  We study the effect of a large obstacle on the so called residence time,
i.e., the time that a particle performing a symmetric random walk in a
rectangular (2D) domain needs to cross the strip. We observe a complex
behavior, that is we find out that the residence time does not depend
monotonically on the geometric properties of the obstacle, such as its width,
length, and position. In some cases, due to the presence of the obstacle, the
mean residence time is shorter with respect to the one measured for the
obstacle--free strip. We explain the residence time behavior by developing a 1D
analog of the 2D model where the role of the obstacle is played by two defect
sites having a smaller probability to be crossed with respect to all the other
regular sites. The 1D and 2D models behave similarly, but in the 1D case we are
able to compute exactly the residence time finding a perfect match with the
Monte Carlo simulations.
