Despite the Standard Model of elementary particle physics has been very successful in describing all known subatomic processes, it cannot be the final theory describing our world because of its limited range of validity. The Standard Model can only be an approximation for low energies of an extended Model. As the heaviest elementary particle and a mass close to the scale of electroweak symmetry breaking, the top quark has a privileged role in probing physics beyond the Standard Model.The most powerful particle accelerator LHC at CERN near Geneva produces a large amount of top quarks which are studied by the ATLAS experiment for evidence of physics beyond the Standard Model.This work investigates several extensions of the Standard Model, introducing an additional heavy boson, decaying into a top-antitop pair of quarks. The sensitivity of the ATLAS particle detector to such t t resonances is determined for several different properties and types of resonances. Special emphasis is applied to interference effects between resonant production of top quarks and the known t t production in the Standard Model. As interference has not been considered in most previous and similar studies, new tools had to be developed to apply necessary techniques and methods to the present analysis.A new matrix element for the event generator HERWIG++ has been developed, which is able to simulate Standard Model t t production in proton-proton collisions as well as resonant production via a potential heavy t t resonance. It calculates the full process of t t production including all effects of interference while providing options to specify all possible properties of the resonance.The matrix element has been used to simulate t t production in five different extensions of the Standard Model, which have been chosen to cover a wide range of phenomenology. Generated events have been processed by a simulation of the ATLAS detector and reconstructed in the semileptonic channel. Depending on the properties of the resonance, the t t invariant mass distribution is altered characteristically compared to the pure Standard Model t t production. For some models the interference has notable influence on t t events. This study compares some extensions of the Standard Model and the effect of interference on the invariant mass distribution for each of these models.Statistical methods based on a frequentistic approach are applied to determine the sensitivity of the ATLAS detector to the studied extensions of the Standard Model. Based on these results, exclusion limits for all considered models are determined for both cases, whether interference is taken into account or not.A second part of this work concentrates on the technical difficulties arising in processing the huge amounts of data collected at the LHC. In order to provide the needed computing power, a global batch system, called the Grid, has been developed and established by institutes participating in the LHC project. Analyses are distributed over all offered computing clusters, globally. Connecting all sorts of computing clusters to form a globally uniform computing interface is still a complicated and error-prone technology, although it is already used heavily in many kinds of scientific research.This work describes an effort to improve the quality and usability of the Grid. Based on information provided by an earlier development of a Job Execution Monitor (JEM), a Grid expert system has been developed to classify and categorise error messages collected from grid jobs. By supervising the status of many grid jobs, it is possible to draw conclusions about the origin of certain job failures, which could not be determined by a single user or with the information from a single grid site. If a certain grid job fails, the grid expert system tries to find an explanation for this failure. In some cases, a solution can be given to fix the error so that it does not have to occur again.