Most analysis and simulation of wireless systems assumes that the nodes are randomly located, sampled from a uniform distribution. Although in many real-world scenarios the nodes are non-uniformly distributed, the research community lacks a common approach to generate such inhomogeneities. This paper intends to go a step in this direction. We present an algorithm to create a random inhomogeneous node distribution based on a simple neighborhood-dependent thinning of a homogeneous Poisson process. We derive some useful stochastic properties of the resulting distribution (in particular the probability density of the nearest neighbor distance) and offer a reference implementation. Our goal is to enable fellow researchers to easily use inhomogeneous distributions with well-defined stochastic properties.

Abstract-The spatial distribution of nodes in wireless networks has important impact on network performance properties, such as capacity and connectivity. Although random sample models based on a uniform distribution are widely used in the research community, they are inappropriate for scenarios with clustered, inhomogeneous node distribution. This paper proposes a well-defined measure for the level of inhomogeneity of a node distribution. It is based on the local deviation of the actual value of the density of nodes from its expected value. Desired properties of the measure are defined and mathematically proven to be fulfilled. The inhomogeneity measure is also compared to human perception of inhomogeneity gained via an online survey. The results reveal that the measure well fits human perception, although there are notable deviations if linear operations are applied.

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Consider n nodes competing for access on a channel using slotted ALOHA. Our aim is to maximize the probability Φ that the first message within s slots does not collide. We derive an expression for the transmit probabilities in each slot, maximizing Φ. As opposed to previous work, the expression is non-recursive, thus easier to calculate and more convenient for practical implementations. Furthermore, we address the problem that, in practical applications, the number of competing nodes n is likely to be unknown and has to be estimated by each node. We study the sensitivity of channel access scheme with respect to deviations from the actual n via simulations. It is shown that overestimation of n is a better strategy than underestimation.