. It is proved that if p41; then the stochastic and average error bounds are essentially smaller than the deterministic error bounds. Nonlinear methods, adaptive methods, or even method...

The problem of computing both upper and lower bounds for the steady-state performance of timed and stochastic Marked Graphs is studied. In particular, Linear Programming problems deened on the incidence matrix of the underlying Petri nets are used to compute tight (i.e., reachable) bounds for the throughput of transitions for live and bounded Marked Graphs with time associated with transitions....

We consider recently-derived error bounds that can be used to bound the quality of solutions found by heuristic search algorithms for stochastic shortest path problems. In their original form, the bounds can only be used for problems with positive action costs. We show how to generalize the bounds so that they can be used in solving any stochastic shortest path problem, regardless of cost struc...