This paper discusses the numerical precision of five spreadsheets (Calc, Excel, Gnumeric, NeoOffice and Oleo) running on two hardware platforms (i386 and amd64) and on three operating systems (Windows Vista, Ubuntu Intrepid and Mac OS Leopard). The methodology consists of checking the number of correct significant digits returned by each spreadsheet when computing the sample mean, standard deviation, first-order autocorrelation, F statistic in ANOVA tests, linear and nonlinear regression and distribution functions. A discussion about the algorithms for pseudorandom number generation provided by these platforms is also conducted. We conclude that there is no safe choice among the spreadsheets here assessed: they all fail in nonlinear regression and they are not suited for Monte Carlo experiments.

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In this work, we analyze an alternative model for obstructed wireless networks. The model is based on a grid structure of one-dimensional street segments and two-dimensional street intersections. This structure provides a realistic representation of a variety of network scenarios with obstacles and, at the same time, allows a simple enough analysis, which is partly based on percolation theory and partly based on geometric properties. We propose three different ways of modeling the geometric part of the network and derive analytical bounds for the connectivity probability and the critical transmission range for connectivity in the network. Finally, we present extensive simulations that demonstrate that our analytical results provide good approximations, especially for high density scenarios.

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Connectivity properties of wireless networks in open space are typically modeled using geometric random graphs and have been analyzed in depth in different studies. Such scenarios, however, do not often represent situations encountered in practice, like urban environments or indoor spaces, which are deeply affected by obstacles. In this work, we present a model for obstructed wireless ad hoc networks consisting of a set of n nodes, deployed at random in a lattice square of size g×g, with a common transmission range r. For positioning the nodes in the field, all segments are considered as one-dimensional, but for communication purposes, we add a parameter to model the segments' width. Our model can be used to study the structure of obstructed networks analytically, as well as to simulate and evaluate a variety of node deployment strategies and the resulting network topologies. We derive analytical forms for the probability of existing crossing links between parallel and perpendicular segments sharing an intersection, toward a first topological characterization of our model. Moreover, we compute a lower bound for the probability of connectivity at intersections between segments, and apply percolation theory to derivate the Critical Transmission Range for connectivity in the overall network, i.e., the minimum transmission range that generates communication graphs that are connected with high probability.